From b185f32f189664bb5c73340ae1422fcd0053d87a Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Thu, 28 Aug 2025 16:41:56 +0100
Subject: [PATCH 01/59] Perceval circuit conversion

---
 optyx/classical.py                  |  39 ++++-
 optyx/core/__init__.py              |   3 +-
 optyx/core/backends.py              |   8 +-
 optyx/core/channel.py               |  90 +++++++++-
 optyx/core/control.py               |  13 +-
 optyx/core/diagram.py               |   6 +-
 optyx/core/path.py                  |  12 +-
 optyx/core/zw.py                    |   7 +-
 optyx/core/zx.py                    |   5 +-
 optyx/photonic.py                   |  82 +++++-----
 optyx/qubits.py                     |   6 +-
 optyx/utils/perceval_conversion.py  | 244 ++++++++++++++++++++++++++++
 optyx/utils/postselect_parser.py    | 214 ++++++++++++++++++++++++
 optyx/{_utils.py => utils/utils.py} |   7 +
 test/test_classical.py              |   2 +-
 test/test_conjugation.py            |   5 +-
 test/test_feed_forward.py           |   4 +-
 test/test_perceval.py               | 244 +++++++++++++++++++++++++++-
 test/test_postselect_parser.py      | 167 +++++++++++++++++++
 test/test_zw.py                     |   5 +-
 test/test_zw_2_circuit.py           |   2 +-
 test/test_zw_truncated_arrays.py    |  37 +++++
 22 files changed, 1096 insertions(+), 106 deletions(-)
 create mode 100644 optyx/utils/perceval_conversion.py
 create mode 100644 optyx/utils/postselect_parser.py
 rename optyx/{_utils.py => utils/utils.py} (98%)
 create mode 100644 test/test_postselect_parser.py

diff --git a/optyx/classical.py b/optyx/classical.py
index 033519d5..4dc71f19 100644
--- a/optyx/classical.py
+++ b/optyx/classical.py
@@ -145,6 +145,7 @@
     bit,
     mode,
     qmode,
+    qubit,
     Discard,
     CQMap,
     Channel,
@@ -163,30 +164,50 @@ class _BitControlledSingleBox(Channel):
         def __init__(
             self,
             control_gate,
-            default_gate=None
+            default_gate=None,
+            classical=False
         ):
             if isinstance(control_gate, (Diagram, Channel)):
                 assert control_gate.is_pure, \
                     "The input gates must be pure quantum channels"
                 control_gate_single = control_gate.get_kraus()
+            else:
+                control_gate_single = control_gate
+
             if isinstance(default_gate, (Diagram, Channel)):
                 assert default_gate.is_pure, \
                     "The input gates must be pure quantum channels"
-                default_gate = default_gate.get_kraus()
-            kraus = control.BitControlledBox(control_gate_single, default_gate)
+                default_gate_single = default_gate.get_kraus()
+            else:
+                default_gate_single = default_gate
+
+            if control_gate_single.dom[0] == diagram.bit:
+                tp = qubit if not classical else bit
+            else:
+                tp = qmode if not classical else mode
+
+            kraus = control.BitControlledBox(
+                control_gate_single,
+                default_gate_single
+            )
+
             super().__init__(
                 f"BitControlledGate({control_gate}, {default_gate})",
                 kraus,
-                bit @ control_gate.dom,
-                control_gate.cod
+                bit @ tp**len(control_gate_single.dom),
+                tp**len(control_gate_single.cod)
             )
 
-    def __new__(cls, diag, default_box=None, is_dagger=False):
+    def __new__(cls, diag, default_box=None, is_dagger=False, classical=False):
         if default_box is not None:
             return cls._BitControlledSingleBox(
-                diag, default_box
+                diag, default_box, classical=classical
             ).dagger() if is_dagger else \
-                 cls._BitControlledSingleBox(diag, default_box)
+                 cls._BitControlledSingleBox(
+                    diag,
+                    default_box,
+                    classical=classical
+                )
 
         boxes = []
         for i in range(len(diag)):
@@ -679,4 +700,4 @@ def Id(n):
     """
     if isinstance(n, channel.Ty):
         return Diagram.id(n)
-    raise TypeError(f"Expected a channel.Ty, got {type(n)}")
+    raise TypeError(f"Expected a channel.Ty, got {type(n)}")
\ No newline at end of file
diff --git a/optyx/core/__init__.py b/optyx/core/__init__.py
index d5b8cfff..5951cfd1 100644
--- a/optyx/core/__init__.py
+++ b/optyx/core/__init__.py
@@ -13,4 +13,5 @@
     path
     zw
     zx
-"""
+    backends
+"""
\ No newline at end of file
diff --git a/optyx/core/backends.py b/optyx/core/backends.py
index 92e3a5ec..b68bb195 100644
--- a/optyx/core/backends.py
+++ b/optyx/core/backends.py
@@ -1,4 +1,5 @@
 """
+
 Overview
 --------
 
@@ -26,7 +27,6 @@
     :nosignatures:
     :toctree:
 
-    StateType
     EvalResult
     AbstractBackend
     QuimbBackend
@@ -136,8 +136,8 @@ def amplitudes(self, normalise=True) -> dict[tuple[int, ...], float]:
         """
         Get the amplitudes from the result tensor.
         Returns:
-            dict: A dictionary mapping
-            occupation configurations to amplitudes.
+            dict: A dictionary mapping occupation
+        configurations to amplitudes.
         """
         if self.state_type != StateType.AMP:
             raise TypeError(
@@ -568,4 +568,4 @@ def eval(
             ),
             output_types=diagram.cod,
             state_type=StateType.PROB
-        )
+        )
\ No newline at end of file
diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index 2c8192ca..aa65b7bd 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -115,7 +115,7 @@
 from pytket.extensions.pyzx import pyzx_to_tk
 from pyzx import extract_circuit
 
-from optyx._utils import explode_channel
+from optyx.utils.utils import explode_channel
 
 
 class Ob(symmetric.Ob):
@@ -236,6 +236,7 @@ def double(self):
     @property
     def is_pure(self):
         are_layers_pure = []
+        are_layers_classical = []
         for layer in self:
             generator = layer.inside[0][1]
 
@@ -245,7 +246,12 @@ def is_pure(self):
                 isinstance(generator, Discard)
             )
 
-        return not any(are_layers_pure)
+            are_layers_classical.append(
+                all(ty.is_classical for ty in generator.cod.inside) and
+                all(ty.is_classical for ty in generator.dom.inside)
+            )
+
+        return not any(are_layers_pure) or all(are_layers_classical)
 
     def get_kraus(self):
         assert self.is_pure, "Cannot get a Kraus map of non-pure circuit"
@@ -380,6 +386,75 @@ def from_graphix(cls, measurement_pattern):
         from optyx.qubits import Circuit
         return Circuit(measurement_pattern)
 
+    @classmethod
+    def from_perceval(cls, p):
+        """
+        Convert pcvl.Circuit or pcvl.Processor
+        into optyx diagrams.
+
+        Cannot convert objects involving components
+        acting on polarisation modes, time delays,
+        and with symbols.
+        """
+        from optyx import photonic
+        from optyx.utils import perceval_conversion
+        import perceval as pcvl
+
+        if isinstance(p, pcvl.Circuit):
+            p_ = pcvl.Processor("SLOS", p.m)
+            p_.add(0, p)
+
+            p_new = pcvl.Processor("SLOS", p.m)
+            for c in p_.flatten():
+                p_new.add(c[0][0], c[1])
+            p = p_new
+
+        n_modes = p.circuit_size
+        circuit = photonic.Id(n_modes)
+        heralds = p.heralds
+
+        circuit = perceval_conversion.heralds_diagram(
+            heralds, n_modes, circuit, "in"
+        ) >> circuit
+
+        for wires, component in p.components:
+            left = circuit.cod[:min(wires)]
+            right = circuit.cod[max(wires) + 1:]
+
+            if isinstance(component, pcvl.Detector):
+                box = perceval_conversion.detector(component, wires)
+            elif isinstance(
+                component,
+                pcvl.components.feed_forward_configurator.FFCircuitProvider
+            ):
+                box, left, right = perceval_conversion.ff_circuit_provider(
+                    component, wires, circuit
+                )
+            elif isinstance(
+                component,
+                pcvl.components.feed_forward_configurator.FFConfigurator
+            ):
+                box, left, right = perceval_conversion.ff_configurator(
+                    component, wires, circuit
+                )
+            elif isinstance(component, pcvl.components.Barrier):
+                continue
+            elif hasattr(component, "U"):
+                box = perceval_conversion.unitary(component, wires)
+            else:
+                raise ValueError(
+                    f"Unsupported perceval component type: {type(component)}"
+                )
+
+            circuit >>= (left @ box @ right)
+
+        circuit >>= perceval_conversion.heralds_diagram(
+            heralds, n_modes, circuit, "out"
+        )
+        if p.post_select_fn is not None:
+            circuit >>= perceval_conversion.postselection(circuit, p)
+        return circuit
+
     # pylint: disable=invalid-name
     def __pow__(self, n):
         if n == 1:
@@ -404,7 +479,14 @@ class Channel(symmetric.Box, Diagram):
     Channel initialised by its Kraus map.
     """
 
-    def __init__(self, name, kraus, dom=None, cod=None, env=diagram.Ty()):
+    def __init__(
+            self,
+            name,
+            kraus,
+            dom=None,
+            cod=None,
+            env=diagram.Ty()
+        ):
         assert isinstance(kraus, diagram.Diagram)
         if dom is None:
             dom = Ty.from_optyx(kraus.dom)
@@ -761,4 +843,4 @@ class Hypergraph(hypergraph.Hypergraph):  # pragma: no cover
 Diagram.spider_factory = Spider
 Diagram.hypergraph_factory = Hypergraph
 Diagram.braid_factory = Swap
-Diagram.sum_factory = Sum
+Diagram.sum_factory = Sum
\ No newline at end of file
diff --git a/optyx/core/control.py b/optyx/core/control.py
index f2701323..1216af58 100644
--- a/optyx/core/control.py
+++ b/optyx/core/control.py
@@ -19,15 +19,6 @@
     BitControlledBox
     ControlledPhaseShift
 
-Functions
----------
-
-.. autosummary::
-    :template: function.rst
-    :nosignatures:
-    :toctree:
-
-    truncation_tensor
 
 Examples
 --------
@@ -49,7 +40,7 @@
 from discopy import tensor
 from discopy.frobenius import Dim
 import numpy as np
-from optyx._utils import BasisTransition
+from optyx.utils.utils import BasisTransition
 
 from optyx.core import diagram, zw
 
@@ -436,4 +427,4 @@ def dagger(self):
         return BinaryMatrixBox(self.matrix, not self.is_dagger)
 
     def conjugate(self):
-        return self
+        return self
\ No newline at end of file
diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index 4f0d1890..2a6775be 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -121,7 +121,7 @@
 Let's check the branching law from [FC23]_.
 
 >>> from optyx.core.zw import Create, W
->>> from optyx._utils import compare_arrays_of_different_sizes
+>>> from optyx.utils.utils import compare_arrays_of_different_sizes
 >>> branching_l = Create(1) >> W(2)
 >>> branching_r = Create(1) @ Create(0) + Create(0) @ Create(1)
 
@@ -226,7 +226,7 @@
 from discopy.cat import factory, rsubs
 from discopy.frobenius import Dim
 from discopy.quantum.gates import format_number
-from optyx._utils import (
+from optyx.utils.utils import (
     modify_io_dims_against_max_dim,
     BasisTransition
 )
@@ -1020,4 +1020,4 @@ class Hypergraph(hypergraph.Hypergraph):  # pragma: no cover
 Diagram.braid_factory, Diagram.spider_factory = Swap, Spider
 Diagram.ty_factory = Ty
 Diagram.sum_factory = Sum
-Id = Diagram.id
+Id = Diagram.id
\ No newline at end of file
diff --git a/optyx/core/path.py b/optyx/core/path.py
index 973f79fb..22c7e847 100644
--- a/optyx/core/path.py
+++ b/optyx/core/path.py
@@ -122,14 +122,6 @@
 >>> expectation = lambda n: Create(n) >> num_op >> Select(n)
 >>> assert np.allclose(expectation(5).to_path().eval().array, np.array([5.]))
 
-References
-----------
-.. [FGL+23] Heurtel, N., Fyrillas, A., Gliniasty, G., Le Bihan, R., \
-    Malherbe, S., Pailhas, M., Bertasi, E., Bourdoncle, B., Emeriau, \
-    P.E., Mezher, R., Music, L., Belabas, N., Valiron, B., Senellart, \
-    P., Mansfield, S., & Senellart, J. (2023). Perceval: A Software \
-    Platform for Discrete Variable Photonic Quantum Computing. Quantum, 7, 931.
-
 """
 
 from __future__ import annotations
@@ -143,7 +135,7 @@
 from discopy.utils import unbiased
 import discopy.matrix as underlying
 from discopy.tensor import Tensor
-from optyx._utils import occupation_numbers, amplitudes_2_tensor
+from optyx.utils.utils import occupation_numbers, amplitudes_2_tensor
 
 
 def npperm(matrix):
@@ -552,4 +544,4 @@ def normalise(self) -> Probabilities:
             array=self.array / self.array.sum(axis=1)[:, None],
             dom=self.dom,
             cod=self.cod,
-        )
+        )
\ No newline at end of file
diff --git a/optyx/core/zw.py b/optyx/core/zw.py
index 69a784c9..f85b412f 100644
--- a/optyx/core/zw.py
+++ b/optyx/core/zw.py
@@ -27,7 +27,6 @@
     Create
     Select
     Endo
-    Scalar
 
 
 Examples of usage
@@ -40,7 +39,7 @@
 
 **W commutativity**
 
->>> from optyx._utils import compare_arrays_of_different_sizes
+>>> from optyx.utils.utils import compare_arrays_of_different_sizes
 >>> from discopy.drawing import Equation
 >>> bSym_l = W(2)
 >>> bSym_r = W(2) >> SWAP
@@ -151,7 +150,7 @@
 from discopy.frobenius import Dim
 from discopy import tensor
 from optyx.core import diagram
-from optyx._utils import (
+from optyx.utils.utils import (
     occupation_numbers,
     multinomial,
     BasisTransition
@@ -820,4 +819,4 @@ def Merge(n):
 
 def Id(n):
     return diagram.Diagram.id(n) if \
-          isinstance(n, diagram.Ty) else diagram.Diagram.id(diagram.Mode(n))
+          isinstance(n, diagram.Ty) else diagram.Diagram.id(diagram.Mode(n))
\ No newline at end of file
diff --git a/optyx/core/zx.py b/optyx/core/zx.py
index 63a5e674..bfa94d42 100644
--- a/optyx/core/zx.py
+++ b/optyx/core/zx.py
@@ -15,7 +15,7 @@
     :nosignatures:
     :toctree:
 
-    Box
+    ZXBox
     Spider
     Z
     X
@@ -30,7 +30,6 @@
     zx_to_path
     decomp
     zx2path
-    circuit2zx
 
 
 Examples of usage
@@ -766,4 +765,4 @@ def dagger(self):
         return Or(n=self.dom.n, is_dagger=not self.is_dagger)
 
     def conjugate(self):
-        return Or(n=self.dom.n, is_dagger=self.is_dagger)
+        return Or(n=self.dom.n, is_dagger=self.is_dagger)
\ No newline at end of file
diff --git a/optyx/photonic.py b/optyx/photonic.py
index 33ad5ea7..85e52b2a 100644
--- a/optyx/photonic.py
+++ b/optyx/photonic.py
@@ -36,7 +36,7 @@
     ansatz
 
 Dual rail encoded operators
-------------------------
+----------------------------
 
 .. autosummary::
     :template: class.rst
@@ -242,18 +242,6 @@
 ...         .dot(np.array(internal_state_2).conjugate()))**2, 3
 ... )
 
-References
-----------
-.. [FC23] de Felice, G., & Coecke, B. (2023). Quantum Linear Optics \
-    via String Diagrams. In Proceedings 19th International \
-    Conference on Quantum Physics and Logic, Wolfson College, \
-    Oxford, UK, 27 June - 1 July 2022 (pp. 83-100). \
-        Open Publishing Association.
-.. [FSP+23] de Felice, G., Shaikh, R., Poór, B., Yeh, L., Wang, Q., \
-    & Coecke, B. (2023). Light-Matter Interaction in the \
-    ZXW Calculus. In  Proceedings of the Twentieth \
-    International Conference on Quantum Physics and Logic,  \
-    Paris, France, 17-21st July 2023 (pp. 20-46). Open Publishing Association.
 """
 
 
@@ -272,7 +260,7 @@
 )
 
 from optyx.classical import ClassicalFunction, DiscardMode
-from optyx._utils import matrix_to_zw
+from optyx.utils.utils import matrix_to_zw
 
 from optyx import (
     bit,
@@ -342,11 +330,11 @@ class PhotonThresholdMeasurement(Channel):
     Detects whether one or more photons are present.
     """
 
-    def __init__(self):
+    def __init__(self, n=1):
         super().__init__(
             "PhotonThresholdMeasurement",
-            diagram.PhotonThresholdDetector(),
-            cod=bit
+            diagram.PhotonThresholdDetector()**n,
+            cod=bit**n
         )
 
 
@@ -590,7 +578,7 @@ def _compute_array(self):
             array = [-1j * cos, sin, sin, -1j * cos]
         else:
             array = [1j * cos, sin, sin, 1j * cos]
-        return np.array(array)
+        return np.array(array).reshape(2, 2)
 
     def lambdify(self, *symbols, **kwargs):
         return lambda *xs: type(self)(
@@ -640,24 +628,23 @@ class TBS(AbstractGate):
 
     def __init__(self,
                  theta,
-                 is_dagger=False,
+                 is_gate_dagger=False,
                  is_conj=False):
         self.theta = theta
-        self.is_dagger = is_dagger
+        self.is_gate_dagger = is_gate_dagger
         self.is_conj = is_conj
         super().__init__(
             2, 2,
             f"TBS({theta})",
             data=theta
         )
-        self.is_dagger = is_dagger
 
     @cached_property
     def global_phase(self):
         backend = sp if self.dtype is Expr else np
         return (
             -1j * backend.exp(-1j * self.theta * backend.pi)
-            if self.is_dagger
+            if self.is_gate_dagger or self.is_conj
             else 1j * backend.exp(1j * self.theta * backend.pi)
         )
 
@@ -665,19 +652,23 @@ def _compute_array(self):
         backend = sp if self.dtype is Expr else np
         sin = backend.sin(self.theta * backend.pi)
         cos = backend.cos(self.theta * backend.pi)
-        array = np.array([sin, cos, cos, -sin])
-        return np.conjugate(array * self.global_phase) if \
-            self.is_conj else array * self.global_phase
+        array = np.array([sin, cos, cos, -sin]).reshape(2, 2)
+        if self.is_gate_dagger:
+            array = np.conjugate(array.T)
+        if self.is_conj:
+            array = np.conjugate(array)
+        return array * self.global_phase
 
     def lambdify(self, *symbols, **kwargs):
         return lambda *xs: type(self)(
             lambdify(symbols, self.theta, **kwargs)(*xs),
-            is_dagger=self.is_dagger,
+            is_gate_dagger=self.is_gate_dagger,
+            is_conj=self.is_conj
         )
 
     def _decomp(self):
         d = BS >> qmode @ Phase(self.theta) >> BS
-        return d.dagger() if self.is_dagger else d
+        return d.dagger() if self.is_gate_dagger else d
 
     def grad(self, var):
         """Gradient with respect to :code:`var`."""
@@ -686,10 +677,10 @@ def grad(self, var):
         return self._decomp().grad(var)
 
     def conjugate(self):
-        return TBS(self.theta, self.is_dagger, not self.is_conj)
+        return TBS(self.theta, self.is_gate_dagger, not self.is_conj)
 
     def dagger(self):
-        return TBS(self.theta, is_dagger=not self.is_dagger)
+        return TBS(self.theta, is_gate_dagger=not self.is_gate_dagger, is_conj=self.is_conj)
 
 
 class MZI(AbstractGate):
@@ -735,24 +726,23 @@ class MZI(AbstractGate):
     def __init__(self,
                  theta,
                  phi,
-                 is_dagger=False,
+                 is_gate_dagger=False,
                  is_conj=False):
         self.theta, self.phi = theta, phi
-        self.is_dagger = is_dagger
+        self.is_gate_dagger = is_gate_dagger
         self.is_conj = is_conj
         super().__init__(
             2, 2,
             f"MZI({theta}, {phi})",
             data=(theta, phi)
         )
-        self.is_dagger = is_dagger
 
     @cached_property
     def global_phase(self):
         backend = sp if self.dtype is Expr else np
         return (
             -1j * backend.exp(-1j * self.theta * backend.pi)
-            if self.is_dagger
+            if self.is_gate_dagger or self.is_conj
             else 1j * backend.exp(1j * self.theta * backend.pi)
         )
 
@@ -761,20 +751,24 @@ def _compute_array(self):
         cos = backend.cos(backend.pi * self.theta)
         sin = backend.sin(backend.pi * self.theta)
         exp = backend.exp(1j * 2 * backend.pi * self.phi)
-        array = np.array([exp * sin, cos, exp * cos, -sin])
-        return np.conjugate(array * self.global_phase) if \
-            self.is_conj else array * self.global_phase
+        array = np.array([exp * sin, cos, exp * cos, -sin]).reshape(2, 2)
+        if self.is_gate_dagger:
+            array = np.conjugate(array.T)
+        if self.is_conj:
+            array = np.conjugate(array)
+        return array * self.global_phase
 
     def lambdify(self, *symbols, **kwargs):
         return lambda *xs: type(self)(
             *lambdify(symbols, [self.theta, self.phi], **kwargs)(*xs),
-            is_dagger=self.is_dagger,
+            is_gate_dagger=self.is_gate_dagger,
+            is_conj=self.is_conj
         )
 
     def _decomp(self):
         x, y = self.theta, self.phi
         d = BS >> qmode @ Phase(x) >> BS >> Phase(y) @ qmode
-        return d.dagger() if self.is_dagger else d
+        return d.dagger() if self.is_gate_dagger else d
 
     def grad(self, var):
         """Gradient with respect to :code:`var`."""
@@ -783,10 +777,10 @@ def grad(self, var):
         return self._decomp().grad(var)
 
     def dagger(self):
-        return MZI(self.theta, self.phi, is_dagger=not self.is_dagger)
+        return MZI(self.theta, self.phi, is_gate_dagger=not self.is_gate_dagger, is_conj=self.is_conj)
 
     def conjugate(self):
-        return MZI(self.theta, self.phi, self.is_dagger, not self.is_conj)
+        return MZI(self.theta, self.phi, self.is_gate_dagger, not self.is_conj)
 
 
 def ansatz(width, depth):
@@ -821,8 +815,10 @@ def p(i, j):
         n_mzi = (width - 1) // 2 if i % 2 else width // 2
         left = qmode**(i % 2)
         right = qmode**(width - (i % 2) - 2 * n_mzi)
-        d >>= left @ Diagram.tensor(*[MZI(*p(i, j))
-                                      for j in range(n_mzi)]) @ right
+        l = Diagram.id(qmode**0)
+        for j in range(n_mzi):
+            l @= MZI(*p(i, j))
+        d >>= left @ l @ right
 
     return d
 
@@ -1113,4 +1109,4 @@ def fusion_II_function(x):
 
 def Id(n):
     return Diagram.id(n) if \
-          isinstance(n, channel.Ty) else Diagram.id(qmode**n)
+          isinstance(n, channel.Ty) else Diagram.id(qmode**n)
\ No newline at end of file
diff --git a/optyx/qubits.py b/optyx/qubits.py
index c7f15631..7a34d88a 100644
--- a/optyx/qubits.py
+++ b/optyx/qubits.py
@@ -7,7 +7,7 @@
 
 
 Circuits (from tket, discopy, or PyZX)
-------------------------
+---------------------------------------
 
 .. autosummary::
     :template: class.rst
@@ -273,7 +273,7 @@
 from discopy import quantum as quantum_discopy
 from discopy import symmetric
 # from pytket import circuit as tket_circuit
-from optyx._utils import explode_channel
+from optyx.utils.utils import explode_channel
 from optyx.core import (
     channel,
     diagram,
@@ -727,4 +727,4 @@ def Id(n):
     Qubit identity wire.
     """
     return Diagram.id(n) if \
-        isinstance(n, channel.Ty) else Diagram.id(qubit**n)
+        isinstance(n, channel.Ty) else Diagram.id(qubit**n)
\ No newline at end of file
diff --git a/optyx/utils/perceval_conversion.py b/optyx/utils/perceval_conversion.py
new file mode 100644
index 00000000..baa44225
--- /dev/null
+++ b/optyx/utils/perceval_conversion.py
@@ -0,0 +1,244 @@
+from optyx.utils.utils import matrix_to_zw, invert_perm
+from optyx import Channel, mode, qmode, photonic, bit
+from optyx.classical import ClassicalFunction, BitControlledGate
+from perceval.components.detector import DetectionType
+from optyx.core.channel import Spider, Diagram, Measure
+from optyx.classical import Select
+from optyx.photonic import Create
+from optyx.utils.postselect_parser import compile_postselect
+from optyx.core.zw import Endo
+import numpy as np
+import perceval as pcvl
+
+
+def _default_action(component):
+    return matrix_to_zw(
+        np.array(component.default_circuit.U.T, dtype=np.complex128)
+    )
+
+
+def _state_predicate(state, ty):
+    """Return ClassicalFunction that outputs 1 iff input equals 'state'."""
+    def f(x):
+        return [1 if all(s == a for s, a in zip(state, x)) else 0]
+    return ClassicalFunction(f, ty**len(state), bit)
+
+
+def _rewire_and_context(*, component, wires, circuit,
+                        n_classical, n_action, n_offset,
+                        perm_dom_neg, perm_dom_pos):
+    """Compute (input_perm, output_perm, left, right)
+    based on component._offset sign."""
+    if component._offset < 0:
+        # classical wires after action+offset
+        p_input = (
+            list(range(n_action + n_offset,
+                       n_action + n_offset + n_classical)) +
+            list(range(0, n_action)) +
+            list(range(n_action, n_action + n_offset))
+        )
+        input_perm = Diagram.permutation(p_input, perm_dom_neg)
+        output_perm = Diagram.permutation(invert_perm(p_input), input_perm.cod)
+        left = circuit.cod[:min(wires) - n_offset - n_action]
+        right = circuit.cod[max(wires) + 1:]
+    else:
+        # classical wires before offset+action
+        p_input = (
+            list(range(n_classical, n_classical + n_offset)) +
+            list(range(0, n_classical)) +
+            list(range(n_classical + n_offset,
+                       n_classical + n_offset + n_action))
+        )
+        input_perm = Diagram.permutation(p_input, perm_dom_pos)
+        output_perm = Diagram.permutation(invert_perm(p_input), input_perm.cod)
+        left = circuit.cod[:min(wires)]
+        right = circuit.cod[max(wires) + n_offset + n_action + 1:]
+    return input_perm, output_perm, left, right
+
+
+def _assemble_controlled_box(
+        map_items, *,
+        input_wires,
+        default_action,
+    ):
+    """
+    Build the feed-forward controlled box from (state, action_box) pairs.
+    action_box must already be a ZW diagram (matrix_to_zw applied).
+    """
+    box = None
+    n_action = len(default_action.dom)
+    for i, (state, action) in enumerate(map_items):
+        if i == 0:
+            box = input_wires[:len(state)] @ photonic.Id(n_action)
+        # duplicate classical control and compute predicate
+        copy = Spider(1, 2, input_wires[0])**len(state)
+        permutation = Diagram.permutation(
+            list(range(0, 2*len(state), 2)) + list(range(1, 2*len(state), 2)),
+            input_wires[0]**(2*len(state))
+        )
+        func = _state_predicate(list(state), input_wires[0])
+
+        ctrl_box = BitControlledGate(action, default_action)
+        q_wires = qmode**n_action
+
+        box >>= (
+            copy @ q_wires >>
+            permutation @ q_wires >>
+            Diagram.id(input_wires[:len(state)]) @ func @ q_wires >>
+            Diagram.id(input_wires[:len(state)]) @ ctrl_box
+        )
+    return box
+
+
+def _feedforward_common(*, component, wires, circuit,
+                        map_iter, action_from_item,
+                        use_provider_dom: bool):
+    """
+    Shared implementation for both FFCircuitProvider and FFConfigurator.
+    """
+    default_action = _default_action(component)
+
+    # numbers and offset
+    n_classical = len(next(iter(map_iter.keys())))
+    n_action = len(default_action.dom)
+    n_offset = abs(component._offset)
+
+    # build permutation domains for input permutation
+    # if use_provider_dom:
+    #    perm_dom_neg = qmode**(n_action + n_offset) @ mode**n_classical
+    #    perm_dom_pos = mode**n_classical @ qmode**(n_action + n_offset)
+    # else:
+        # configurator: the dom is a slice of the current circuit wires
+    perm_dom_neg = circuit.cod[min(wires) - n_offset -
+                                n_action: max(wires) + 1]
+    perm_dom_pos = circuit.cod[min(wires): max(wires) +
+                                n_offset + n_action + 1]
+
+    input_perm, output_perm, left, right = _rewire_and_context(
+        component=component, wires=wires, circuit=circuit,
+        n_classical=n_classical, n_action=n_action, n_offset=n_offset,
+        perm_dom_neg=perm_dom_neg, perm_dom_pos=perm_dom_pos
+    )
+
+    # prepare (state, action_box) pairs
+    action_pairs = []
+    for state, payload in map_iter.items():
+        action_pairs.append((state, action_from_item(payload)))
+
+    # figure out the "offset wires" identity block to thread through
+    if component._offset < 0:
+        offset_wires = circuit.cod[
+            len(left) + n_action: len(left) + n_action + n_offset
+        ]
+    else:
+        offset_wires = circuit.cod[
+            len(left) + n_classical: len(left) + n_classical + n_offset
+        ]
+
+    box = _assemble_controlled_box(
+            action_pairs,
+            input_wires=input_perm.cod[len(offset_wires):],
+            default_action=default_action
+        )
+
+    return (input_perm >> offset_wires @ box >> output_perm), left, right
+
+
+def ff_circuit_provider(component, wires, circuit):
+    def action_from_item(action_circuit):
+        return matrix_to_zw(np.array(action_circuit.U.T, dtype=np.complex128))
+
+    box, left, right = _feedforward_common(
+        component=component,
+        wires=wires,
+        circuit=circuit,
+        map_iter=component._map,
+        action_from_item=action_from_item,
+        use_provider_dom=True,
+    )
+    return box, left, right
+
+
+def ff_configurator(component, wires, circuit):
+    free_symbols = component._controlled.U.free_symbols
+
+    def action_from_item(symbol_values):
+        # substitute symbol values and convert to ZW
+        subs_map = {s: v for s, v in zip(free_symbols, symbol_values.values())}
+        action_U = np.array(
+            component._controlled.U.subs(subs_map).evalf().T,
+            dtype=np.complex128
+        )
+        return matrix_to_zw(action_U)
+
+    box, left, right = _feedforward_common(
+        component=component,
+        wires=wires,
+        circuit=circuit,
+        map_iter=component._configs,
+        action_from_item=action_from_item,
+        use_provider_dom=False,
+    )
+    return box, left, right
+
+
+def unitary(component, wires):
+    if component.U.is_symbolic and not isinstance(component.U, pcvl.MatrixN):
+        if len(component.U.free_symbols) != 0:
+            raise TypeError("Symbolic circuits are not currently supported")
+    U = np.array(component.U, dtype=np.complex128)
+    if U.shape[0] != len(wires):
+        raise ValueError("A component acting on polarisation modes.")
+    return Channel(name=component.name, kraus=matrix_to_zw(U.T))
+
+
+def heralds_diagram(heralds, n_modes, circuit, in_out):
+    layer = photonic.Id(0)
+    create_select = (
+        Create if in_out == "in" else
+        Select if in_out == "out" else None
+    )
+    if create_select is None:
+        raise ValueError("in_out must be either 'in' or 'out'")
+
+    if heralds is not None:
+        for m in range(n_modes):
+            if m in heralds:
+                layer @= create_select(heralds[m])
+            else:
+                layer @= circuit.cod[m] if in_out == "out" else photonic.Id(1)
+    return layer
+
+
+def detector(component, wires):
+    if component.type == DetectionType.PNR:
+        return photonic.NumberResolvingMeasurement(len(wires))
+    if component.type == DetectionType.Threshold:
+        return photonic.PhotonThresholdMeasurement(len(wires))
+    raise ValueError(f"Unsupported perceval detector type: {component.type}")
+
+
+def postselection(circuit, p):
+    measure = Measure(circuit.cod)
+    n_post = len(circuit.cod)
+
+    copy = Spider(1, 2, mode)**n_post
+    permutation = Diagram.permutation(
+        list(range(0, 2*n_post, 2)) + list(range(1, 2*n_post, 2)),
+        mode**(2*n_post)
+    )
+    measure >>= copy >> permutation
+
+    postselect_f = ClassicalFunction(
+        compile_postselect(str(p.post_select_fn)), mode**n_post, bit
+    )
+    measure >>= postselect_f @ mode**n_post
+
+    postselection = BitControlledGate(
+        Diagram.id(mode**n_post),
+        Channel("PostSelection", Endo(0)**n_post, mode**n_post, mode**n_post),
+        classical=True
+    )
+    measure >>= postselection
+
+    return measure
diff --git a/optyx/utils/postselect_parser.py b/optyx/utils/postselect_parser.py
new file mode 100644
index 00000000..d6fdb08f
--- /dev/null
+++ b/optyx/utils/postselect_parser.py
@@ -0,0 +1,214 @@
+
+import re
+from typing import List
+
+
+class _Tok:
+    def __init__(self, kind: str, value: str):
+        self.kind = kind
+        self.value = value
+
+
+def _tokenize(s: str):
+    s = s.strip()
+    # textual logical operators to symbols
+    s = re.sub(r"\bAND\b|\band\b", "&", s)
+    s = re.sub(r"\bOR\b|\bor\b", "|", s)
+    s = re.sub(r"\bXOR\b|\bxor\b", "^", s)
+    s = re.sub(r"\bNOT\b|\bnot\b", "!", s)
+
+    tokens = []
+    i = 0
+    while i < len(s):
+        c = s[i]
+        if c.isspace():
+            i += 1
+            continue
+        if c in "[](),&|^!":
+            tokens.append(_Tok(c, c))
+            i += 1
+            continue
+        if c in "<>=":
+            if s.startswith("==", i):
+                tokens.append(_Tok("OP", "=="))
+                i += 2
+                continue
+            if s.startswith(">=", i):
+                tokens.append(_Tok("OP", ">="))
+                i += 2
+                continue
+            if s.startswith("<=", i):
+                tokens.append(_Tok("OP", "<="))
+                i += 2
+                continue
+            if c == ">":
+                tokens.append(_Tok("OP", ">"))
+                i += 1
+                continue
+            if c == "<":
+                tokens.append(_Tok("OP", "<"))
+                i += 1
+                continue
+            raise ValueError(f"Unexpected operator at position {i}")
+        if c.isdigit():
+            j = i
+            while j < len(s) and s[j].isdigit():
+                j += 1
+            tokens.append(_Tok("INT", s[i:j]))
+            i = j
+            continue
+        if c == ",":
+            tokens.append(_Tok(",", ","))
+            i += 1
+            continue
+        raise ValueError(f"Unexpected character {c!r} at position {i}")
+    tokens.append(_Tok("EOF", ""))
+    return tokens
+
+
+class _Cond:
+    def __init__(self, modes: List[int], op: str, rhs: int):
+        self.modes = modes
+        self.op = op
+        self.rhs = rhs
+
+    def eval(self, counts: List[int]) -> bool:
+        s = 0
+        for m in self.modes:
+            if m < 0:
+                raise ValueError("Mode indices must be non-negative")
+            s += counts[m] if m < len(counts) else 0
+        if self.op == "==":
+            return s == self.rhs
+        if self.op == ">=":
+            return s >= self.rhs
+        if self.op == "<=":
+            return s <= self.rhs
+        if self.op == ">":
+            return s > self.rhs
+        if self.op == "<":
+            return s < self.rhs
+        raise ValueError(f"Unknown operator {self.op!r}")
+
+
+class _Not:
+    def __init__(self, x): self.x = x
+    def eval(self, counts: List[int]) -> bool: return not self.x.eval(counts)
+
+
+class _Bin:
+    def __init__(self, op: str, xs):
+        self.op = op
+        self.xs = xs
+
+    def eval(self, counts: List[int]) -> bool:
+        if self.op == "&":
+            out = True
+            for x in self.xs:
+                out = out and x.eval(counts)
+            return out
+        if self.op == "|":
+            out = False
+            for x in self.xs:
+                out = out or x.eval(counts)
+            return out
+        if self.op == "^":
+            acc = False
+            for x in self.xs:
+                acc ^= x.eval(counts)
+            return acc
+        raise ValueError(f"Unknown logical op {self.op!r}")
+
+
+class _Parser:
+    def __init__(self, tokens):
+        self.toks = tokens
+        self.i = 0
+
+    def _peek(self):
+        return self.toks[self.i]
+
+    def _eat(self, kind):
+        t = self._peek()
+        if (
+            (isinstance(kind, tuple) and
+                t.kind in kind) or
+                t.kind == kind or t.value == kind
+        ):
+            self.i += 1
+            return t
+        raise ValueError(f"Expected {kind}, got {t.kind}:{t.value}")
+
+    def parse(self):
+        node = self._parse_or()
+        if self._peek().kind != "EOF":
+            raise ValueError("Unexpected trailing input")
+        return node
+
+    # Precedence: ! > & > ^ > |
+    def _parse_or(self):
+        left = self._parse_xor()
+        xs = [left]
+        while self._peek().value == "|":
+            self._eat("|")
+            xs.append(self._parse_xor())
+        return xs[0] if len(xs) == 1 else _Bin("|", xs)
+
+    def _parse_xor(self):
+        left = self._parse_and()
+        xs = [left]
+        while self._peek().value == "^":
+            self._eat("^")
+            xs.append(self._parse_and())
+        return xs[0] if len(xs) == 1 else _Bin("^", xs)
+
+    def _parse_and(self):
+        left = self._parse_not()
+        xs = [left]
+        while self._peek().value == "&":
+            self._eat("&")
+            xs.append(self._parse_not())
+        return xs[0] if len(xs) == 1 else _Bin("&", xs)
+
+    def _parse_not(self):
+        if self._peek().value == "!":
+            self._eat("!")
+            return _Not(self._parse_not())
+        return self._parse_primary()
+
+    def _parse_primary(self):
+        t = self._peek()
+        if t.value == "(":
+            self._eat("(")
+            e = self._parse_or()
+            self._eat(")")
+            return e
+        if t.value == "[":
+            self._eat("[")
+            modes = [int(self._eat("INT").value)]
+            while self._peek().value == ",":
+                self._eat(",")
+                modes.append(int(self._eat("INT").value))
+            self._eat("]")
+            op = self._eat("OP").value
+            rhs = int(self._eat("INT").value)
+            if rhs < 0:
+                raise ValueError("Photon count must be a non-negative integer")
+            return _Cond(modes, op, rhs)
+        raise ValueError(f"Expected condition or '(', got {t.kind}:{t.value}")
+
+
+def compile_postselect(expression: str):
+    """
+    Compile a PostSelect expression into a callable:
+        f(counts) -> [1] if expression is satisfied on 'counts', otherwise [0].
+
+    - counts: list of non-negative integers (photons per mode; index = mode id)
+    - Missing modes referenced by the expression are treated as 0.
+    """
+    ast = _Parser(_tokenize(expression)).parse()
+
+    def predicate(counts):
+        ok = ast.eval(counts)
+        return [1] if ok else [0]
+    return predicate
diff --git a/optyx/_utils.py b/optyx/utils/utils.py
similarity index 98%
rename from optyx/_utils.py
rename to optyx/utils/utils.py
index e04bf24d..14926aa7 100644
--- a/optyx/_utils.py
+++ b/optyx/utils/utils.py
@@ -296,6 +296,13 @@ def filter_occupation_numbers(
     ]
 
 
+def invert_perm(p):
+    q = [0] * len(p)
+    for out, inn in enumerate(p):
+        q[inn] = out
+    return q
+
+
 class BasisTransition(NamedTuple):
     """
     A single non-zero transition emitted by `truncation_specification`.
diff --git a/test/test_classical.py b/test/test_classical.py
index 70aa361b..c2a63b7f 100644
--- a/test/test_classical.py
+++ b/test/test_classical.py
@@ -1,5 +1,5 @@
 from optyx.classical import *
-from optyx._utils import compare_arrays_of_different_sizes
+from optyx.utils.utils import compare_arrays_of_different_sizes
 
 def test_addn():
     d_1 = Digit(2, 3) >> AddN(2)
diff --git a/test/test_conjugation.py b/test/test_conjugation.py
index 63df0b5e..fc3859cd 100644
--- a/test/test_conjugation.py
+++ b/test/test_conjugation.py
@@ -37,14 +37,14 @@ def test_conjugation_LO_Gate():
 def test_conjugation_LO_channel(box):
     gate = box(0.27)
     hbs_array = gate.array
-    assert np.allclose(gate.conjugate().to_path().array.flatten(),
+    assert np.allclose(gate.conjugate().to_path().array,
                        hbs_array.conjugate())
 
 
 def test_conjugation_MZI_channel():
     gate = photonic.MZI(0.27, 0.76)
     hbs_array = gate.array
-    assert np.allclose(gate.conjugate().to_path().array.flatten(),
+    assert np.allclose(gate.conjugate().to_path().array,
                        hbs_array.conjugate())
 
 
@@ -65,4 +65,3 @@ def test_conjugation_ZW():
     lhs_tensor = lhs.double().to_tensor().eval().array
     rhs_tensor = rhs.double().to_tensor().eval().array
     assert np.allclose(lhs_tensor, rhs_tensor)
-
diff --git a/test/test_feed_forward.py b/test/test_feed_forward.py
index 971951b2..84893b50 100644
--- a/test/test_feed_forward.py
+++ b/test/test_feed_forward.py
@@ -6,7 +6,7 @@
 from optyx.core.zw import Create, W, ZBox
 from optyx.core.diagram import PhotonThresholdDetector, Mode, Swap, Bit, Id
 from optyx.photonic import Phase, BS, MZI
-from optyx._utils import matrix_to_zw
+from optyx.utils.utils import matrix_to_zw
 from optyx.classical import BitControlledGate, BitControlledPhaseShift
 from optyx.core.channel import Channel, qmode
 from optyx import photonic
@@ -333,4 +333,4 @@ def test_matrix_to_zw(self):
         )
 
         assert np.allclose(diagram1.to_tensor().eval().array,
-                           diagram2.to_tensor().eval().array)
+                           diagram2.to_tensor().eval().array)
\ No newline at end of file
diff --git a/test/test_perceval.py b/test/test_perceval.py
index 0d88f4a1..6f2bffa3 100644
--- a/test/test_perceval.py
+++ b/test/test_perceval.py
@@ -1,13 +1,25 @@
 import pytest
-
+import math
 from optyx.core.zw import *
 from optyx.photonic import (
     BS as BS_,
 	BBS as BBS_,
 	Phase as Phase_,
+	Create as Create_,
+    ansatz
 )
+from perceval.components.unitary_components import BS as BS_p
 from optyx.core.diagram import Mode, Diagram
 import numpy as np
+import perceval as pcvl
+from perceval import catalog
+from optyx.qubits import Z, Scalar, Ket
+from optyx.photonic import DualRail
+from optyx import Channel
+import random
+from perceval.backends import SLOSBackend
+from perceval.simulators import Simulator
+from perceval.components import Source
 
 BS = BS_.get_kraus()
 BBS = lambda theta: BBS_(theta).get_kraus()
@@ -35,3 +47,233 @@ def test_perceval_probs_equivalence(circuit: Diagram, n_photons: int):
 	qpath_probs = circuit.to_path().prob(n_photons).normalise()
 	perceval_probs = circuit.to_path().prob(n_photons, with_perceval=True)
 	assert np.isclose(qpath_probs.array, perceval_probs.array).all()
+
+@pytest.mark.skip(reason="Helper function for testing")
+def dict_allclose(d1: dict, d2: dict, *, rel_tol=1e-05, abs_tol=1e-10) -> bool:
+    all_keys = set(d1.keys()) | set(d2.keys())
+    for key in all_keys:
+        v1 = d1.get(key, 0.0)
+        v2 = d2.get(key, 0.0)
+        if not math.isclose(v1, v2, rel_tol=rel_tol, abs_tol=abs_tol):
+            return False
+    return True
+
+@pytest.mark.skip(reason="Helper function for testing")
+def check_dict_agreement(d1, d2, rtol=1e-5, atol=1e-8):
+    for key in d1.keys() - d2.keys():
+        assert np.isclose(d1[key], 0, rtol=rtol, atol=atol)
+    for key in d2.keys() - d1.keys():
+        assert np.isclose(d2[key], 0, rtol=rtol, atol=atol)
+    for key in d1.keys() & d2.keys():
+        assert np.isclose(d1[key], d2[key], rtol=rtol, atol=atol)
+
+def test_perceval_ff_teleportation():
+	p = pcvl.Processor("SLOS", 6)
+	p.add(0, catalog["postprocessed cnot"].build_processor())
+	p.add(0, pcvl.BS.H())
+	p.add(2, pcvl.Detector.pnr())
+	p.add(3, pcvl.Detector.pnr())
+	p.add(0, pcvl.Detector.pnr())
+	p.add(1, pcvl.Detector.pnr())
+
+	ff_X = pcvl.FFCircuitProvider(2, 0, pcvl.Circuit(2))
+	ff_X.add_configuration([0, 1], pcvl.PERM([1, 0]))
+	p.add(2, ff_X)
+	phi = pcvl.P("phi")
+	ff_Z = pcvl.FFConfigurator(2, 3, pcvl.PS(phi), {"phi": 0}).add_configuration([0, 1], {"phi": np.pi})
+	p.add(0, ff_Z)
+
+	to_transmit = (0.7071067811865476+0j)*pcvl.BasicState([1, 0]) + (-0.21850801222441052+0.6724985119639574j)*pcvl.BasicState([0, 1])
+	to_transmit.normalize()
+
+	sg = pcvl.StateGenerator(pcvl.Encoding.DUAL_RAIL)
+	bell_state = sg.bell_state("phi+")
+
+	input_state = to_transmit * bell_state
+	p.min_detected_photons_filter(2)
+
+	input_state *= pcvl.BasicState([0, 0])
+
+	p.with_input(input_state)
+	res = p.probs()
+
+	bell_state = Z(0, 2) @ Scalar(0.5**0.5)
+	transmit = Ket("+") >> Z(1, 1, 0.3)
+
+	dist = (
+		transmit @ bell_state >>
+		DualRail(3) >>
+		Channel.from_perceval(p)
+	).eval().prob_dist()
+
+	check_dict_agreement(
+    	{tuple(k): v for k, v in dict(res["results"]).items()},
+    	dist
+	)
+
+
+def test_timedelay():
+	HOM = pcvl.Processor("SLOS", 2)
+
+	HOM.add(0, pcvl.BS())
+	HOM.add(1, pcvl.TD(1))
+	HOM.add(0, pcvl.BS())
+
+	with pytest.raises(ValueError):
+		Channel.from_perceval(HOM)
+
+
+def test_symbolic():
+	N=5
+
+	bs = pcvl.GenericInterferometer(N,
+		lambda idx: pcvl.BS(theta=pcvl.P("theta_%d" % idx)) // (0, pcvl.PS(phi=np.pi * 2 * random.random())),
+		shape=pcvl.InterferometerShape.RECTANGLE,
+		depth=2 * N,
+		phase_shifter_fun_gen=lambda idx: pcvl.PS(phi=np.pi*2*random.random()))
+
+	with pytest.raises(TypeError):
+		Channel.from_perceval(bs)
+
+
+def test_polarisation():
+	p = pcvl.Processor("SLOS", 2)
+
+	p.add(0, pcvl.HWP(0.8))
+
+	with pytest.raises(ValueError):
+		Channel.from_perceval(p)
+
+
+def test_walk():
+	steps = 4
+	n = 2*steps
+
+	BS_array = [[[0]*2]*(i+1) for i in range(steps)]
+
+	i_0 = n/2
+	for s in range(steps):
+		if s==0:
+			BS_array[s][0] = [i_0, i_0-1]
+		else:
+			z = 0
+			for i, j in BS_array[s-1]:
+				if [i+1, i] not in BS_array[s]:
+					BS_array[s][z] = [i+1, i]
+					z += 1
+				if [j, j-1] not in BS_array[s]:
+					BS_array[s][z] = [j, j-1]
+					z += 1
+
+	circuit = pcvl.Circuit(n)
+	for s in range(steps):
+		for bs in BS_array[s]:
+			circuit.add(int(bs[1]), BS_p())
+
+	# define input state by inserting a photon in the first mode
+	mode = 3
+	in_list = [0]*n
+	in_list[mode] = 1
+	in_state = pcvl.BasicState(in_list)
+
+	# select a backend and define the simulator on the circuit
+	simulator = Simulator(SLOSBackend())
+	simulator.set_circuit(circuit)
+
+	#Define a source and input distribution due to source noise
+	source = Source(losses=0, indistinguishability=1)
+	input_distribution = source.generate_distribution(expected_input=in_state)
+
+	prob_dist = simulator.probs_svd(input_distribution)
+	p_optyx = Channel.from_perceval(circuit)
+
+	prob_dist_optyx = (
+		Create_(*in_list) >>
+		p_optyx
+	).eval().prob_dist()
+
+	check_dict_agreement(
+    	{tuple(k): v for k, v in dict(prob_dist["results"]).items()},
+    	prob_dist_optyx
+	)
+
+	# two photons input state
+	in_list = [0]*n
+	in_list[3], in_list[4] = 1, 1
+	in_state = pcvl.BasicState(in_list)
+
+	# select a backend and define the simulator on the circuit
+	simulator = Simulator(SLOSBackend())
+	simulator.set_circuit(circuit)
+
+	# define a source and input distribution due to source noise
+	source = Source(losses=0, indistinguishability=1)
+	input_distribution = source.generate_distribution(expected_input=in_state)
+
+	prob_dist = simulator.probs_svd(input_distribution)
+
+	optyx_res = (
+		Create_(*in_list) >>
+		p_optyx
+	).eval().prob_dist()
+
+	check_dict_agreement(
+    	{tuple(k): v for k, v in dict(prob_dist["results"]).items()},
+    	optyx_res
+	)
+
+def test_cnot():
+	QPU = pcvl.Processor("SLOS", 4)
+	QPU.add(0, pcvl.BS.H())
+	p = pcvl.catalog['postprocessed cnot'].build_processor()
+	QPU.add(0, p)
+
+	a = pcvl.Parameter("a")
+	b = pcvl.Parameter("b")
+
+	QPU.add(0, pcvl.BS.H(theta=a))
+	QPU.add(2, pcvl.BS.H(theta=b))
+
+	a.set_value(0)
+	b.set_value(0)
+	QPU.min_detected_photons_filter(2)
+	QPU.with_input(pcvl.BasicState([1, 0, 1, 0]))
+	output_distribution=QPU.probs()["results"]
+	QPU_optyx = Channel.from_perceval(QPU)
+	dist_optyx = (Create_(1, 0, 1, 0) >> QPU_optyx).eval().prob_dist()
+
+	check_dict_agreement(
+    	{tuple(k): v for k, v in dict(output_distribution).items()},
+    	dist_optyx
+	)
+
+def test_unitaries():
+	from optyx import Diagram
+	from optyx.photonic import Create
+
+	def chip_mzi(w, l):
+		ansatz_ = ansatz(w, l)
+		symbs = list(ansatz_.free_symbols)
+		s = [(i, np.random.uniform(0, 1)) for i in symbs]
+		return ansatz_.subs(*s)
+
+	ansatz_ = chip_mzi(6, 3)
+	m = ansatz_.to_path().array
+	c = pcvl.Matrix(m.T)
+	c = pcvl.components.Unitary(U=c)
+	state = pcvl.BasicState([1, 1, 1, 1, 1, 1])
+	p = pcvl.Processor("SLOS", 6)
+	p.add(0, c)
+	p.with_input(state)
+	p_res = p.probs()["results"]
+	p_res = {tuple(key): val for key, val in p_res.items()}
+
+	o_res = (Create(1, 1, 1, 1, 1, 1) >> Diagram.from_perceval(p)).eval().prob_dist()
+
+	rounded_result_optyx = {idx: np.round(val, 6) for idx, val in o_res.items()}
+	non_zero_dict_optyx = {idx: val for idx, val in rounded_result_optyx.items() if val != 0}
+
+	rounded_result_perceval = {idx: np.round(val, 6) for idx, val in p_res.items()}
+	non_zero_dict_perceval = {idx: val for idx, val in rounded_result_perceval.items() if val != 0}
+
+	assert dict_allclose(non_zero_dict_optyx, non_zero_dict_perceval, rel_tol=1e-03)
\ No newline at end of file
diff --git a/test/test_postselect_parser.py b/test/test_postselect_parser.py
new file mode 100644
index 00000000..86c2c130
--- /dev/null
+++ b/test/test_postselect_parser.py
@@ -0,0 +1,167 @@
+
+import random
+import pytest
+from optyx.utils.postselect_parser import compile_postselect
+
+def run(expr, counts):
+    return compile_postselect(expr)(counts)
+
+@pytest.mark.parametrize("expr,counts,expected", [
+    # Simple equality & inequality
+    ("[0]==0", [0,1,2,0], [1]),
+    ("[1]==1", [0,1,2,0], [1]),
+    ("[2]==2", [0,1,2,0], [1]),
+    ("[2]==1", [0,1,2,0], [0]),
+    ("[0]>0",  [0,1,2,0], [0]),
+    ("[1]>=1", [0,1,2,0], [1]),
+    ("[2]<2",  [0,1,2,0], [0]),
+    ("[2]<=2", [0,1,2,0], [1]),
+
+    # Multi-mode sums
+    ("[0,1]==1", [0,1,2,0], [1]),
+    ("[0,1,2]==3", [0,1,2,0], [1]),
+    ("[0,3]<1", [0,1,2,0], [1]),
+
+    # AND
+    ("[0,1]==1 & [2]==2", [0,1,2,0], [1]),
+    ("[0,1]==1 & [2]==1", [0,1,2,0], [0]),
+
+    # OR
+    ("[0]==1 | [1]==1", [0,1,2,0], [1]),
+    ("[0]==1 | [2]==1", [0,1,2,0], [0]),
+
+    # XOR
+    ("[0]==0 ^ [1]==1", [0,1,2,0], [0]),   # both true -> false
+    ("[0]==1 ^ [1]==1", [0,1,2,0], [1]),   # false ^ true
+
+    # NOT variants
+    ("!([0]==1)", [0,1,2,0], [1]),
+    ("not ([1]==1)", [0,1,2,0], [0]),
+    ("NOT ([2]==1)", [0,1,2,0], [1]),
+
+    # Parentheses
+    ("([0]==0 & [1]==1) | [2]==0", [0,1,2,0], [1]),
+    ("[0]==0 & ([1]==0 | [2]==0)", [0,1,2,0], [0]),
+
+    # Textual logical operators
+    ("[0,1]==1 and [2]==2", [0,1,2,0], [1]),
+    ("[0,1]==2 or [2]==2", [0,1,2,0], [1]),
+    ("[1]==1 xor [2]==2", [0,1,2,0], [0]),
+    ("not [1]==1", [0,1,2,0], [0]),
+
+    # Out-of-range modes treated as 0
+    ("[10]==0", [0,1,2,0], [1]),
+    ("[10,0]==0", [0,1,2,0], [1]),
+    ("[10,2]>=2", [0,1,2,0], [1]),
+
+    # More complex datasets
+    ("[0,1,2]==2 & [3,4]>=4", [1,0,1,2,3], [1]),
+    ("([0,1]==1) ^ ([2,3]==3)", [1,0,1,2,3], [0]),
+    ("!([0]==1 ^ [1]==0) | [4]<3", [1,0,1,2,3], [1]),
+
+    # All zeros
+    ("[0,1,2]==0", [0,0,0], [1]),
+    ("[0]>0 | [1]>0 | [2]>0", [0,0,0], [0]),
+    ("!([0]==0 & [1]==0 & [2]==0)", [0,0,0], [0]),
+
+    # All twos
+    ("[0,1]>=4 & [2,3]>=4", [2,2,2,2], [1]),
+    ("[0,1,2,3]==8", [2,2,2,2], [1]),
+    ("[0,1]<4 ^ [2,3]<4", [2,2,2,2], [0]),
+
+    # Mixed parens & ops
+    ("( [0,1]==2 & [2,3]==0 ) | ( [0]==1 ^ [1]==1 )", [1,1,0,0], [1]),
+    ("([0]==1 & [1]==1) ^ ([2]==0 & [3]==0)", [1,1,0,0], [0]),
+    ("([0]==2 | [1]==2) & !([2]==0 & [3]==0)", [1,1,0,0], [0]),
+
+    # <=, >= and more nesting
+    ("[0,1]<=2 & [2]>=1", [0,2,1], [1]),
+    ("[0,2]<1 | [1]>2", [0,2,1], [0]),
+    ("([0,1]==2) ^ !([2]==0)", [0,2,1], [0]),
+
+    # Out-of-range again
+    ("[0,10]==3 & [3]==1", [3,0,0,1], [1]),
+    ("[1,2,5]==0", [3,0,0,1], [1]),
+    ("!([0]==3) | [2]==1", [3,0,0,1], [0]),
+
+    # textual mix
+    ("[0]==1 and ([1]==0 or [2]==0)", [1,0,0], [1]),
+    ("not ([0]==1) or [1]==0", [1,0,0], [1]),
+    ("[0]==0 xor [1]==0", [1,0,0], [1]),
+
+    # Larger list combos
+    ("[0,2,4]==6 & ([1,3]==0 | [0,1]<3)", [2,0,2,0,2], [1]),
+    ("([0,1]==2) ^ ([2,3]==2) ^ ([4]==2)", [2,0,2,0,2], [1]),
+    ("!([0]==2 & [2]==2) | [1,3]>=1", [2,0,2,0,2], [0]),
+])
+def test_explicit(expr, counts, expected):
+    assert run(expr, counts) == expected
+
+def random_condition(max_mode: int) -> str:
+    k = random.randint(1, min(3, max_mode+1))
+    modes = sorted(random.sample(range(max_mode+1), k))
+    op = random.choice(["==", ">=", "<=", ">", "<"])
+    rhs = random.randint(0, 3)
+    return f"[{','.join(map(str,modes))}] {op} {rhs}"
+
+def random_group(max_mode: int) -> str:
+    # group uses a single operator among conditions, as per spec
+    n_conds = random.randint(1, 3)
+    conds = [random_condition(max_mode) for _ in range(n_conds)]
+    op = random.choice(["&", "|", "^"])
+    s = f" {op} ".join(conds)
+    return f"({s})" if random.random() < 0.9 else s
+
+def random_expression(max_mode: int) -> str:
+    # combine groups with explicit parentheses to avoid ambiguity
+    n_groups = random.randint(1, 3)
+    groups = []
+    for _ in range(n_groups):
+        g = random_group(max_mode)
+        if random.random() < 0.4:
+            g = "!" + f"({g})"
+        groups.append(g)
+    expr = groups[0]
+    for g in groups[1:]:
+        op = random.choice(["&", "|", "^"])
+        expr = f"({expr}) {op} ({g})"
+    return expr
+
+def eval_reference(expr: str, counts):
+    # a simple reference evaluator by evaluating each condition and using Python's boolean ops
+    import re
+    e = expr
+    e = re.sub(r"\bAND\b|\band\b", "&", e)
+    e = re.sub(r"\bOR\b|\bor\b", "|", e)
+    e = re.sub(r"\bXOR\b|\bxor\b", "^", e)
+    e = re.sub(r"\bNOT\b|\bnot\b", "!", e)
+
+    cond_pat = re.compile(r"\[(?P<modes>\s*\d+(?:\s*,\s*\d+)*\s*)\]\s*(?P<op>==|>=|<=|>|<)\s*(?P<rhs>\d+)")
+    def cond_repl(m):
+        modes = [int(x.strip()) for x in m.group("modes").split(",")]
+        rhs = int(m.group("rhs"))
+        op = m.group("op")
+        s = sum(counts[i] if i < len(counts) else 0 for i in modes)
+        val = {
+            "==": s == rhs,
+            ">=": s >= rhs,
+            "<=": s <= rhs,
+            ">":  s >  rhs,
+            "<":  s <  rhs,
+        }[op]
+        return f"({str(val)})"
+    prev = None
+    while prev != e:
+        prev = e
+        e = cond_pat.sub(cond_repl, e)
+    e = re.sub(r"!", " not ", e)
+    return [1] if bool(eval(e, {"__builtins__": {}}, {})) else [0]
+
+@pytest.mark.parametrize("seed", [0, 1, 2, 3, 4])
+def test_randomized(seed):
+    random.seed(seed)
+    for _ in range(25): 
+        max_mode = random.randint(2, 6)
+        counts = [random.randint(0, 3) for _ in range(max_mode+1)]
+        expr = random_expression(max_mode)
+        assert run(expr, counts) == eval_reference(expr, counts)
diff --git a/test/test_zw.py b/test/test_zw.py
index d4c9f74b..63410cc0 100644
--- a/test/test_zw.py
+++ b/test/test_zw.py
@@ -1,9 +1,8 @@
 import math
 
 from optyx.core.zw import *
-from optyx._utils import calculate_num_creations_selections
 from optyx.core.diagram import mode, DualRail, EmbeddingTensor, Swap, Diagram, Mode, Spider, Scalar
-from optyx._utils import compare_arrays_of_different_sizes
+from optyx.utils.utils import compare_arrays_of_different_sizes, calculate_num_creations_selections
 import optyx.core.zx as zx
 from optyx import photonic
 import itertools
@@ -481,4 +480,4 @@ def test_DR_beamsplitter():
 def test_DR_phase_shift(phase):
     left = DualRail() >> Mode(1) @ photonic.Phase(phase).get_kraus()
     right = zx.Z(1, 1, phase=phase) >> DualRail()
-    assert np.allclose(right.to_tensor().eval().array, left.to_tensor().eval().array)
+    assert np.allclose(right.to_tensor().eval().array, left.to_tensor().eval().array)
\ No newline at end of file
diff --git a/test/test_zw_2_circuit.py b/test/test_zw_2_circuit.py
index 34b294a9..bde3b60d 100644
--- a/test/test_zw_2_circuit.py
+++ b/test/test_zw_2_circuit.py
@@ -1,6 +1,6 @@
 import optyx.core.zw as zw
 from optyx import photonic, classical
-from optyx._utils import tensor_2_amplitudes, calculate_num_creations_selections
+from optyx.utils.utils import tensor_2_amplitudes, calculate_num_creations_selections
 import itertools
 import pytest
 import perceval as pcvl
diff --git a/test/test_zw_truncated_arrays.py b/test/test_zw_truncated_arrays.py
index fdd880fd..3e3f24bc 100644
--- a/test/test_zw_truncated_arrays.py
+++ b/test/test_zw_truncated_arrays.py
@@ -2,6 +2,8 @@
 from optyx.core.diagram import mode, Swap
 import numpy as np
 import pytest
+from optyx.photonic import ansatz, MZI, TBS
+from optyx.utils.utils import matrix_to_zw
 
 @pytest.mark.skip(reason="Helper function for testing")
 def kron_truncation_swap(input_dims: list[int]) -> np.ndarray[complex]:
@@ -168,3 +170,38 @@ def kron_truncation_Z(diagram, input_dims: list[int]) -> np.ndarray[complex]:
         else:
             result_matrix += np.outer(vec_out, vec_in) * diagram.amplitudes[i]
     return result_matrix
+
+@pytest.mark.skip(reason="Helper function for testing")
+def chip_mzi(w, l):
+    ansatz_ = ansatz(w, l)
+    symbs = list(ansatz_.free_symbols)
+    s = [(i, np.random.uniform(0, 1)) for i in symbs]
+    return ansatz_.subs(*s)
+
+unitaries = [
+    chip_mzi(6, 3),
+    chip_mzi(2, 5),
+    chip_mzi(4, 4),
+]
+
+@pytest.mark.parametrize("unitary", unitaries)
+def test_unitary_array_commutation(unitary):
+
+    array1 = unitary.to_path().array
+    array2 = matrix_to_zw(array1).to_path().array
+    assert np.allclose(array1, array2)
+
+    array1 = unitary.dagger().to_path().array
+    array2 = matrix_to_zw(unitary.to_path().array).dagger().to_path().array
+    assert np.allclose(array1, array2)
+
+def test_MZI_TBS_array_commutation():
+    unitary = MZI(0.32, -0.2)
+    assert np.allclose(unitary.array, unitary.to_path().array)
+
+    assert np.allclose(unitary.dagger().array, unitary.dagger().to_path().array)
+
+    unitary = TBS(-0.2)
+    assert np.allclose(unitary.array, unitary.to_path().array)
+
+    assert np.allclose(unitary.dagger().array, unitary.dagger().to_path().array)
\ No newline at end of file

From 7f6e322b172e0a51145718e5c41958b3901e58e9 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Thu, 28 Aug 2025 16:52:26 +0100
Subject: [PATCH 02/59] linting

---
 optyx/classical.py                 |  2 +-
 optyx/core/__init__.py             |  5 +++--
 optyx/core/backends.py             |  2 +-
 optyx/core/channel.py              |  5 ++---
 optyx/core/control.py              |  2 +-
 optyx/core/diagram.py              |  2 +-
 optyx/core/path.py                 |  2 +-
 optyx/core/zw.py                   |  2 +-
 optyx/core/zx.py                   |  2 +-
 optyx/photonic.py                  |  8 +++++---
 optyx/qubits.py                    |  2 +-
 optyx/utils/perceval_conversion.py | 10 ++++------
 12 files changed, 22 insertions(+), 22 deletions(-)

diff --git a/optyx/classical.py b/optyx/classical.py
index 4dc71f19..0faa558e 100644
--- a/optyx/classical.py
+++ b/optyx/classical.py
@@ -700,4 +700,4 @@ def Id(n):
     """
     if isinstance(n, channel.Ty):
         return Diagram.id(n)
-    raise TypeError(f"Expected a channel.Ty, got {type(n)}")
\ No newline at end of file
+    raise TypeError(f"Expected a channel.Ty, got {type(n)}")
diff --git a/optyx/core/__init__.py b/optyx/core/__init__.py
index 5951cfd1..7e41228e 100644
--- a/optyx/core/__init__.py
+++ b/optyx/core/__init__.py
@@ -1,5 +1,6 @@
 """
-Core back-end classes of Optyx. These include the graphical
+Core back-end classes of Optyx.
+These include the graphical
 languages of ZX, ZW, and Path.
 
 .. autosummary::
@@ -14,4 +15,4 @@
     zw
     zx
     backends
-"""
\ No newline at end of file
+"""
diff --git a/optyx/core/backends.py b/optyx/core/backends.py
index b68bb195..f677e4b2 100644
--- a/optyx/core/backends.py
+++ b/optyx/core/backends.py
@@ -568,4 +568,4 @@ def eval(
             ),
             output_types=diagram.cod,
             state_type=StateType.PROB
-        )
\ No newline at end of file
+        )
diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index aa65b7bd..e839231e 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -485,8 +485,7 @@ def __init__(
             kraus,
             dom=None,
             cod=None,
-            env=diagram.Ty()
-        ):
+            env=diagram.Ty()):
         assert isinstance(kraus, diagram.Diagram)
         if dom is None:
             dom = Ty.from_optyx(kraus.dom)
@@ -843,4 +842,4 @@ class Hypergraph(hypergraph.Hypergraph):  # pragma: no cover
 Diagram.spider_factory = Spider
 Diagram.hypergraph_factory = Hypergraph
 Diagram.braid_factory = Swap
-Diagram.sum_factory = Sum
\ No newline at end of file
+Diagram.sum_factory = Sum
diff --git a/optyx/core/control.py b/optyx/core/control.py
index 1216af58..5a078af3 100644
--- a/optyx/core/control.py
+++ b/optyx/core/control.py
@@ -427,4 +427,4 @@ def dagger(self):
         return BinaryMatrixBox(self.matrix, not self.is_dagger)
 
     def conjugate(self):
-        return self
\ No newline at end of file
+        return self
diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index 2a6775be..eeb55507 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -1020,4 +1020,4 @@ class Hypergraph(hypergraph.Hypergraph):  # pragma: no cover
 Diagram.braid_factory, Diagram.spider_factory = Swap, Spider
 Diagram.ty_factory = Ty
 Diagram.sum_factory = Sum
-Id = Diagram.id
\ No newline at end of file
+Id = Diagram.id
diff --git a/optyx/core/path.py b/optyx/core/path.py
index 22c7e847..2fdb68b0 100644
--- a/optyx/core/path.py
+++ b/optyx/core/path.py
@@ -544,4 +544,4 @@ def normalise(self) -> Probabilities:
             array=self.array / self.array.sum(axis=1)[:, None],
             dom=self.dom,
             cod=self.cod,
-        )
\ No newline at end of file
+        )
diff --git a/optyx/core/zw.py b/optyx/core/zw.py
index f85b412f..a54f9862 100644
--- a/optyx/core/zw.py
+++ b/optyx/core/zw.py
@@ -819,4 +819,4 @@ def Merge(n):
 
 def Id(n):
     return diagram.Diagram.id(n) if \
-          isinstance(n, diagram.Ty) else diagram.Diagram.id(diagram.Mode(n))
\ No newline at end of file
+          isinstance(n, diagram.Ty) else diagram.Diagram.id(diagram.Mode(n))
diff --git a/optyx/core/zx.py b/optyx/core/zx.py
index bfa94d42..cbaf3b51 100644
--- a/optyx/core/zx.py
+++ b/optyx/core/zx.py
@@ -765,4 +765,4 @@ def dagger(self):
         return Or(n=self.dom.n, is_dagger=not self.is_dagger)
 
     def conjugate(self):
-        return Or(n=self.dom.n, is_dagger=self.is_dagger)
\ No newline at end of file
+        return Or(n=self.dom.n, is_dagger=self.is_dagger)
diff --git a/optyx/photonic.py b/optyx/photonic.py
index 85e52b2a..d752f428 100644
--- a/optyx/photonic.py
+++ b/optyx/photonic.py
@@ -680,7 +680,8 @@ def conjugate(self):
         return TBS(self.theta, self.is_gate_dagger, not self.is_conj)
 
     def dagger(self):
-        return TBS(self.theta, is_gate_dagger=not self.is_gate_dagger, is_conj=self.is_conj)
+        return TBS(self.theta, is_gate_dagger=not self.is_gate_dagger,
+                   is_conj=self.is_conj)
 
 
 class MZI(AbstractGate):
@@ -777,7 +778,8 @@ def grad(self, var):
         return self._decomp().grad(var)
 
     def dagger(self):
-        return MZI(self.theta, self.phi, is_gate_dagger=not self.is_gate_dagger, is_conj=self.is_conj)
+        return MZI(self.theta, self.phi,
+                   is_gate_dagger=not self.is_gate_dagger, is_conj=self.is_conj)
 
     def conjugate(self):
         return MZI(self.theta, self.phi, self.is_gate_dagger, not self.is_conj)
@@ -1109,4 +1111,4 @@ def fusion_II_function(x):
 
 def Id(n):
     return Diagram.id(n) if \
-          isinstance(n, channel.Ty) else Diagram.id(qmode**n)
\ No newline at end of file
+          isinstance(n, channel.Ty) else Diagram.id(qmode**n)
diff --git a/optyx/qubits.py b/optyx/qubits.py
index 7a34d88a..c2212c82 100644
--- a/optyx/qubits.py
+++ b/optyx/qubits.py
@@ -727,4 +727,4 @@ def Id(n):
     Qubit identity wire.
     """
     return Diagram.id(n) if \
-        isinstance(n, channel.Ty) else Diagram.id(qubit**n)
\ No newline at end of file
+        isinstance(n, channel.Ty) else Diagram.id(qubit**n)
diff --git a/optyx/utils/perceval_conversion.py b/optyx/utils/perceval_conversion.py
index baa44225..16cf572e 100644
--- a/optyx/utils/perceval_conversion.py
+++ b/optyx/utils/perceval_conversion.py
@@ -59,8 +59,7 @@ def _rewire_and_context(*, component, wires, circuit,
 def _assemble_controlled_box(
         map_items, *,
         input_wires,
-        default_action,
-    ):
+        default_action,):
     """
     Build the feed-forward controlled box from (state, action_box) pairs.
     action_box must already be a ZW diagram (matrix_to_zw applied).
@@ -98,7 +97,6 @@ def _feedforward_common(*, component, wires, circuit,
     """
     default_action = _default_action(component)
 
-    # numbers and offset
     n_classical = len(next(iter(map_iter.keys())))
     n_action = len(default_action.dom)
     n_offset = abs(component._offset)
@@ -108,11 +106,11 @@ def _feedforward_common(*, component, wires, circuit,
     #    perm_dom_neg = qmode**(n_action + n_offset) @ mode**n_classical
     #    perm_dom_pos = mode**n_classical @ qmode**(n_action + n_offset)
     # else:
-        # configurator: the dom is a slice of the current circuit wires
+    # configurator: the dom is a slice of the current circuit wires
     perm_dom_neg = circuit.cod[min(wires) - n_offset -
-                                n_action: max(wires) + 1]
+                               n_action: max(wires) + 1]
     perm_dom_pos = circuit.cod[min(wires): max(wires) +
-                                n_offset + n_action + 1]
+                               n_offset + n_action + 1]
 
     input_perm, output_perm, left, right = _rewire_and_context(
         component=component, wires=wires, circuit=circuit,

From fc89a206a72ac325671a3823f97fbdf65814073e Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Thu, 28 Aug 2025 16:54:22 +0100
Subject: [PATCH 03/59] linting

---
 optyx/photonic.py | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/optyx/photonic.py b/optyx/photonic.py
index d752f428..2f67f199 100644
--- a/optyx/photonic.py
+++ b/optyx/photonic.py
@@ -779,7 +779,8 @@ def grad(self, var):
 
     def dagger(self):
         return MZI(self.theta, self.phi,
-                   is_gate_dagger=not self.is_gate_dagger, is_conj=self.is_conj)
+                   is_gate_dagger=not self.is_gate_dagger,
+                   is_conj=self.is_conj)
 
     def conjugate(self):
         return MZI(self.theta, self.phi, self.is_gate_dagger, not self.is_conj)
@@ -817,10 +818,10 @@ def p(i, j):
         n_mzi = (width - 1) // 2 if i % 2 else width // 2
         left = qmode**(i % 2)
         right = qmode**(width - (i % 2) - 2 * n_mzi)
-        l = Diagram.id(qmode**0)
+        wire = Diagram.id(qmode**0)
         for j in range(n_mzi):
-            l @= MZI(*p(i, j))
-        d >>= left @ l @ right
+            wire @= MZI(*p(i, j))
+        d >>= left @ wire @ right
 
     return d
 

From 357354fd9da300826b24db476013638869a85e70 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Sun, 31 Aug 2025 16:19:46 +0100
Subject: [PATCH 04/59] fix(backend/quimb): sanitise tn dtypes & values before
 compressed contraction

---
 optyx/core/backends.py |  9 +++++++++
 optyx/utils/utils.py   | 22 ++++++++++++++++++++++
 2 files changed, 31 insertions(+)

diff --git a/optyx/core/backends.py b/optyx/core/backends.py
index f677e4b2..d510dff0 100644
--- a/optyx/core/backends.py
+++ b/optyx/core/backends.py
@@ -81,6 +81,7 @@
 from quimb.tensor import TensorNetwork
 from optyx.core.channel import Diagram
 from optyx.core.channel import Ty, mode, bit
+from optyx.utils.utils import preprocess_quimb_tensors_safe
 
 
 class StateType(Enum):
@@ -396,6 +397,11 @@ def eval(
         quimb_tn = self._get_quimb_tensor(diagram)
         tensor_diagram = self._get_discopy_tensor(diagram)
 
+        for t in quimb_tn:
+            dt = t.data.dtype
+            if dt.kind in {'i', 'u', 'b'}:
+                t.modify(data=t.data.astype(np.complex128, copy=False))
+
         if self.hyperoptimiser is None:
             results = quimb_tn ^ ...
         else:
@@ -417,6 +423,9 @@ def eval(
                     "HyperCompressedOptimizer."
                 )
 
+            if is_approx:
+                quimb_tn = preprocess_quimb_tensors_safe(quimb_tn)
+
             contract = quimb_tn.contract_compressed if \
                 is_approx else quimb_tn.contract
             results = contract(
diff --git a/optyx/utils/utils.py b/optyx/utils/utils.py
index 14926aa7..29b35d7d 100644
--- a/optyx/utils/utils.py
+++ b/optyx/utils/utils.py
@@ -323,3 +323,25 @@ class BasisTransition(NamedTuple):
     """
     out: Tuple[int, ...]
     amp: Number
+
+
+def preprocess_quimb_tensors_safe(tn, epsilon=1e-12, value_limit=1e10):
+    for t in tn:
+        data = t.data
+
+        if data.dtype.kind in {'i', 'u'}:
+            t.modify(data=data.astype('complex128'))
+            continue
+
+        if data.ndim == 2 and np.linalg.matrix_rank(data) < min(data.shape):
+            data += np.random.normal(0, epsilon, size=data.shape)
+
+        if np.any(data == 0):
+            data[data == 0] = epsilon
+
+        if np.max(np.abs(data)) > value_limit:
+            data = np.clip(data, -value_limit, value_limit)
+
+        t.modify(data=data)
+
+    return tn

From 9bc060f726507a522905da3aa6919e116f4d2878 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Tue, 2 Sep 2025 11:28:31 +0100
Subject: [PATCH 05/59] draft auto max dim calculation

---
 examples/channel_error.ipynb |  0
 optyx/core/control.py        | 14 +++++++++++-
 optyx/core/diagram.py        | 25 +++++++++++++--------
 optyx/core/zw.py             |  9 ++++----
 optyx/utils/utils.py         | 42 ++++++++++++++++++++++++++++++++++--
 5 files changed, 74 insertions(+), 16 deletions(-)
 create mode 100644 examples/channel_error.ipynb

diff --git a/examples/channel_error.ipynb b/examples/channel_error.ipynb
new file mode 100644
index 00000000..e69de29b
diff --git a/optyx/core/control.py b/optyx/core/control.py
index 5a078af3..b5f293f1 100644
--- a/optyx/core/control.py
+++ b/optyx/core/control.py
@@ -119,7 +119,19 @@ def __init__(
         self.action_box = action_box
         self.default_box = default_box
         self.is_dagger = is_dagger
-
+        # --- Photon-budget contract: max over the two branches.
+        def _safe_out(b):
+            f = getattr(b, "output_photons", None)
+            return f if callable(f) else (lambda s: s)
+
+        f_action  = _safe_out(self.action_box)
+        f_default = _safe_out(self.default_box)
+
+        # Bits carry no photons; total_in is the sum over Mode inputs only.
+        self.output_photons = lambda total_in: max(
+            int(f_action(total_in)),
+            int(f_default(total_in))
+        )
     def determine_output_dimensions(self, input_dims: List[int]) -> List[int]:
 
         action_box_dims = (
diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index eeb55507..9661d203 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -228,7 +228,8 @@
 from discopy.quantum.gates import format_number
 from optyx.utils.utils import (
     modify_io_dims_against_max_dim,
-    BasisTransition
+    BasisTransition,
+    total_photons_created
 )
 from typing import List, Tuple, Iterable
 
@@ -312,10 +313,11 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
         else:
             layer_dims = input_dims
 
-            if max_dim is not None:
-                layer_dims, _ = modify_io_dims_against_max_dim(
-                    layer_dims, None, max_dim
-                )
+        max_dim = total_photons_created(self, layer_dims) + 1
+
+        layer_dims, _ = modify_io_dims_against_max_dim(
+            layer_dims, None, max_dim
+        )
 
         if len(self.boxes) == 0 and len(self.offsets) == 0:
             return tensor.Diagram.id(list_to_dim(layer_dims))
@@ -326,10 +328,14 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
 
             dims_out = box.determine_output_dimensions(dims_in)
 
-            if max_dim is not None:
-                dims_out, _ = modify_io_dims_against_max_dim(
-                    dims_out, None, max_dim
-                )
+            if hasattr(box, "output_photons"):
+                output_photons = int(max(dims_out, default=0))
+                if max_dim < output_photons:
+                    max_dim = output_photons
+            #if max_dim is not None:
+            dims_out, _ = modify_io_dims_against_max_dim(
+                dims_out, None, max_dim
+            )
 
             left = Dim()
             if off > 0:
@@ -828,6 +834,7 @@ def __init__(self,
         super().__init__("2R", dom, cod)
         self.internal_state = internal_state
         self.is_dagger = is_dagger
+        self.output_photons = self.determine_output_dimensions
 
     def conjugate(self):
         return self
diff --git a/optyx/core/zw.py b/optyx/core/zw.py
index a54f9862..42e693e1 100644
--- a/optyx/core/zw.py
+++ b/optyx/core/zw.py
@@ -291,6 +291,7 @@ def __init__(
         super().__init__(legs_in, legs_out, diagram.Mode(1))
         self.legs_in = legs_in
         self.legs_out = legs_out
+        self.output_photons = self.determine_output_dimensions
 
     def conjugate(self):
         return ZBox(self.legs_in, self.legs_out, self.amplitudes.conjugate())
@@ -429,6 +430,7 @@ def __init__(self,
 
         name = "Create(1)" if self.photons == (1,) else f"Create({photons})"
         super().__init__(name, 0, len(self.photons))
+        self.output_photons = self.determine_output_dimensions
 
     def conjugate(self):
         return self
@@ -532,6 +534,7 @@ def __init__(self,
         self.photons = photons or (1,)
         name = "Select(1)" if self.photons == (1,) else f"Select({photons})"
         super().__init__(name, len(self.photons), 0)
+        self.output_photons = lambda _: 0
 
     def inflate(self, d):
 
@@ -700,8 +703,7 @@ def __init__(self, is_dagger: bool = False):
         cod = diagram.Mode(2) if is_dagger else diagram.Mode(1)
 
         super().__init__("Multiply", dom, cod)
-
-        self.is_dagger = is_dagger
+        self.output_photons = self.determine_output_dimensions
 
     def truncation_specification(
         self,
@@ -740,10 +742,9 @@ class Divide(ZWBox):
     def __init__(self, is_dagger: bool = False):
         dom = diagram.Mode(1) if is_dagger else diagram.Mode(2)
         cod = diagram.Mode(2) if is_dagger else diagram.Mode(1)
-
         super().__init__("Divide", dom, cod)
-
         self.is_dagger = is_dagger
+        self.output_photons = self.determine_output_dimensions
 
     def truncation_specification(
         self,
diff --git a/optyx/utils/utils.py b/optyx/utils/utils.py
index 29b35d7d..0e31f8f8 100644
--- a/optyx/utils/utils.py
+++ b/optyx/utils/utils.py
@@ -9,10 +9,14 @@
 """
 
 import numpy as np
-from typing import NamedTuple, Tuple
+from typing import (
+    NamedTuple,
+    Tuple,
+    Optional,
+    List
+)
 from numbers import Number
 
-
 def _build_w_layer(n_nonzero_counts, dagger=False):
     # pylint: disable=import-outside-toplevel
     from optyx.core import zw
@@ -345,3 +349,37 @@ def preprocess_quimb_tensors_safe(tn, epsilon=1e-12, value_limit=1e10):
         t.modify(data=data)
 
     return tn
+
+
+def total_photons_created(diagram, input_dims: Optional[List[int]] = None) -> int:
+    """
+    Scan `diagram` once and return the total number of photons created.
+
+    Counts:
+      - zw.Create(*photons) -> +sum(photons)
+    Everything else is ignored for 'creation' (they conserve or consume photons).
+
+    Parameters
+    ----------
+    diagram : optyx.core.diagram.Diagram
+        The diagram to scan (sequential list of boxes is in `diagram.boxes`).
+    input_dims : Optional[List[int]]
+
+    Returns
+    -------
+    int
+        Total number of photons created in the diagram.
+    """
+    created = 0
+
+    from optyx.core import zw
+
+    if input_dims is None:
+        input_dims = []
+
+    for box in diagram.boxes:
+        if isinstance(box, zw.Create):
+            created += sum(int(p) for p in box.photons)
+            continue
+
+    return max(int(created) + int(sum(input_dims, 0)), 3)
\ No newline at end of file

From 03ad4cc83a9b2796e5f17b3abda1da079d274665 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Tue, 2 Sep 2025 13:13:55 +0100
Subject: [PATCH 06/59] auto max dim finding

---
 optyx/core/diagram.py     | 10 ++++++++--
 optyx/utils/utils.py      | 35 +++++++++++++++++++++++++++++++++--
 test/test_channel.py      |  9 ++-------
 test/test_feed_forward.py |  1 +
 4 files changed, 44 insertions(+), 11 deletions(-)

diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index 9661d203..3c2deaf7 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -229,7 +229,8 @@
 from optyx.utils.utils import (
     modify_io_dims_against_max_dim,
     BasisTransition,
-    total_photons_created
+    total_photons_created,
+    max_postselection
 )
 from typing import List, Tuple, Iterable
 
@@ -314,6 +315,10 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
             layer_dims = input_dims
 
         max_dim = total_photons_created(self, layer_dims) + 1
+        max_post_selection = max_postselection(self, layer_dims) + 1
+
+        if max_dim < max_post_selection:
+            max_dim = max_post_selection
 
         layer_dims, _ = modify_io_dims_against_max_dim(
             layer_dims, None, max_dim
@@ -331,7 +336,8 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
             if hasattr(box, "output_photons"):
                 output_photons = int(max(dims_out, default=0))
                 if max_dim < output_photons:
-                    max_dim = output_photons
+                    max_dim = output_photons + 1
+
             #if max_dim is not None:
             dims_out, _ = modify_io_dims_against_max_dim(
                 dims_out, None, max_dim
diff --git a/optyx/utils/utils.py b/optyx/utils/utils.py
index 0e31f8f8..2f3ccfd0 100644
--- a/optyx/utils/utils.py
+++ b/optyx/utils/utils.py
@@ -350,7 +350,6 @@ def preprocess_quimb_tensors_safe(tn, epsilon=1e-12, value_limit=1e10):
 
     return tn
 
-
 def total_photons_created(diagram, input_dims: Optional[List[int]] = None) -> int:
     """
     Scan `diagram` once and return the total number of photons created.
@@ -382,4 +381,36 @@ def total_photons_created(diagram, input_dims: Optional[List[int]] = None) -> in
             created += sum(int(p) for p in box.photons)
             continue
 
-    return max(int(created) + int(sum(input_dims, 0)), 3)
\ No newline at end of file
+    return max(int(created) + int(sum(input_dims, 0)), 3)
+
+def max_postselection(diagram, input_dims: Optional[List[int]] = None) -> int:
+    """
+    Scan `diagram` once and return the maximum post-selection dimension.
+
+    Counts:
+      - zw.Create(*photons) -> +sum(photons)
+    Everything else is ignored for 'selection'
+    Parameters
+    ----------
+    diagram : optyx.core.diagram.Diagram
+        The diagram to scan (sequential list of boxes is in `diagram.boxes`).
+    input_dims : Optional[List[int]]
+
+    Returns
+    -------
+    int
+        Maximum post-selection dimension in the diagram.
+    """
+    max_dim = 0
+
+    from optyx.core import zw
+
+    if input_dims is None:
+        input_dims = []
+
+    for box in diagram.boxes:
+        if isinstance(box, zw.Select):
+            max_dim = max(max_dim, max(int(p) for p in box.photons))
+            continue
+
+    return max(int(max_dim) + int(sum(input_dims, 0)), 3)
\ No newline at end of file
diff --git a/test/test_channel.py b/test/test_channel.py
index 1ef7750a..9d07de6c 100644
--- a/test/test_channel.py
+++ b/test/test_channel.py
@@ -57,10 +57,5 @@ def test_from_bosonic_op():
             terms.append(term)
 
     hamiltonian = Diagram.sum_factory(terms)
-    sum_1 = np.sum([(term.double().to_tensor(input_dims = [3,3,3,3], max_dim=3).to_quimb()^...).data for term in terms])
-
-    terms_2 = hamiltonian.double().terms
-
-    sum = np.sum([(term_2.to_tensor(input_dims = [3,3,3,3], max_dim=3).to_quimb()^...).data for term_2 in terms_2])
-
-    assert np.allclose(sum, sum_1)
\ No newline at end of file
+    sum_1 = hamiltonian.eval()
+    assert np.allclose(sum_1.array, 0.0)
\ No newline at end of file
diff --git a/test/test_feed_forward.py b/test/test_feed_forward.py
index 84893b50..f4b98423 100644
--- a/test/test_feed_forward.py
+++ b/test/test_feed_forward.py
@@ -279,6 +279,7 @@ def test_dagger_controlled_phase_shift_2(self, diagram):
     @pytest.mark.parametrize("f", REAL_FUNCS)
     @pytest.mark.parametrize("x", xs)
     def test_controlled_phase_shift_numeric(self, f, x):
+        print(f"Testing ControlledPhaseShift with x: {x}")
         """
         For each real-valued function f and input x, build a circuit with
         ControlledPhaseShift, compare to a ZBox with the matching phase exponent.

From c786826bfe6c491304485fa5cc3d96a1fca7346c Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Thu, 4 Sep 2025 12:02:07 +0100
Subject: [PATCH 07/59] flake8

---
 optyx/core/control.py | 15 ++-------------
 optyx/core/diagram.py | 13 +++++++------
 optyx/core/zw.py      | 10 +++++-----
 optyx/utils/utils.py  | 27 ++++++++++++++++++++-------
 4 files changed, 34 insertions(+), 31 deletions(-)

diff --git a/optyx/core/control.py b/optyx/core/control.py
index b5f293f1..f691b6c8 100644
--- a/optyx/core/control.py
+++ b/optyx/core/control.py
@@ -119,19 +119,8 @@ def __init__(
         self.action_box = action_box
         self.default_box = default_box
         self.is_dagger = is_dagger
-        # --- Photon-budget contract: max over the two branches.
-        def _safe_out(b):
-            f = getattr(b, "output_photons", None)
-            return f if callable(f) else (lambda s: s)
-
-        f_action  = _safe_out(self.action_box)
-        f_default = _safe_out(self.default_box)
-
-        # Bits carry no photons; total_in is the sum over Mode inputs only.
-        self.output_photons = lambda total_in: max(
-            int(f_action(total_in)),
-            int(f_default(total_in))
-        )
+        self.photon_sum_preserving = False
+
     def determine_output_dimensions(self, input_dims: List[int]) -> List[int]:
 
         action_box_dims = (
diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index 3c2deaf7..29ff2f43 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -333,12 +333,12 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
 
             dims_out = box.determine_output_dimensions(dims_in)
 
-            if hasattr(box, "output_photons"):
-                output_photons = int(max(dims_out, default=0))
-                if max_dim < output_photons:
-                    max_dim = output_photons + 1
+            if hasattr(box, "photon_sum_preserving"):
+                if not box.photon_sum_preserving:
+                    output_photons = int(max(dims_out, default=0))
+                    if max_dim < output_photons:
+                        max_dim = output_photons + 1
 
-            #if max_dim is not None:
             dims_out, _ = modify_io_dims_against_max_dim(
                 dims_out, None, max_dim
             )
@@ -445,6 +445,7 @@ class Box(frobenius.Box, Diagram):
 
     def __init__(self, name, dom, cod, array=None, **params):
         self._array = array
+        self.photon_sum_preserving = True
         super().__init__(name, dom, cod, **params)
 
     @classmethod
@@ -840,7 +841,7 @@ def __init__(self,
         super().__init__("2R", dom, cod)
         self.internal_state = internal_state
         self.is_dagger = is_dagger
-        self.output_photons = self.determine_output_dimensions
+        self.photon_sum_preserving = False
 
     def conjugate(self):
         return self
diff --git a/optyx/core/zw.py b/optyx/core/zw.py
index 42e693e1..9d9195bc 100644
--- a/optyx/core/zw.py
+++ b/optyx/core/zw.py
@@ -291,7 +291,7 @@ def __init__(
         super().__init__(legs_in, legs_out, diagram.Mode(1))
         self.legs_in = legs_in
         self.legs_out = legs_out
-        self.output_photons = self.determine_output_dimensions
+        self.photon_sum_preserving = False
 
     def conjugate(self):
         return ZBox(self.legs_in, self.legs_out, self.amplitudes.conjugate())
@@ -430,7 +430,7 @@ def __init__(self,
 
         name = "Create(1)" if self.photons == (1,) else f"Create({photons})"
         super().__init__(name, 0, len(self.photons))
-        self.output_photons = self.determine_output_dimensions
+        self.photon_sum_preserving = False
 
     def conjugate(self):
         return self
@@ -534,7 +534,7 @@ def __init__(self,
         self.photons = photons or (1,)
         name = "Select(1)" if self.photons == (1,) else f"Select({photons})"
         super().__init__(name, len(self.photons), 0)
-        self.output_photons = lambda _: 0
+        self.photon_sum_preserving = False
 
     def inflate(self, d):
 
@@ -703,7 +703,7 @@ def __init__(self, is_dagger: bool = False):
         cod = diagram.Mode(2) if is_dagger else diagram.Mode(1)
 
         super().__init__("Multiply", dom, cod)
-        self.output_photons = self.determine_output_dimensions
+        self.photon_sum_preserving = False
 
     def truncation_specification(
         self,
@@ -744,7 +744,7 @@ def __init__(self, is_dagger: bool = False):
         cod = diagram.Mode(2) if is_dagger else diagram.Mode(1)
         super().__init__("Divide", dom, cod)
         self.is_dagger = is_dagger
-        self.output_photons = self.determine_output_dimensions
+        self.photon_sum_preserving = False
 
     def truncation_specification(
         self,
diff --git a/optyx/utils/utils.py b/optyx/utils/utils.py
index 2f3ccfd0..f3b9f292 100644
--- a/optyx/utils/utils.py
+++ b/optyx/utils/utils.py
@@ -17,6 +17,7 @@
 )
 from numbers import Number
 
+
 def _build_w_layer(n_nonzero_counts, dagger=False):
     # pylint: disable=import-outside-toplevel
     from optyx.core import zw
@@ -350,18 +351,24 @@ def preprocess_quimb_tensors_safe(tn, epsilon=1e-12, value_limit=1e10):
 
     return tn
 
-def total_photons_created(diagram, input_dims: Optional[List[int]] = None) -> int:
+
+def total_photons_created(
+        diagram,
+        input_dims: Optional[List[int]] = None
+) -> int:
     """
     Scan `diagram` once and return the total number of photons created.
 
     Counts:
       - zw.Create(*photons) -> +sum(photons)
-    Everything else is ignored for 'creation' (they conserve or consume photons).
+    Everything else is ignored for 'creation'
+    (they conserve or consume photons).
 
     Parameters
     ----------
     diagram : optyx.core.diagram.Diagram
-        The diagram to scan (sequential list of boxes is in `diagram.boxes`).
+        The diagram to scan (sequential list of
+        boxes is in `diagram.boxes`).
     input_dims : Optional[List[int]]
 
     Returns
@@ -383,9 +390,14 @@ def total_photons_created(diagram, input_dims: Optional[List[int]] = None) -> in
 
     return max(int(created) + int(sum(input_dims, 0)), 3)
 
-def max_postselection(diagram, input_dims: Optional[List[int]] = None) -> int:
+
+def max_postselection(
+        diagram,
+        input_dims: Optional[List[int]] = None
+) -> int:
     """
-    Scan `diagram` once and return the maximum post-selection dimension.
+    Scan `diagram` once and return the
+    maximum post-selection dimension.
 
     Counts:
       - zw.Create(*photons) -> +sum(photons)
@@ -393,7 +405,8 @@ def max_postselection(diagram, input_dims: Optional[List[int]] = None) -> int:
     Parameters
     ----------
     diagram : optyx.core.diagram.Diagram
-        The diagram to scan (sequential list of boxes is in `diagram.boxes`).
+        The diagram to scan (sequential list
+        of boxes is in `diagram.boxes`).
     input_dims : Optional[List[int]]
 
     Returns
@@ -413,4 +426,4 @@ def max_postselection(diagram, input_dims: Optional[List[int]] = None) -> int:
             max_dim = max(max_dim, max(int(p) for p in box.photons))
             continue
 
-    return max(int(max_dim) + int(sum(input_dims, 0)), 3)
\ No newline at end of file
+    return max(int(max_dim) + int(sum(input_dims, 0)), 3)

From ad429d8dbae42d3e7fcdcee6a3ec5fd119138562 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Thu, 4 Sep 2025 12:15:35 +0100
Subject: [PATCH 08/59] removing max_dim arg from tests

---
 optyx/core/diagram.py            |  6 ++--
 optyx/photonic.py                |  2 +-
 test/test_distinguishability.py  | 10 +++---
 test/test_zw.py                  | 54 ++++++++++++++------------------
 test/test_zw_truncated_arrays.py |  2 +-
 5 files changed, 33 insertions(+), 41 deletions(-)

diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index 29ff2f43..678b4976 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -299,7 +299,7 @@ def to_path(self, dtype: type = complex):
 
     # pylint: disable=too-many-locals
     def to_tensor(
-        self, input_dims: list = None, max_dim: int = None
+        self, input_dims: list = None
     ) -> tensor.Diagram:
         """Returns a :class:`tensor.Diagram` for evaluation"""
         # pylint: disable=import-outside-toplevel
@@ -697,9 +697,9 @@ def eval(self, n_photons=0, permanent=None, dtype=complex):
             for term in self.terms
         )
 
-    def to_tensor(self, input_dims=None, max_dim=None):
+    def to_tensor(self, input_dims=None):
 
-        terms = [t.to_tensor(input_dims, max_dim) for t in self]
+        terms = [t.to_tensor(input_dims) for t in self]
         cods = [list(t.cod.inside) for t in terms]
 
         # figure out the max dims for each idx and set it for all the terms
diff --git a/optyx/photonic.py b/optyx/photonic.py
index 2f67f199..2b6de50c 100644
--- a/optyx/photonic.py
+++ b/optyx/photonic.py
@@ -224,7 +224,7 @@
 
 >>> channel_HOM = channel_HOM.inflate(len(internal_state_1))
 >>> result = (
-...     channel_HOM.double().to_tensor(max_dim=3).to_quimb()^...
+...     channel_HOM.double().to_tensor().to_quimb()^...
 ... ).data
 
 Let's get the probabilities of the outcomes:
diff --git a/test/test_distinguishability.py b/test/test_distinguishability.py
index 19c4d6ce..5be34f69 100644
--- a/test/test_distinguishability.py
+++ b/test/test_distinguishability.py
@@ -60,7 +60,7 @@ def test_beamsplitter_non_distinguishable(internal_state: np.ndarray) -> None:
 
     probs = (
         channel_bs.double()
-        .to_tensor(max_dim=3)
+        .to_tensor()
         .eval()
         .array
     )
@@ -81,7 +81,7 @@ def test_beamsplitter_distinguishable(state1: np.ndarray, state2: np.ndarray) ->
 
     probs = (
         channel_bs.double()
-        .to_tensor(max_dim=3)
+        .to_tensor()
         .eval()
         .array
     )
@@ -104,7 +104,7 @@ def test_dualrail_identity(qubit_state, internal_state) -> None:
     dr_drdagger = (
         encoded
         >> DualRail(internal_state=internal_state).inflate(len(internal_state)).dagger()
-    ).to_tensor(max_dim=2).eval().array
+    ).to_tensor().eval().array
 
     expected = qubit_state.to_tensor().eval().array
     assert np.allclose(dr_drdagger, expected)
@@ -143,8 +143,8 @@ def test_photon_threshold_detector():
     d_1 = Create(1, internal_states=([1, 0])) >> PhotonThresholdDetector()
     d_2 = X(1, 0, 0.5) @ Scalar(0.5**0.5)
 
-    arr_1 = d_1.inflate(2).to_tensor(max_dim=3).eval().array
-    arr_2 = d_2.to_tensor(max_dim=3).eval().array
+    arr_1 = d_1.inflate(2).to_tensor().eval().array
+    arr_2 = d_2.to_tensor().eval().array
 
     assert np.allclose(arr_1, arr_2)
 
diff --git a/test/test_zw.py b/test/test_zw.py
index 63410cc0..b4160298 100644
--- a/test/test_zw.py
+++ b/test/test_zw.py
@@ -15,7 +15,6 @@
 legs_a_out = range(1, 3)
 legs_b_out = range(1, 3)
 legs_between = range(1, 3)
-max_dim = [None, 2, 4, 6]
 
 # a set of arbitrary functions of i
 fs = [
@@ -27,13 +26,13 @@
 # get all combinations of legs etc
 fs_legs_combinations = list(
     itertools.product(
-        fs, legs_a_in, legs_b_in, legs_a_out, legs_b_out, legs_between, max_dim
+        fs, legs_a_in, legs_b_in, legs_a_out, legs_b_out, legs_between
     )
 )
 
 
 @pytest.mark.parametrize(
-    "fs, legs_a_in, legs_b_in, legs_a_out, legs_b_out, legs_between, max_dim",
+    "fs, legs_a_in, legs_b_in, legs_a_out, legs_b_out, legs_between",
     fs_legs_combinations,
 )
 def test_spider_fusion(
@@ -42,8 +41,7 @@ def test_spider_fusion(
     legs_b_in: int,
     legs_a_out: int,
     legs_b_out: int,
-    legs_between: int,
-    max_dim: int
+    legs_between: int
 ):
 
     S1_infty_l = ZBox(legs_a_in, legs_a_out + legs_between, fs) @ Id(legs_b_in)
@@ -57,8 +55,8 @@ def test_spider_fusion(
     S1_infty_r = ZBox(legs_a_in + legs_b_in, legs_a_out + legs_b_out, fn_mult)
 
     assert compare_arrays_of_different_sizes(
-        S1_infty_l.to_tensor(max_dim = max_dim).eval().array,
-        S1_infty_r.to_tensor(max_dim = max_dim).eval().array,
+        S1_infty_l.to_tensor().eval().array,
+        S1_infty_r.to_tensor().eval().array,
     )
 
 
@@ -183,16 +181,15 @@ def test_Id_dagger_Id(k: int):
     )
 
 
-@pytest.mark.parametrize("max_dim", [None, 3, 4, 6])
-def test_bBa(max_dim):
+def test_bBa():
     bBa_l = (
         W(2) @ W(2) >> Id(1) @ Swap(mode, mode) @ Id(1) >> W(2).dagger() @ W(2).dagger()
     )
     bBa_r = W(2).dagger() >> W(2)
 
     assert compare_arrays_of_different_sizes(
-        bBa_l.to_tensor(max_dim=max_dim).eval().array,
-        bBa_r.to_tensor(max_dim=max_dim).eval().array,
+        bBa_l.to_tensor().eval().array,
+        bBa_r.to_tensor().eval().array,
     )
 
 
@@ -206,8 +203,7 @@ def test_bId():
     )
 
 
-@pytest.mark.parametrize("max_dim", [None, 2, 4, 6])
-def test_bZBA(max_dim):
+def test_bZBA():
     from math import factorial
 
     N = [float(np.sqrt(factorial(i))) for i in range(5)]
@@ -222,12 +218,11 @@ def test_bZBA(max_dim):
     bZBA_r = W(2).dagger() >> ZBox(1, 2, lambda i: 1)
 
     assert compare_arrays_of_different_sizes(
-        bZBA_l.to_tensor(max_dim=max_dim).eval().array,
-        bZBA_r.to_tensor(max_dim=max_dim).eval().array,
+        bZBA_l.to_tensor().eval().array,
+        bZBA_r.to_tensor().eval().array,
     )
 
-@pytest.mark.parametrize("max_dim", [None, 2, 4, 6])
-def test_bZBA_optyx_Spider(max_dim):
+def test_bZBA_optyx_Spider():
     from math import factorial
 
     N = [float(np.sqrt(factorial(i))) for i in range(5)]
@@ -243,8 +238,8 @@ def test_bZBA_optyx_Spider(max_dim):
     bZBA_r = W(2).dagger() >> Spider(1, 2, Mode(1))
 
     assert compare_arrays_of_different_sizes(
-        bZBA_l.to_tensor(max_dim=max_dim).eval().array,
-        bZBA_r.to_tensor(max_dim=max_dim).eval().array,
+        bZBA_l.to_tensor().eval().array,
+        bZBA_r.to_tensor().eval().array,
     )
 
 def test_K0_infty():
@@ -355,8 +350,7 @@ def test_calculate_num_creations_selections():
     ) == calculate_num_creations_selections(d3)
 
 
-@pytest.mark.parametrize("max_dim", [None, 2, 4, 6])
-def test_lemma_B8(max_dim):
+def test_lemma_B8():
     lemma_B8_l = (
             Create(1)
             >> ZBox(1, 2, [1, 1])
@@ -367,13 +361,12 @@ def test_lemma_B8(max_dim):
     lemma_B8_r = Create(1) >> W(2) >> ZBox(1, 2, [1, 1]) @ ZBox(1, 0, [1, 1])
 
     assert compare_arrays_of_different_sizes(
-        lemma_B8_l.to_tensor(max_dim=max_dim).eval().array,
-        lemma_B8_r.to_tensor(max_dim=max_dim).eval().array,
+        lemma_B8_l.to_tensor().eval().array,
+        lemma_B8_r.to_tensor().eval().array,
     )
 
 
-@pytest.mark.parametrize("max_dim", [None, 2, 4, 6])
-def test_lemma_B7(max_dim):
+def test_lemma_B7():
     lemma_B7_l = Id(1) @ W(2).dagger() >> ZBox(2, 0, lambda i: 1)
 
     lemma_B7_r = (
@@ -384,13 +377,12 @@ def test_lemma_B7(max_dim):
     )
 
     assert compare_arrays_of_different_sizes(
-        lemma_B7_l.to_tensor(max_dim=max_dim).eval().array,
-        lemma_B7_r.to_tensor(max_dim=max_dim).eval().array,
+        lemma_B7_l.to_tensor().eval().array,
+        lemma_B7_r.to_tensor().eval().array,
     )
 
 
-@pytest.mark.parametrize("max_dim", [None, 3, 4, 6])
-def test_prop_54(max_dim):
+def test_prop_54():
     prop_54_l = (
             Create(1) @ Id(1)
             >> ZBox(1, 2, lambda i: 1) @ Id(1)
@@ -409,8 +401,8 @@ def test_prop_54(max_dim):
     )
 
     assert compare_arrays_of_different_sizes(
-        prop_54_l.to_tensor(max_dim=max_dim).eval().array,
-        prop_54_r.to_tensor(max_dim=max_dim).eval().array,
+        prop_54_l.to_tensor().eval().array,
+        prop_54_r.to_tensor().eval().array,
     )
 
 
diff --git a/test/test_zw_truncated_arrays.py b/test/test_zw_truncated_arrays.py
index 3e3f24bc..e13fd342 100644
--- a/test/test_zw_truncated_arrays.py
+++ b/test/test_zw_truncated_arrays.py
@@ -3,7 +3,7 @@
 import numpy as np
 import pytest
 from optyx.photonic import ansatz, MZI, TBS
-from optyx.utils.utils import matrix_to_zw
+from optyx.utils.utils import matrix_to_zw, filter_occupation_numbers
 
 @pytest.mark.skip(reason="Helper function for testing")
 def kron_truncation_swap(input_dims: list[int]) -> np.ndarray[complex]:

From 5da35f7af2d8bf338f205f0f74ec0daef618fdb2 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Wed, 10 Sep 2025 19:35:59 +0100
Subject: [PATCH 09/59] scanning diagrams

---
 optyx/core/diagram.py |  79 ++++++++++++---------
 optyx/core/zw.py      |  10 +++
 optyx/core/zx.py      |   2 +-
 optyx/utils/utils.py  | 156 ++++++++++++++++++++++++++++++++++++++++++
 4 files changed, 213 insertions(+), 34 deletions(-)

diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index 678b4976..c6011288 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -229,8 +229,8 @@
 from optyx.utils.utils import (
     modify_io_dims_against_max_dim,
     BasisTransition,
-    total_photons_created,
-    max_postselection
+    calculate_right_offset,
+    get_max_dim_for_box
 )
 from typing import List, Tuple, Iterable
 
@@ -302,69 +302,81 @@ def to_tensor(
         self, input_dims: list = None
     ) -> tensor.Diagram:
         """Returns a :class:`tensor.Diagram` for evaluation"""
-        # pylint: disable=import-outside-toplevel
         from optyx.core import zw
 
+        prev_layers: List[Tuple[int, Box]] = []
+
+        # pylint: disable=import-outside-toplevel
         def list_to_dim(dims: np.ndarray | list) -> Dim:
             """Converts a list of dimensions to a Dim object"""
             return Dim(*[int(i) for i in dims])
 
+        number_of_input_layer_wires = len(self.dom)
+
         if input_dims is None:
             layer_dims = [2 for _ in range(len(self.dom))]
         else:
+            assert len(self.dom) == len(input_dims), (
+                f"Input dims length {len(input_dims)} does not match number of input wires {len(self.dom)}"
+            )
             layer_dims = input_dims
 
-        max_dim = total_photons_created(self, layer_dims) + 1
-        max_post_selection = max_postselection(self, layer_dims) + 1
-
-        if max_dim < max_post_selection:
-            max_dim = max_post_selection
-
-        layer_dims, _ = modify_io_dims_against_max_dim(
-            layer_dims, None, max_dim
-        )
-
         if len(self.boxes) == 0 and len(self.offsets) == 0:
             return tensor.Diagram.id(list_to_dim(layer_dims))
 
-        right_dim = len(self.dom)
-        for i, (box, off) in enumerate(zip(self.boxes, self.offsets)):
-            dims_in = layer_dims[off:off + len(box.dom)]
-
-            dims_out = box.determine_output_dimensions(dims_in)
+        for i, (box, left_offset) in enumerate(zip(self.boxes, self.offsets)):
+            right_offset = calculate_right_offset(
+                number_of_input_layer_wires, left_offset, len(box.dom)
+            )
 
-            if hasattr(box, "photon_sum_preserving"):
-                if not box.photon_sum_preserving:
-                    output_photons = int(max(dims_out, default=0))
-                    if max_dim < output_photons:
-                        max_dim = output_photons + 1
+            max_dim = get_max_dim_for_box(
+                left_offset,
+                box,
+                right_offset,
+                layer_dims,
+                prev_layers
+            )
 
+            dims_in = layer_dims[left_offset:left_offset + len(box.dom)]
             dims_out, _ = modify_io_dims_against_max_dim(
-                dims_out, None, max_dim
+                box.determine_output_dimensions(dims_in),
+                None,
+                max_dim
             )
+            if isinstance(box, zw.LO_ELEMENTS):
+                prev_layers.append((left_offset, box))
+            else:
+                d = Id(mode**(len(dims_in)))
+                if len(dims_in) > 0:
+                    d >>= zw.Select(*dims_in)
+                if len(dims_out) > 0:
+                    d >>= zw.Create(*dims_out)
+                prev_layers.append(
+                    (left_offset, d)
+                )
 
             left = Dim()
-            if off > 0:
-                left = list_to_dim(layer_dims[0:off])
+            if left_offset > 0:
+                left = list_to_dim(layer_dims[0:left_offset])
             right = Dim()
-            if off + len(box.dom) < right_dim:
+            if left_offset + len(box.dom) < number_of_input_layer_wires:
                 right = list_to_dim(
-                    layer_dims[off + len(box.dom): right_dim]
+                    layer_dims[left_offset + len(box.dom): number_of_input_layer_wires]
                 )
 
-            cod_right_dim = right_dim - len(box.dom) + len(box.cod)
+            number_of_input_layer_wires += -len(box.dom) + len(box.cod)
             cod_layer_dims = (
-                layer_dims[0:off]
+                layer_dims[0:left_offset]
                 + dims_out
-                + layer_dims[off + len(box.dom):]
+                + layer_dims[left_offset + len(box.dom):]
             )
-
             diagram_ = left @ box.truncation(dims_in, dims_out) @ right
+
             if i == 0:
                 diagram = diagram_
             else:
                 diagram = diagram >> diagram_
-            right_dim = cod_right_dim
+
             layer_dims = cod_layer_dims
 
         zboxes = tensor.Id(Dim(1))
@@ -377,6 +389,7 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
         diagram >>= zboxes
         return diagram
 
+
     @classmethod
     def from_bosonic_operator(cls, n_modes, operators, scalar=1):
         """Create a :class:`zw` diagram from a bosonic operator."""
diff --git a/optyx/core/zw.py b/optyx/core/zw.py
index 9d9195bc..d23b95d8 100644
--- a/optyx/core/zw.py
+++ b/optyx/core/zw.py
@@ -821,3 +821,13 @@ def Merge(n):
 def Id(n):
     return diagram.Diagram.id(n) if \
           isinstance(n, diagram.Ty) else diagram.Diagram.id(diagram.Mode(n))
+
+
+LO_ELEMENTS = (
+    Create,
+    W,
+    Select,
+    Add,
+    Endo,
+    diagram.Swap
+)
\ No newline at end of file
diff --git a/optyx/core/zx.py b/optyx/core/zx.py
index cbaf3b51..8a441dc1 100644
--- a/optyx/core/zx.py
+++ b/optyx/core/zx.py
@@ -70,7 +70,7 @@
 
 >>> assert np.allclose(graph_path.to_tensor().eval().array, \\
 ... ((graph >> dual_rail(4)).to_tensor() >> \\
-... (tensor.Id(Dim(*[2]*7)) @ embedding_tensor(1, 5))).eval().array)
+... (tensor.Id(Dim(*[2]*7)) @ embedding_tensor(1, 4))).eval().array)
 
 As shown in the example above, we need to decompose a ZX diagram
 into more elementary spiders before mapping it to a path diagram.
diff --git a/optyx/utils/utils.py b/optyx/utils/utils.py
index f3b9f292..b25e70fc 100644
--- a/optyx/utils/utils.py
+++ b/optyx/utils/utils.py
@@ -427,3 +427,159 @@ def max_postselection(
             continue
 
     return max(int(max_dim) + int(sum(input_dims, 0)), 3)
+
+
+def update_connections(
+    wires_in_light_cone: List[bool],
+    previous_left_offset: int,
+    previous_box,
+    previous_right_offset: int,
+) -> List[bool]:
+    """
+    Replace the previous box's COD segment in the light-cone by a DOM-length
+    segment that is either all True (if connected) or all False.
+    This pulls the cone one layer backward.
+    """
+    connected = is_previous_box_connected_to_current_box(
+        wires_in_light_cone,
+        previous_left_offset,
+        len(previous_box.cod),
+        previous_right_offset,
+    )
+
+    start = previous_left_offset
+    end = len(wires_in_light_cone) - previous_right_offset
+
+    # replace cod slice with a dom-length slice of the same boolean
+    return (
+        wires_in_light_cone[:start]
+        + [connected] * len(previous_box.dom)
+        + wires_in_light_cone[end:]
+    )
+
+def calculate_right_offset(total_wires: int, left_offset: int, span_len: int) -> int:
+    """Right offset = number of wires to the right of a span."""
+    return total_wires - span_len - left_offset
+
+def is_previous_box_connected_to_current_box(
+    wires_in_light_cone: List[bool],
+    previous_left_offset: int,
+    previous_box_cod_len: int,
+    previous_right_offset: int,
+) -> bool:
+    """
+    Do the current light-cone wires intersect the COD of the previous box?
+    """
+    mask = (
+        [False] * previous_left_offset
+        + [True] * previous_box_cod_len
+        + [False] * previous_right_offset
+    )
+    # lengths should match by construction
+    assert len(mask) == len(wires_in_light_cone), (
+        f"Mask/wires length mismatch: {len(mask)} != {len(wires_in_light_cone)}"
+    )
+
+    return any(w and m for w, m in zip(wires_in_light_cone, mask))
+
+def get_previous_box_cod_index_in_light_cone(
+    wires_in_light_cone: List[bool],
+    previous_left_offset: int,
+    previous_box_cod_len: int,
+    previous_right_offset: int,
+) -> List[int]:
+    """
+    Get the indices of the COD of the previous box that are in the current light-cone.
+    """
+    mask = (
+        [False] * previous_left_offset
+        + [True] * previous_box_cod_len
+        + [False] * previous_right_offset
+    )
+    # lengths should match by construction
+    assert len(mask) == len(wires_in_light_cone), (
+        f"Mask/wires length mismatch: {len(mask)} != {len(wires_in_light_cone)}"
+    )
+
+    return [
+        i - previous_left_offset for i, (w, m) in enumerate(zip(wires_in_light_cone, mask))
+        if w and m
+    ]
+
+
+def get_max_dim_for_box(
+    left_offset: int,
+    box,
+    right_offset: int,
+    input_dims: List[int],
+    prev_layers,
+):
+    from optyx.core.diagram import Swap
+    from optyx.core.zw import Create, Endo
+
+    # Boxes with no inputs (or a pure Swap) don't constrain the bound here.
+    if len(box.dom) == 0 or isinstance(box, (Swap, Endo)):
+        return 1e20
+
+    dim_for_box = 0
+
+    # Light-cone at the current layer inputs
+    wires_in_light_cone: List[bool] = (
+        [False] * left_offset
+        + [True] * len(box.dom)
+        + [False] * right_offset
+    )
+
+    # Walk previous layers from nearest to farthest
+    for previous_left_offset, previous_box in prev_layers[::-1]:
+        total = len(wires_in_light_cone)
+        cod_len = len(previous_box.cod)
+
+        # Clamp the left offset so the (left, cod_len) span fits this frame.
+        # This guarantees previous_right_offset >= 0 and len(mask) == total.
+        max_left = max(0, total - cod_len)
+        adj_left = previous_left_offset
+        if adj_left < 0:
+            adj_left = 0
+        elif adj_left > max_left:
+            adj_left = max_left
+
+        previous_right_offset = calculate_right_offset(total, adj_left, cod_len)
+
+        # If connected, count created photons that lie on LC wires.
+        if is_previous_box_connected_to_current_box(
+            wires_in_light_cone,
+            adj_left,
+            cod_len,
+            previous_right_offset,
+        ):
+            if isinstance(previous_box, Create):
+                idxs = get_previous_box_cod_index_in_light_cone(
+                    wires_in_light_cone,
+                    adj_left,
+                    cod_len,
+                    previous_right_offset,
+                )
+                if idxs:
+                    dim_for_box += sum(previous_box.photons[i] for i in idxs)
+
+        # Pull the LC back through this box (use the same clamped offsets)
+        if isinstance(previous_box, Swap):
+            # Swaps always connect all their wires
+            wires_in_light_cone = (
+                wires_in_light_cone[:adj_left]
+                + [wires_in_light_cone[adj_left + 1]]
+                + [wires_in_light_cone[adj_left]]
+                + wires_in_light_cone[adj_left + 2:]
+            )
+        else:
+            wires_in_light_cone = update_connections(
+                wires_in_light_cone,
+                adj_left,
+                previous_box,
+                previous_right_offset,
+            )
+
+    # Baseline contribution from current inputs still in the LC (+1 safety)
+    dim_for_box += sum(2 * dim for wire, dim in zip(wires_in_light_cone, input_dims) if wire) + 1
+    return max(dim_for_box, 3)

From 4d7dcaf175786adb51b23aaf18b394c361dc8fe4 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Mon, 15 Sep 2025 14:13:34 +0100
Subject: [PATCH 10/59] fixed a bug in dimension scanning algo

---
 optyx/core/diagram.py | 23 +++++++++++++++++------
 optyx/utils/utils.py  |  6 ++++++
 2 files changed, 23 insertions(+), 6 deletions(-)

diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index c6011288..ce5bf36c 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -346,14 +346,20 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
             if isinstance(box, zw.LO_ELEMENTS):
                 prev_layers.append((left_offset, box))
             else:
-                d = Id(mode**(len(dims_in)))
                 if len(dims_in) > 0:
-                    d >>= zw.Select(*dims_in)
+                    prev_layers.append(
+                        (
+                            left_offset,
+                            zw.Select(*[int(i) for i in np.array(dims_in)-1])
+                        )
+                    )
                 if len(dims_out) > 0:
-                    d >>= zw.Create(*dims_out)
-                prev_layers.append(
-                    (left_offset, d)
-                )
+                    prev_layers.append(
+                        (
+                            left_offset,
+                            zw.Create(*[int(i) for i in np.array(dims_out)-1])
+                        )
+                    )
 
             left = Dim()
             if left_offset > 0:
@@ -381,6 +387,11 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
 
         zboxes = tensor.Id(Dim(1))
 
+        # print("------------------")
+        # for d_ in prev_layers:
+        #     d_[1].draw()
+        # print("------------------")
+
         # pylint: disable=invalid-name
         for c in diagram.cod:
             zboxes @= zw.ZBox(1, 1, lambda i: 1).truncation(
diff --git a/optyx/utils/utils.py b/optyx/utils/utils.py
index b25e70fc..65b23b4d 100644
--- a/optyx/utils/utils.py
+++ b/optyx/utils/utils.py
@@ -546,6 +546,9 @@ def get_max_dim_for_box(
 
         previous_right_offset = calculate_right_offset(total, adj_left, cod_len)
 
+        # if isinstance(previous_box, Create):
+        #     print(previous_box.photons)
+
         # If connected, count created photons that lie on LC wires.
         if is_previous_box_connected_to_current_box(
             wires_in_light_cone,
@@ -562,6 +565,9 @@ def get_max_dim_for_box(
                 )
                 if idxs:
                     dim_for_box += sum(previous_box.photons[i] for i in idxs)
+                if sum(previous_box.photons) == 2:
+                    print(idxs)
+                    print(dim_for_box)
 
         # Pull the LC back through this box (use the same clamped offsets)
         if isinstance(previous_box, Swap):

From 6842d10053d10da91f62898058f8ed9175891973 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Mon, 15 Sep 2025 14:32:14 +0100
Subject: [PATCH 11/59] remove debugging code

---
 optyx/core/diagram.py | 5 -----
 optyx/utils/utils.py  | 6 ------
 2 files changed, 11 deletions(-)

diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index ce5bf36c..cb81f403 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -387,11 +387,6 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
 
         zboxes = tensor.Id(Dim(1))
 
-        # print("------------------")
-        # for d_ in prev_layers:
-        #     d_[1].draw()
-        # print("------------------")
-
         # pylint: disable=invalid-name
         for c in diagram.cod:
             zboxes @= zw.ZBox(1, 1, lambda i: 1).truncation(
diff --git a/optyx/utils/utils.py b/optyx/utils/utils.py
index 65b23b4d..b25e70fc 100644
--- a/optyx/utils/utils.py
+++ b/optyx/utils/utils.py
@@ -546,9 +546,6 @@ def get_max_dim_for_box(
 
         previous_right_offset = calculate_right_offset(total, adj_left, cod_len)
 
-        # if isinstance(previous_box, Create):
-        #     print(previous_box.photons)
-
         # If connected, count created photons that lie on LC wires.
         if is_previous_box_connected_to_current_box(
             wires_in_light_cone,
@@ -565,9 +562,6 @@ def get_max_dim_for_box(
                 )
                 if idxs:
                     dim_for_box += sum(previous_box.photons[i] for i in idxs)
-                if sum(previous_box.photons) == 2:
-                    print(idxs)
-                    print(dim_for_box)
 
         # Pull the LC back through this box (use the same clamped offsets)
         if isinstance(previous_box, Swap):

From 410d1e44df6796f69fa80e57895959f3761205e1 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Tue, 16 Sep 2025 16:31:56 +0100
Subject: [PATCH 12/59] further improvements to the scanning algo

---
 docs/notebooks/graphix_workshop.ipynb | 20977 ++++++++++++++++++++++++
 optyx/core/backends.py                |     6 +-
 optyx/core/diagram.py                 |     4 +
 optyx/utils/utils.py                  |    10 +-
 4 files changed, 20990 insertions(+), 7 deletions(-)
 create mode 100644 docs/notebooks/graphix_workshop.ipynb

diff --git a/docs/notebooks/graphix_workshop.ipynb b/docs/notebooks/graphix_workshop.ipynb
new file mode 100644
index 00000000..e9c850a5
--- /dev/null
+++ b/docs/notebooks/graphix_workshop.ipynb
@@ -0,0 +1,20977 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "45687b1a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'\\n- diagrams + syntax (building blocks + types)\\n- qubit teleportation\\n- evaluation + backends\\n- interfaces + extensions\\n- distributed fusion\\n- distinguishability\\n'"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "'''\n",
+    "- diagrams + syntax (building blocks + types)\n",
+    "- qubit teleportation\n",
+    "- evaluation + backends\n",
+    "- interfaces + extensions\n",
+    "- distributed fusion\n",
+    "- distinguishability\n",
+    "'''"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "28076593",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'\\nDiagrams + syntax (building blocks + types)\\n- diagrams are syntax\\n- function and normal syntax\\n- types of diagrams (qubit + mode, classical + quantum)\\n'"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "'''\n",
+    "Diagrams + syntax (building blocks + types)\n",
+    "- diagrams are syntax\n",
+    "- function and normal syntax\n",
+    "- types of diagrams (qubit + mode, classical + quantum)\n",
+    "'''"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "22456298",
+   "metadata": {},
+   "source": [
+    "# Building blocks"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "36f0ed2d",
+   "metadata": {},
+   "source": [
+    "## Photonic generators and syntax"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "66790776",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.photonic import BBS"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "13dbbb3a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/svg+xml": [
+       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
+       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
+       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
+       "<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"161.609375pt\" height=\"86.4pt\" viewBox=\"0 0 161.609375 86.4\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
+       " <metadata>\n",
+       "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
+       "   <cc:Work>\n",
+       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
+       "    <dc:date>2025-09-16T12:01:49.627815</dc:date>\n",
+       "    <dc:format>image/svg+xml</dc:format>\n",
+       "    <dc:creator>\n",
+       "     <cc:Agent>\n",
+       "      <dc:title>Matplotlib v3.10.5, https://matplotlib.org/</dc:title>\n",
+       "     </cc:Agent>\n",
+       "    </dc:creator>\n",
+       "   </cc:Work>\n",
+       "  </rdf:RDF>\n",
+       " </metadata>\n",
+       " <defs>\n",
+       "  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n",
+       " </defs>\n",
+       " <g id=\"figure_1\">\n",
+       "  <g id=\"patch_1\">\n",
+       "   <path d=\"M 0 86.4 \n",
+       "L 161.609375 86.4 \n",
+       "L 161.609375 0 \n",
+       "L 0 0 \n",
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+       "\" style=\"fill: #ffffff\"/>\n",
+       "  </g>\n",
+       "  <g id=\"axes_1\">\n",
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+       "<Figure size 200x100 with 1 Axes>"
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+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "beam_splitter = BBS(0)\n",
+    "beam_splitter.draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "5623660f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.photonic import Create"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "79ab4b08",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "hong_ou_mandel = (\n",
+    "    Create(1) @ Create(1) >>\n",
+    "    beam_splitter\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "cc4724df",
+   "metadata": {},
+   "outputs": [
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+       "  </clipPath>\n",
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+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 200x300 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "hong_ou_mandel.draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "801f0884",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{(0, 2): 0.5, (1, 1): 4.9303806576313227e-32, (2, 0): 0.5}"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# evaluation => the semantics of the diagram\n",
+    "hong_ou_mandel.eval().prob_dist()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "aa602937",
+   "metadata": {},
+   "source": [
+    "## Qubit and classical generators"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "8d45cf0f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ZX-calculus\n",
+    "from optyx.qubits import Ket, Z, X, H"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "c4999dab",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "diagram = Ket(1) >> X(1, 1, 0.5) >> H() >> Z(1, 1, 0.5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "83c7f83a",
+   "metadata": {},
+   "outputs": [
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+       "  </clipPath>\n",
+       " </defs>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 100x400 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "diagram.draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "f7f0cf81",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{(0,): (0.7071067811865476+0j),\n",
+       " (1,): (-0.7071067811865476+2.5978681687064796e-16j)}"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "diagram.eval().amplitudes()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "7c1af845",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# measurement\n",
+    "from optyx.qubits import Measure"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "e43b8f77",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "measured_diagram = diagram >> Measure(1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "4e217d96",
+   "metadata": {},
+   "outputs": [
+    {
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+    }
+   ],
+   "source": [
+    "measured_diagram.draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "be987eb1",
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "TypeError",
+     "evalue": "Cannot get amplitudes from density matrix or probability distribution.",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
+      "\u001b[31mTypeError\u001b[39m                                 Traceback (most recent call last)",
+      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[16]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[43mmeasured_diagram\u001b[49m\u001b[43m.\u001b[49m\u001b[43meval\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mamplitudes\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/optyx/optyx/core/backends.py:144\u001b[39m, in \u001b[36mEvalResult.amplitudes\u001b[39m\u001b[34m(self, normalise)\u001b[39m\n\u001b[32m    137\u001b[39m \u001b[38;5;250m\u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    138\u001b[39m \u001b[33;03mGet the amplitudes from the result tensor.\u001b[39;00m\n\u001b[32m    139\u001b[39m \u001b[33;03mReturns:\u001b[39;00m\n\u001b[32m    140\u001b[39m \u001b[33;03m    dict: A dictionary mapping occupation\u001b[39;00m\n\u001b[32m    141\u001b[39m \u001b[33;03mconfigurations to amplitudes.\u001b[39;00m\n\u001b[32m    142\u001b[39m \u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    143\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m.state_type != StateType.AMP:\n\u001b[32m--> \u001b[39m\u001b[32m144\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\n\u001b[32m    145\u001b[39m         (\u001b[33m\"\u001b[39m\u001b[33mCannot get amplitudes from density \u001b[39m\u001b[33m\"\u001b[39m +\n\u001b[32m    146\u001b[39m          \u001b[33m\"\u001b[39m\u001b[33mmatrix or probability distribution.\u001b[39m\u001b[33m\"\u001b[39m)\n\u001b[32m    147\u001b[39m     )\n\u001b[32m    148\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m.tensor.dom) != \u001b[32m0\u001b[39m:\n\u001b[32m    149\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[32m    150\u001b[39m         \u001b[33m\"\u001b[39m\u001b[33mResult tensor must represent a state with inputs.\u001b[39m\u001b[33m\"\u001b[39m\n\u001b[32m    151\u001b[39m     )\n",
+      "\u001b[31mTypeError\u001b[39m: Cannot get amplitudes from density matrix or probability distribution."
+     ]
+    }
+   ],
+   "source": [
+    "measured_diagram.eval().amplitudes()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "f02f6b44",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{(0,): (0.5+0j), (1,): (0.5+0j)}"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "measured_diagram.eval().prob_dist()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "14fff50d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.classical import AndBit\n",
+    "\n",
+    "circuit = (\n",
+    "    measured_diagram @ measured_diagram >>\n",
+    "    AndBit()\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "6d735aae",
+   "metadata": {},
+   "outputs": [
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+       "<Figure size 200x1100 with 1 Axes>"
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+   ],
+   "source": [
+    "circuit.draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "d77483b2",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{(0,): (0.7500000000000001-2.0526832973508108e-48j),\n",
+       " (1,): (0.25+2.0526832973508108e-48j)}"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "circuit.eval().prob_dist()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b1f34bd2",
+   "metadata": {},
+   "source": [
+    "### Qubit teleportation - function syntax and backends"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "47e64a7d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.classical import (\n",
+    "  BitControlledGate\n",
+    ")\n",
+    "from optyx import qubit, bit"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "2049d62b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "teleportation = (\n",
+    "    Z(1, 2) @ Z(0, 2) >>\n",
+    "    qubit @ X(2, 1) @ qubit >>\n",
+    "    H() @ qubit @ qubit >>\n",
+    "    Measure(1) @ Measure(1) @ qubit >>\n",
+    "    bit @ BitControlledGate(\n",
+    "                X(1, 1, 0.5)\n",
+    "    ) >>\n",
+    "    BitControlledGate(\n",
+    "        Z(1, 1, 0.5)\n",
+    "    )\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "cae3c5a8",
+   "metadata": {},
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+     "metadata": {},
+     "output_type": "display_data"
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+   ],
+   "source": [
+    "teleportation.foliation().draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "393f7c4a",
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "ValueError",
+     "evalue": "Result tensor must represent a state with inputs.",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
+      "\u001b[31mValueError\u001b[39m                                Traceback (most recent call last)",
+      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[24]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[43mteleportation\u001b[49m\u001b[43m.\u001b[49m\u001b[43meval\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mprob_dist\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/optyx/optyx/core/backends.py:169\u001b[39m, in \u001b[36mEvalResult.prob_dist\u001b[39m\u001b[34m(self, round_digits)\u001b[39m\n\u001b[32m    161\u001b[39m \u001b[38;5;250m\u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    162\u001b[39m \u001b[33;03mGet the probability distribution from the result tensor.\u001b[39;00m\n\u001b[32m    163\u001b[39m \n\u001b[32m   (...)\u001b[39m\u001b[32m    166\u001b[39m \u001b[33;03m      configurations to probabilities.\u001b[39;00m\n\u001b[32m    167\u001b[39m \u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    168\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m.tensor.dom) != \u001b[32m0\u001b[39m:\n\u001b[32m--> \u001b[39m\u001b[32m169\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[32m    170\u001b[39m         \u001b[33m\"\u001b[39m\u001b[33mResult tensor must represent a state with inputs.\u001b[39m\u001b[33m\"\u001b[39m\n\u001b[32m    171\u001b[39m     )\n\u001b[32m    172\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m.state_type \u001b[38;5;129;01mis\u001b[39;00m StateType.AMP:\n\u001b[32m    173\u001b[39m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m._prob_dist_pure(round_digits)\n",
+      "\u001b[31mValueError\u001b[39m: Result tensor must represent a state with inputs."
+     ]
+    }
+   ],
+   "source": [
+    "teleportation.eval().prob_dist()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "f7f2b98b",
+   "metadata": {},
+   "outputs": [
+    {
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+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from optyx.qubits import Id\n",
+    "\n",
+    "Id(1).draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "bb29783a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "np.allclose(\n",
+    "    teleportation.eval().tensor.array,\n",
+    "    Id(1).double().to_tensor().eval().array\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "8c0301af",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx import Diagram\n",
+    "\n",
+    "@Diagram.from_callable(\n",
+    "  dom=qubit, cod=qubit\n",
+    ")\n",
+    "def teleportation(a):\n",
+    "  b = (\n",
+    "    Z(1, 2) @ Z(0, 2)\n",
+    "  )(a)\n",
+    "  d = X(2, 1)(b[1], b[2])\n",
+    "  e = (Measure(1) @ Measure(1))(H()(b[0]), d)\n",
+    "  f = BitControlledGate(\n",
+    "    X(1, 1, 0.5)\n",
+    "  )(e[1], b[3])\n",
+    "  return BitControlledGate(\n",
+    "    Z(1, 1, 0.5)\n",
+    "  )(e[0], f)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "id": "7925be20",
+   "metadata": {},
+   "outputs": [
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+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 500x600 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "teleportation.foliation().draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "id": "499fe3f9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.core.backends import (\n",
+    "    DiscopyBackend,\n",
+    "    QuimbBackend\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "id": "936fd7d2",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[[[ 1.+0.j, -0.+0.j],\n",
+       "         [-0.+0.j,  0.+0.j]],\n",
+       "\n",
+       "        [[ 0.+0.j,  1.+0.j],\n",
+       "         [ 0.-0.j,  0.+0.j]]],\n",
+       "\n",
+       "\n",
+       "       [[[ 0.+0.j,  0.+0.j],\n",
+       "         [ 1.-0.j, -0.+0.j]],\n",
+       "\n",
+       "        [[ 0.+0.j,  0.+0.j],\n",
+       "         [ 0.+0.j,  1.+0.j]]]])"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "teleportation.eval(DiscopyBackend()).tensor.array"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "id": "a1feb431",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from cotengra import HyperCompressedOptimizer\n",
+    "optimiser = HyperCompressedOptimizer(\n",
+    "    chi=1\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "id": "5139ef70",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[[[ 0.04264946+0.j, -0.04264946-0.j],\n",
+       "         [-0.04264946+0.j,  0.04264946-0.j]],\n",
+       "\n",
+       "        [[ 0.04264946+0.j, -0.04264946-0.j],\n",
+       "         [-0.04264946+0.j,  0.04264946-0.j]]],\n",
+       "\n",
+       "\n",
+       "       [[[ 0.04264946+0.j, -0.04264946-0.j],\n",
+       "         [-0.04264946+0.j,  0.04264946-0.j]],\n",
+       "\n",
+       "        [[ 0.04264946+0.j, -0.04264946-0.j],\n",
+       "         [-0.04264946+0.j,  0.04264946-0.j]]]])"
+      ]
+     },
+     "execution_count": 40,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "teleportation.eval(QuimbBackend(optimiser)).tensor.array"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "id": "6113a332",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "optimiser = HyperCompressedOptimizer(\n",
+    "    chi=2\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "id": "f24413ca",
+   "metadata": {},
+   "outputs": [
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+       "         [0.+0.j, 0.-0.j]],\n",
+       "\n",
+       "        [[0.+0.j, 1.+0.j],\n",
+       "         [0.+0.j, 0.+0.j]]],\n",
+       "\n",
+       "\n",
+       "       [[[0.-0.j, 0.-0.j],\n",
+       "         [1.-0.j, 0.-0.j]],\n",
+       "\n",
+       "        [[0.+0.j, 0.+0.j],\n",
+       "         [0.-0.j, 1.-0.j]]]])"
+      ]
+     },
+     "execution_count": 42,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "teleportation.eval(QuimbBackend(optimiser)).tensor.array"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a727d58e",
+   "metadata": {},
+   "source": [
+    "# Interfacing with external libraries"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5086ad32",
+   "metadata": {},
+   "source": [
+    "## Graphix graphs"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "id": "eaaced50",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import graphix\n",
+    "from optyx import qubits\n",
+    "\n",
+    "circuit = graphix.Circuit(2)\n",
+    "circuit.rz(0, 0.5)\n",
+    "circuit.rz(1, 0.5)\n",
+    "circuit.cnot(0, 1)\n",
+    "circuit.s(0)\n",
+    "circuit.cnot(1, 0)\n",
+    "\n",
+    "pattern = circuit.transpile().pattern\n",
+    "\n",
+    "# open graph zx diagram\n",
+    "optyx_zx = qubits.Circuit(pattern)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "id": "d921eb1a",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The pattern is not consistent with flow or gflow structure.\n"
+     ]
+    },
+    {
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+       "    <!-- Z(2, 1) -->\n",
+       "    <g transform=\"translate(66.048438 765.959375) scale(0.1 -0.1)\">\n",
+       "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-32\" transform=\"translate(107.519531 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-2c\" transform=\"translate(171.142578 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-20\" transform=\"translate(202.929688 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(234.716797 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-29\" transform=\"translate(298.339844 0)\"/>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "   <g id=\"text_47\">\n",
+       "    <!-- H -->\n",
+       "    <g transform=\"translate(79.155469 837.959375) scale(0.1 -0.1)\">\n",
+       "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "   <g id=\"text_48\">\n",
+       "    <!-- Z(1, 2) -->\n",
+       "    <g transform=\"translate(66.048438 909.959375) scale(0.1 -0.1)\">\n",
+       "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(107.519531 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-2c\" transform=\"translate(171.142578 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-20\" transform=\"translate(202.929688 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-32\" transform=\"translate(234.716797 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-29\" transform=\"translate(298.339844 0)\"/>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "   <g id=\"text_49\">\n",
+       "    <!-- H -->\n",
+       "    <g transform=\"translate(187.155469 909.959375) scale(0.1 -0.1)\">\n",
+       "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "   <g id=\"text_50\">\n",
+       "    <!-- Z(1, 1) -->\n",
+       "    <g transform=\"translate(174.048438 981.959375) scale(0.1 -0.1)\">\n",
+       "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(107.519531 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-2c\" transform=\"translate(171.142578 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-20\" transform=\"translate(202.929688 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(234.716797 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-29\" transform=\"translate(298.339844 0)\"/>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "   <g id=\"text_51\">\n",
+       "    <!-- H -->\n",
+       "    <g transform=\"translate(187.155469 1053.959375) scale(0.1 -0.1)\">\n",
+       "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "   <g id=\"text_52\">\n",
+       "    <!-- Z(1, 1) -->\n",
+       "    <g transform=\"translate(174.048438 1125.959375) scale(0.1 -0.1)\">\n",
+       "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(107.519531 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-2c\" transform=\"translate(171.142578 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-20\" transform=\"translate(202.929688 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(234.716797 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-29\" transform=\"translate(298.339844 0)\"/>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "   <g id=\"text_53\">\n",
+       "    <!-- H -->\n",
+       "    <g transform=\"translate(43.155469 1197.959375) scale(0.1 -0.1)\">\n",
+       "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "   <g id=\"text_54\">\n",
+       "    <!-- Swap(bit, bit) -->\n",
+       "    <g transform=\"translate(121.2875 1197.959375) scale(0.1 -0.1)\">\n",
+       "     <use xlink:href=\"#DejaVuSans-53\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-77\" transform=\"translate(63.476562 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-61\" transform=\"translate(145.263672 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-70\" transform=\"translate(206.542969 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(270.019531 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(309.033203 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-69\" transform=\"translate(372.509766 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-74\" transform=\"translate(400.292969 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-2c\" transform=\"translate(439.501953 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-20\" transform=\"translate(471.289062 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(503.076172 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-69\" transform=\"translate(566.552734 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-74\" transform=\"translate(594.335938 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-29\" transform=\"translate(633.544922 0)\"/>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "   <g id=\"text_55\">\n",
+       "    <!-- H -->\n",
+       "    <g transform=\"translate(115.155469 1269.959375) scale(0.1 -0.1)\">\n",
+       "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "   <g id=\"text_56\">\n",
+       "    <!-- Z(2, 1) -->\n",
+       "    <g transform=\"translate(66.048438 1341.959375) scale(0.1 -0.1)\">\n",
+       "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-32\" transform=\"translate(107.519531 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-2c\" transform=\"translate(171.142578 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-20\" transform=\"translate(202.929688 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(234.716797 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-29\" transform=\"translate(298.339844 0)\"/>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "   <g id=\"text_57\">\n",
+       "    <!-- H -->\n",
+       "    <g transform=\"translate(79.155469 1413.959375) scale(0.1 -0.1)\">\n",
+       "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "   <g id=\"text_58\">\n",
+       "    <!-- Z(1, 1) -->\n",
+       "    <g transform=\"translate(66.048438 1485.959375) scale(0.1 -0.1)\">\n",
+       "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(107.519531 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-2c\" transform=\"translate(171.142578 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-20\" transform=\"translate(202.929688 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(234.716797 0)\"/>\n",
+       "     <use xlink:href=\"#DejaVuSans-29\" transform=\"translate(298.339844 0)\"/>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "  </g>\n",
+       " </g>\n",
+       " <defs>\n",
+       "  <clipPath id=\"p496af50a44\">\n",
+       "   <rect x=\"10.915625\" y=\"7.2\" width=\"216\" height=\"1512\"/>\n",
+       "  </clipPath>\n",
+       " </defs>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 300x2100 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "optyx_zx.foliation().draw()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4870dd44",
+   "metadata": {},
+   "source": [
+    "## Perceval circuits and processors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "id": "3f1613ed",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import perceval as pcvl\n",
+    "from optyx import Channel"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1f07af00",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "p = pcvl.Processor(\"SLOS\", 6)\n",
+    "p.add(0, pcvl.catalog[\"postprocessed cnot\"].build_processor())\n",
+    "\n",
+    "p.add(0, pcvl.BS.H())\n",
+    "p.add(0, pcvl.Detector.pnr())\n",
+    "p.add(1, pcvl.Detector.pnr())\n",
+    "p.add(2, pcvl.Detector.pnr())\n",
+    "p.add(3, pcvl.Detector.pnr())\n",
+    "\n",
+    "ff_X = pcvl.FFCircuitProvider(\n",
+    "  2, 0, pcvl.Circuit(2)\n",
+    ")\n",
+    "ff_X.add_configuration(\n",
+    "  [0, 1], pcvl.PERM([1, 0])\n",
+    ")\n",
+    "p.add(2, ff_X)\n",
+    "\n",
+    "phi = pcvl.P(\"phi\")\n",
+    "ff_Z = pcvl.FFConfigurator(\n",
+    "  2, 3,\n",
+    "  pcvl.PS(phi),\n",
+    "  {\"phi\": 0}\n",
+    ").add_configuration(\n",
+    "  [0, 1],\n",
+    "  {\"phi\": np.pi}\n",
+    ")\n",
+    "p.add(0, ff_Z)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "id": "3b4867c9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/svg+xml": [
+       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
+       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
+       "     width=\"1175.0\" height=\"531.25\" viewBox=\"-45.0 0 940.0 425.0\">\n",
+       "<defs>\n",
+       "</defs>\n",
+       "<path d=\"M10,25.0 L25,25.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M10,75.0 L25,75.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M10,125.0 L25,125.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M10,175.0 L25,175.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M10,225.0 L25,225.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M10,275.0 L25,275.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M28,225 L72,325\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M25,225 L28,225 L72,325 L75,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M28,275 L72,375\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
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+       "<path d=\"M77,2 L473,2 L473,298 L77,298 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"79\" y=\"305\" font-size=\"8\" text-anchor=\"start\">POSTPROCESSED CNOT</text>\n",
+       "<path d=\"M25,125 L53,125 L72,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M78,144 L97,125 L125,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M25,175 L53,175 L72,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M78,156 L97,175 L125,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M50,143 L100,143 L100,157 L50,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"75\" y=\"185\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"75\" y=\"126\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<path d=\"M50,143 L100,143 L100,147 L50,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M93,150 L103,150 L103,160 L93,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"98\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M25,75.0 L125,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M128,75 L172,175\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M125,75 L128,75 L172,175 L175,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M128,125 L172,125\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M125,125 L128,125 L172,125 L175,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M128,175 L172,225\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M125,175 L128,175 L172,225 L175,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M25,25.0 L175,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M175,25 L203,25 L222,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,44 L247,25 L275,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M175,75 L203,75 L222,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,56 L247,75 L275,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M200,43 L250,43 L250,57 L200,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"225\" y=\"80\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"225\" y=\"26\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
+       "<path d=\"M200,43 L250,43 L250,47 L200,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M243,50 L253,50 L253,60 L243,60 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"248\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M175,125 L203,125 L222,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,144 L247,125 L275,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M175,175 L203,175 L222,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,156 L247,175 L275,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M200,143 L250,143 L250,157 L200,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"225\" y=\"180\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"225\" y=\"126\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
+       "<path d=\"M200,143 L250,143 L250,147 L200,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M243,150 L253,150 L253,160 L243,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"248\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M175,225 L203,225 L222,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,244 L247,225 L275,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M175,275 L203,275 L222,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,256 L247,275 L275,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M200,243 L250,243 L250,257 L200,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"225\" y=\"280\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"225\" y=\"226\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
+       "<path d=\"M200,243 L250,243 L250,247 L200,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M243,250 L253,250 L253,260 L243,260 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"248\" y=\"257\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M278,125 L322,125\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M275,125 L278,125 L322,125 L325,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M278,175 L322,75\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M275,175 L278,175 L322,75 L325,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M278,225 L322,175\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M275,225 L278,225 L322,175 L325,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M325,125 L353,125 L372,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M378,144 L397,125 L425,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M325,175 L353,175 L372,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M378,156 L397,175 L425,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M350,143 L400,143 L400,157 L350,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"375\" y=\"185\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"375\" y=\"126\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<path d=\"M350,143 L400,143 L400,147 L350,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M393,150 L403,150 L403,160 L393,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"398\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M275,25.0 L425,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M325,75.0 L425,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M75,325.0 L425,325.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M75,375.0 L425,375.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M428,325 L472,225\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M425,325 L428,325 L472,225 L475,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
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+       "<path d=\"M425,375 L428,375 L472,275 L475,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M425,25 L453,25 L472,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
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+       "<path d=\"M425,75 L453,75 L472,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
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+       "<text x=\"475\" y=\"26\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<path d=\"M450,43 L500,43 L500,47 L450,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
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+       "<text x=\"498\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
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+       "<path d=\"M550,175 L575,175\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
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+       "<text x=\"537\" y=\"162\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
+       "<path d=\"M575,125 L675,125\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M575,175 L675,175\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M625,190.0 L625,205.0\" stroke=\"white\" stroke-width=\"5\" fill=\"none\" />\n",
+       "<path d=\"M625,190.0 L625,205.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" stroke-dasharray=\"4,4\" />\n",
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+       "<text x=\"625\" y=\"155.0\" font-size=\"10\" text-anchor=\"middle\">FFC</text>\n",
+       "<path d=\"M575,225 L675,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M575,275 L675,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
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+       "<text x=\"625\" y=\"250\" font-size=\"10\" text-anchor=\"middle\">U(FFC)</text>\n",
+       "<path d=\"M575,25.0 L675,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
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+       "<path d=\"M675,75.0 L725,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M725,25 L750,25\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M750,25 L775,25\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
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+       "<path d=\"M725,75 L750,75\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M750,75 L775,75\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
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+       "<text x=\"737\" y=\"62\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
+       "<path d=\"M775,25 L825,25\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M775,75 L825,75\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
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+       "<text x=\"800\" y=\"55.0\" font-size=\"10\" text-anchor=\"middle\">FFC</text>\n",
+       "<path d=\"M725,275 L775,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M730,290 L739,290 L753,260 L744,260 L730,290 L739,290 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"747\" y=\"288\" font-size=\"7\" text-anchor=\"start\">Φ=phi</text>\n",
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+       "<text x=\"-2\" y=\"91\" font-size=\"6\" text-anchor=\"start\" font-style=\"italic\">[ctrl]</text>\n",
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+       "<text x=\"-2\" y=\"191\" font-size=\"6\" text-anchor=\"start\" font-style=\"italic\">[data]</text>\n",
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+       "<text x=\"852\" y=\"91\" font-size=\"6\" text-anchor=\"end\" font-style=\"italic\">[ctrl]</text>\n",
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+       "</svg>"
+      ],
+      "text/plain": [
+       "<drawsvg.drawing.Drawing at 0x7207798b9ee0>"
+      ]
+     },
+     "execution_count": 56,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pcvl.pdisplay(p, recursive=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 69,
+   "id": "22342f65",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# convert to Optyx\n",
+    "optyx_diagram = Channel.from_perceval(p)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 70,
+   "id": "8b7699cf",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
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+       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
+       "    <dc:date>2025-09-16T12:45:41.985074</dc:date>\n",
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+       "     <cc:Agent>\n",
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+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 1000x2500 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "optyx_diagram.draw(figsize=(10, 25))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 73,
+   "id": "af82f2ef",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "to_transmit = (0.7071067811865476+0j)*pcvl.BasicState([1, 0]) + (-0.21850801222441052+0.6724985119639574j)*pcvl.BasicState([0, 1])\n",
+    "to_transmit.normalize()\n",
+    "\n",
+    "sg = pcvl.StateGenerator(pcvl.Encoding.DUAL_RAIL)\n",
+    "bell_state = sg.bell_state(\"phi+\")\n",
+    "\n",
+    "input_state = to_transmit * bell_state\n",
+    "p.min_detected_photons_filter(2)\n",
+    "\n",
+    "input_state *= pcvl.BasicState([0, 0])\n",
+    "\n",
+    "p.with_input(input_state)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 75,
+   "id": "4cc23c53",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "result_perceval = p.probs()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 76,
+   "id": "d9bc5f3b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.qubits import Scalar\n",
+    "from optyx.photonic import DualRail\n",
+    "\n",
+    "bell_state = Z(0, 2) @ Scalar(0.5**0.5)\n",
+    "transmit = Ket(\"+\") >> Z(1, 1, 0.3)\n",
+    "\n",
+    "protocol = (\n",
+    "    transmit @ bell_state >>\n",
+    "    DualRail(3) >>\n",
+    "    Channel.from_perceval(p)\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 77,
+   "id": "ad7fe8c0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "result_optyx = protocol.eval().prob_dist()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 78,
+   "id": "e787f65b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def check_dict_agreement(d1, d2, rtol=1e-5, atol=1e-8):\n",
+    "    for key in d1.keys() - d2.keys():\n",
+    "        assert np.isclose(d1[key], 0, rtol=rtol, atol=atol)\n",
+    "    for key in d2.keys() - d1.keys():\n",
+    "        assert np.isclose(d2[key], 0, rtol=rtol, atol=atol)\n",
+    "    for key in d1.keys() & d2.keys():\n",
+    "        assert np.isclose(d1[key], d2[key], rtol=rtol, atol=atol)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e433baf1",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "check_dict_agreement(\n",
+    "    {tuple(k): v for k, v in dict(result_perceval[\"results\"]).items()},\n",
+    "    result_optyx\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "36241fe2",
+   "metadata": {},
+   "source": [
+    "# Fusion teleportation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5721aeab",
+   "metadata": {},
+   "source": [
+    "Graphically, the fusion measurement we would like to use, takes the following form:\n",
+    "\n",
+    "![Fusion II](./fusion_ii.png \"Fusion measurement implementing a Bell measurement in dual rail encoding\")\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1ab1655b",
+   "metadata": {},
+   "source": [
+    "where $\\underline{a}, \\underline{b}, \\underline{c}, \\underline{d}$ are the measurement outcomes as the measured photon numbers. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 81,
+   "id": "5b0a58bb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx import qmode\n",
+    "\n",
+    "from optyx.photonic import (\n",
+    "    DualRail,\n",
+    "    Swap,\n",
+    "    HadamardBS\n",
+    ")\n",
+    "\n",
+    "fusion = (\n",
+    "    HadamardBS() @ HadamardBS() >>\n",
+    "    qmode @ Swap(1, 1) @ qmode >>\n",
+    "    qmode @ HadamardBS() @ qmode >>\n",
+    "    Swap(1, 1) @ qmode @ qmode >>\n",
+    "    qmode @ Swap(1, 1) @ qmode >>\n",
+    "    qmode @ qmode @ HadamardBS()\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 82,
+   "id": "f7998428",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
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+       "<Figure size 400x700 with 1 Axes>"
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+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fusion.draw()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ea1f931a",
+   "metadata": {},
+   "source": [
+    "As we are dealing with dual-rail encoding, we will restrict ourselves to the outcome results where the total measured number of photons is 4. We have that $\\underline{s} = \\underline{a} \\oplus \\underline{b}$ is the Boolean value of success (whether an entangling operation succeeded) and $\\underline{k} = \\underline{s} (\\underline{b} + \\underline{d}) + \\neg \\underline s (1 - \\frac{\\underline{a} + \\underline{b}}{2})$ is the Pauli error.\n",
+    "This means that the error is $\\underline{b} + \\underline{d}$ in case of success and $1 - \\frac{\\underline{a} + \\underline{b}}{2}$ in case of failure.\n",
+    "\n",
+    "We interpret this diagram as a CP-map which means that the sums represent classical mixing and not quantum superposition. We obtain different protocols conditioned on the value of $\\underline{s}$ and $\\underline{k}$.\n",
+    "\n",
+    "In our analysis we will ignore the case when the fusion fails."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 84,
+   "id": "0ce269cb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.classical import (\n",
+    "    ClassicalFunction\n",
+    ")\n",
+    "\n",
+    "from optyx import mode, bit\n",
+    "\n",
+    "def fusion_function(x):\n",
+    "    \"\"\"\n",
+    "    A classical function that returns two bits based on an input x,\n",
+    "    based on the classical logical for the Fusion type II circuit.\n",
+    "    \"\"\"\n",
+    "    a = x[0]\n",
+    "    b = x[1]\n",
+    "    c = x[2]\n",
+    "    d = x[3]\n",
+    "    s = (a % 2) ^ (b % 2)\n",
+    "    k = int(s*(b + d) + (1-s)*(1 - (a + b)/2))%2\n",
+    "    return [s, k]\n",
+    "\n",
+    "classical_function = ClassicalFunction(\n",
+    "    fusion_function,\n",
+    "    mode**4,\n",
+    "    bit**2\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 85,
+   "id": "a1764edb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.classical import PostselectBit\n",
+    "\n",
+    "fusion_failure_processing = PostselectBit(1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 86,
+   "id": "08e9fc37",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.photonic import Phase\n",
+    "from optyx.classical import BitControlledGate\n",
+    "\n",
+    "# apply the box if the control bit is 1, otherwise apply an identity channel\n",
+    "correction = BitControlledGate(\n",
+    "    HadamardBS() >>\n",
+    "    (Phase(0.5) @ qmode) >>\n",
+    "    HadamardBS()\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 87,
+   "id": "76f472af",
+   "metadata": {},
+   "outputs": [
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+   "source": [
+    "correction.draw()"
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+  },
+  {
+   "cell_type": "code",
+   "execution_count": 88,
+   "id": "c557c4b8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.qubits import Z\n",
+    "from optyx.photonic import Scalar\n",
+    "\n",
+    "channel_bell = (\n",
+    "    Z(0, 2) @ Scalar(0.5**0.5) >> DualRail(1) @ DualRail(1)\n",
+    ")\n",
+    "\n",
+    "dual_rail_input = DualRail(1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 89,
+   "id": "4b5ee771",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.photonic import NumberResolvingMeasurement\n",
+    "\n",
+    "teleportation = (\n",
+    "    dual_rail_input @ channel_bell >>\n",
+    "    fusion @ qmode**2 >>\n",
+    "    NumberResolvingMeasurement(4) @ qmode**2 >>\n",
+    "    classical_function @ qmode**2 >>\n",
+    "    fusion_failure_processing @ correction >>\n",
+    "    DualRail(1).dagger()\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 90,
+   "id": "12531eea",
+   "metadata": {},
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+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 800x1500 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "teleportation.foliation().draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 91,
+   "id": "c8c49c91",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "array_teleportation = teleportation.eval().tensor.array"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 92,
+   "id": "5017fe5a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.photonic import Id\n",
+    "\n",
+    "array_id = (\n",
+    "    Id(1) @ Scalar(0.5**0.5)\n",
+    ").double().to_tensor().eval().array"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 93,
+   "id": "c19354d7",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 93,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "np.allclose(array_teleportation, array_id)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "07c143a0",
+   "metadata": {},
+   "source": [
+    "## Fusion with distinguishable photons"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 97,
+   "id": "74e3f64e",
+   "metadata": {},
+   "outputs": [
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+       " </defs>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 600x600 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fusion_channel = fusion >> NumberResolvingMeasurement(4) >> classical_function\n",
+    "fusion_channel.draw(figsize=(6, 6))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 98,
+   "id": "fcbe90b6",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[1, 0] [1. 0.]\n"
+     ]
+    }
+   ],
+   "source": [
+    "amp = 0.1\n",
+    "internal_state_1 = [1, 0]\n",
+    "internal_state_2 = [1, 0]\n",
+    "internal_state_2 = internal_state_2 / np.linalg.norm(internal_state_2)\n",
+    "\n",
+    "print(internal_state_1, internal_state_2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 99,
+   "id": "bdb9611d",
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+       "      <use xlink:href=\"#DejaVuSans-5a\"/>\n",
+       "      <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
+       "      <use xlink:href=\"#DejaVuSans-30\" transform=\"translate(107.519531 0)\"/>\n",
+       "      <use xlink:href=\"#DejaVuSans-29\" transform=\"translate(171.142578 0)\"/>\n",
+       "     </g>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "  </g>\n",
+       " </g>\n",
+       " <defs>\n",
+       "  <clipPath id=\"p060b7d29fe\">\n",
+       "   <rect x=\"7.2\" y=\"7.2\" width=\"576\" height=\"576\"/>\n",
+       "  </clipPath>\n",
+       " </defs>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 800x800 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from optyx.qubits import Z, Scalar, Id, Measure\n",
+    "from optyx.photonic import DualRail\n",
+    "from optyx.classical import PostselectBit\n",
+    "from discopy.drawing import Equation\n",
+    "\n",
+    "bell_state = Z(0, 2) @ Scalar(0.5 ** 0.5)\n",
+    "dual_rail_encoding = lambda state: DualRail(1, internal_states=[state])\n",
+    "encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(internal_state_2)\n",
+    "post_select = PostselectBit(1) @ PostselectBit(0)\n",
+    "experiment = bell_state @ bell_state >> Id(1) @ (encoding_layer >> fusion_channel >> post_select) @ Id(1)\n",
+    "measure = Measure(2)\n",
+    "Equation(experiment >> measure, bell_state >> measure).draw(figsize=(8, 8))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 105,
+   "id": "2fbb6c45",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.qubits import Discard"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 106,
+   "id": "aa3042f9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fidelity = (experiment >> bell_state.dagger())\n",
+    "\n",
+    "normalisation = (experiment >> Discard(2)).inflate(2).double().to_tensor().to_quimb()^..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 108,
+   "id": "c83b686e",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(1.0000000000000002-1.8369701987210297e-16j)"
+      ]
+     },
+     "execution_count": 108,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "f = fidelity.inflate(2).double().to_tensor().to_quimb()^...\n",
+    "f/normalisation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9e5c4078",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": ".venv",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/optyx/core/backends.py b/optyx/core/backends.py
index d510dff0..b87508e5 100644
--- a/optyx/core/backends.py
+++ b/optyx/core/backends.py
@@ -122,7 +122,7 @@ def density_matrix(self) -> discopy_tensor.Box:
         """
         if len(self.tensor.dom) != 0:
             raise ValueError(
-                "Result tensor must represent a state without inputs."
+                "Result tensor must represent a state with inputs."
             )
         if self.state_type not in {StateType.AMP, StateType.DM}:
             raise TypeError(
@@ -147,7 +147,7 @@ def amplitudes(self, normalise=True) -> dict[tuple[int, ...], float]:
             )
         if len(self.tensor.dom) != 0:
             raise ValueError(
-                "Result tensor must represent a state without inputs."
+                "Result tensor must represent a state with inputs."
             )
 
         dic = self._convert_array_to_dict(self.tensor.array)
@@ -167,7 +167,7 @@ def prob_dist(self, round_digits: int = None) -> dict:
         """
         if len(self.tensor.dom) != 0:
             raise ValueError(
-                "Result tensor must represent a state without inputs."
+                "Result tensor must represent a state with inputs."
             )
         if self.state_type is StateType.AMP:
             return self._prob_dist_pure(round_digits)
diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index cb81f403..d0d52299 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -345,6 +345,10 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
             )
             if isinstance(box, zw.LO_ELEMENTS):
                 prev_layers.append((left_offset, box))
+            elif isinstance(box, DualRail):
+                prev_layers.append((left_offset, zw.Select(1)))
+                prev_layers.append((left_offset, zw.Create(0)))
+                prev_layers.append((left_offset, box))
             else:
                 if len(dims_in) > 0:
                     prev_layers.append(
diff --git a/optyx/utils/utils.py b/optyx/utils/utils.py
index b25e70fc..bf3f04a8 100644
--- a/optyx/utils/utils.py
+++ b/optyx/utils/utils.py
@@ -334,6 +334,8 @@ def preprocess_quimb_tensors_safe(tn, epsilon=1e-12, value_limit=1e10):
     for t in tn:
         data = t.data
 
+        data = np.array(data, copy=True)
+
         if data.dtype.kind in {'i', 'u'}:
             t.modify(data=data.astype('complex128'))
             continue
@@ -514,7 +516,7 @@ def get_max_dim_for_box(
     input_dims: List[int],
     prev_layers,
 ):
-    from optyx.core.diagram import Swap
+    from optyx.core.diagram import Swap, DualRail
     from optyx.core.zw import Create, Endo
 
     # Boxes with no inputs (or a pure Swap) don't constrain the bound here.
@@ -529,7 +531,6 @@ def get_max_dim_for_box(
         + [True] * len(box.dom)
         + [False] * right_offset
     )
-
     # Walk previous layers from nearest to farthest
     for previous_left_offset, previous_box in prev_layers[::-1]:
         total = len(wires_in_light_cone)
@@ -563,6 +564,9 @@ def get_max_dim_for_box(
                 if idxs:
                     dim_for_box += sum(previous_box.photons[i] for i in idxs)
 
+            if isinstance(previous_box, DualRail):
+                dim_for_box += 1
+
         # Pull the LC back through this box (use the same clamped offsets)
         if isinstance(previous_box, Swap):
             # Swaps always connect all their wires
@@ -579,7 +583,5 @@ def get_max_dim_for_box(
                 previous_box,
                 previous_right_offset,
             )
-
-    # Baseline contribution from current inputs still in the LC (+1 safety)
     dim_for_box += sum(2 * dim for wire, dim in zip(wires_in_light_cone, input_dims) if wire) + 1
     return max(dim_for_box, 3)

From 69a64bfc7c03571c4fa1dd6ffcf4543891afc4af Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Tue, 16 Sep 2025 19:54:17 +0100
Subject: [PATCH 13/59] an example notebook

---
 docs/notebooks/classical_generators.png |   Bin 0 -> 174763 bytes
 docs/notebooks/generators.png           |   Bin 0 -> 81669 bytes
 docs/notebooks/graphix_workshop.ipynb   | 10033 +++++++++++++---------
 docs/notebooks/photonic_generators.png  |   Bin 0 -> 218623 bytes
 docs/notebooks/qubit_generators.png     |   Bin 0 -> 101147 bytes
 docs/notebooks/teleport.png             |   Bin 0 -> 18428 bytes
 docs/notebooks/teleport.svg             |   998 +++
 optyx/classical.py                      |     2 +-
 8 files changed, 6884 insertions(+), 4149 deletions(-)
 create mode 100644 docs/notebooks/classical_generators.png
 create mode 100644 docs/notebooks/generators.png
 create mode 100644 docs/notebooks/photonic_generators.png
 create mode 100644 docs/notebooks/qubit_generators.png
 create mode 100644 docs/notebooks/teleport.png
 create mode 100644 docs/notebooks/teleport.svg

diff --git a/docs/notebooks/classical_generators.png b/docs/notebooks/classical_generators.png
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HcmV?d00001

diff --git a/docs/notebooks/graphix_workshop.ipynb b/docs/notebooks/graphix_workshop.ipynb
index e9c850a5..912bdcde 100644
--- a/docs/notebooks/graphix_workshop.ipynb
+++ b/docs/notebooks/graphix_workshop.ipynb
@@ -1,65 +1,35 @@
 {
  "cells": [
   {
-   "cell_type": "code",
-   "execution_count": 1,
-   "id": "45687b1a",
+   "cell_type": "markdown",
+   "id": "0d360e60",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'\\n- diagrams + syntax (building blocks + types)\\n- qubit teleportation\\n- evaluation + backends\\n- interfaces + extensions\\n- distributed fusion\\n- distinguishability\\n'"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
    "source": [
-    "'''\n",
-    "- diagrams + syntax (building blocks + types)\n",
-    "- qubit teleportation\n",
-    "- evaluation + backends\n",
-    "- interfaces + extensions\n",
-    "- distributed fusion\n",
-    "- distinguishability\n",
-    "'''"
+    "# Optyx: A ZX-based Python library for networked quantum architectures"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
-   "id": "28076593",
+   "execution_count": null,
+   "id": "9ab492f0",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "22456298",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'\\nDiagrams + syntax (building blocks + types)\\n- diagrams are syntax\\n- function and normal syntax\\n- types of diagrams (qubit + mode, classical + quantum)\\n'"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
    "source": [
-    "'''\n",
-    "Diagrams + syntax (building blocks + types)\n",
-    "- diagrams are syntax\n",
-    "- function and normal syntax\n",
-    "- types of diagrams (qubit + mode, classical + quantum)\n",
-    "'''"
+    "## Building blocks"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "22456298",
+   "id": "b362a4dc",
    "metadata": {},
    "source": [
-    "# Building blocks"
+    " ![generators](./generators.png \"Optyx Generators\")"
    ]
   },
   {
@@ -67,12 +37,20 @@
    "id": "36f0ed2d",
    "metadata": {},
    "source": [
-    "## Photonic generators and syntax"
+    "### Photonic generators and syntax"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a62bf012",
+   "metadata": {},
+   "source": [
+    " ![photonic_generators](./photonic_generators.png \"Photonic Generators\")"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 1,
    "id": "66790776",
    "metadata": {},
    "outputs": [],
@@ -82,7 +60,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 2,
    "id": "13dbbb3a",
    "metadata": {},
    "outputs": [
@@ -97,7 +75,7 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-16T12:01:49.627815</dc:date>\n",
+       "    <dc:date>2025-09-16T19:38:12.041220</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
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@@ -126,27 +104,27 @@
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        "z\n",
-       "\" clip-path=\"url(#pccfdf2b943)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#pccfdf2b943)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_4\">\n",
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-       "\" clip-path=\"url(#pccfdf2b943)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_5\">\n",
        "    <path d=\"M 43.2 61.2 \n",
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-       "\" clip-path=\"url(#pccfdf2b943)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p1423168275)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_6\">\n",
        "    <path d=\"M 115.2 61.2 \n",
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-       "\" clip-path=\"url(#pccfdf2b943)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p1423168275)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
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@@ -154,7 +132,7 @@
        "L 133.2 25.2 \n",
        "L 133.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pccfdf2b943)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p1423168275)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
        "    <!-- qmode -->\n",
@@ -452,7 +430,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"pccfdf2b943\">\n",
+       "  <clipPath id=\"p1423168275\">\n",
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        "  </clipPath>\n",
        " </defs>\n",
@@ -473,7 +451,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "id": "5623660f",
    "metadata": {},
    "outputs": [],
@@ -483,7 +461,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 4,
    "id": "79ab4b08",
    "metadata": {},
    "outputs": [],
@@ -496,7 +474,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 5,
    "id": "cc4724df",
    "metadata": {},
    "outputs": [
@@ -511,7 +489,7 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-16T12:01:49.762468</dc:date>\n",
+       "    <dc:date>2025-09-16T19:38:12.158722</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -540,27 +518,27 @@
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        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p6078395994)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
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        "   </g>\n",
        "   <g id=\"patch_3\">\n",
        "    <path d=\"M 43.2 61.2 \n",
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-       "\" clip-path=\"url(#p6078395994)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p9153d3b25a)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 115.2 133.2 \n",
        "Q 115.2 169.2 115.2 169.2 \n",
-       "\" clip-path=\"url(#p6078395994)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p9153d3b25a)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
        "    <path d=\"M 43.2 205.2 \n",
        "Q 43.2 223.2 43.2 223.2 \n",
-       "\" clip-path=\"url(#p6078395994)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p9153d3b25a)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_6\">\n",
        "    <path d=\"M 115.2 205.2 \n",
        "Q 115.2 223.2 115.2 223.2 \n",
-       "\" clip-path=\"url(#p6078395994)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p9153d3b25a)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -568,7 +546,7 @@
        "L 61.2 25.2 \n",
        "L 61.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p6078395994)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p9153d3b25a)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -576,7 +554,7 @@
        "L 133.2 97.2 \n",
        "L 133.2 133.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p6078395994)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p9153d3b25a)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_9\">\n",
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@@ -584,7 +562,7 @@
        "L 133.2 169.2 \n",
        "L 133.2 205.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p6078395994)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p9153d3b25a)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
        "    <!-- qmode -->\n",
@@ -1033,7 +1011,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p6078395994\">\n",
+       "  <clipPath id=\"p9153d3b25a\">\n",
        "   <rect x=\"7.2\" y=\"7.2\" width=\"144\" height=\"216\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -1051,9 +1029,17 @@
     "hong_ou_mandel.draw()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "a869643c",
+   "metadata": {},
+   "source": [
+    " ![HOM](./hom.png \"Hong-Ou-Mandel Effect\")"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 6,
    "id": "801f0884",
    "metadata": {},
    "outputs": [
@@ -1063,7 +1049,7 @@
        "{(0, 2): 0.5, (1, 1): 4.9303806576313227e-32, (2, 0): 0.5}"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1073,17 +1059,47 @@
     "hong_ou_mandel.eval().prob_dist()"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "f1478f68",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array(-0.+0.j)"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from optyx.classical import Select\n",
+    "(hong_ou_mandel >> Select(1, 1)).eval().tensor.array"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "aa602937",
    "metadata": {},
    "source": [
-    "## Qubit and classical generators"
+    "### Qubit and classical generators"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d1116b59",
+   "metadata": {},
+   "source": [
+    " ![qubit_generators](./qubit_generators.png \"Qubit Generators\")"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 8,
    "id": "8d45cf0f",
    "metadata": {},
    "outputs": [],
@@ -1094,7 +1110,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 9,
    "id": "c4999dab",
    "metadata": {},
    "outputs": [],
@@ -1104,7 +1120,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 10,
    "id": "83c7f83a",
    "metadata": {},
    "outputs": [
@@ -1114,12 +1130,12 @@
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        "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
        "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
-       "<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"86.4pt\" height=\"302.4pt\" viewBox=\"0 0 86.4 302.4\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
+       "<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"158.4pt\" height=\"230.4pt\" viewBox=\"0 0 158.4 230.4\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
        " <metadata>\n",
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-16T12:01:50.909420</dc:date>\n",
+       "    <dc:date>2025-09-16T19:38:12.951413</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -1134,81 +1150,81 @@
        " </defs>\n",
        " <g id=\"figure_1\">\n",
        "  <g id=\"patch_1\">\n",
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-       "L 86.4 302.4 \n",
-       "L 86.4 0 \n",
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        "\" style=\"fill: #ffffff\"/>\n",
        "  </g>\n",
        "  <g id=\"axes_1\">\n",
        "   <g id=\"patch_2\">\n",
-       "    <path d=\"M 7.2 295.2 \n",
-       "L 79.2 295.2 \n",
-       "L 79.2 7.2 \n",
+       "    <path d=\"M 7.2 223.2 \n",
+       "L 151.2 223.2 \n",
+       "L 151.2 7.2 \n",
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        "z\n",
-       "\" clip-path=\"url(#p40884e8298)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pdedc3736d2)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
-       "    <path d=\"M 43.2 61.2 \n",
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-       "\" clip-path=\"url(#p40884e8298)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 79.2 47.7 \n",
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+       "\" clip-path=\"url(#pdedc3736d2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
-       "    <path d=\"M 43.2 115.2 \n",
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-       "\" clip-path=\"url(#p40884e8298)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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+       "\" clip-path=\"url(#pdedc3736d2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
-       "    <path d=\"M 43.2 97.2 \n",
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-       "\" clip-path=\"url(#p40884e8298)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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+       "Q 79.2 88.2 79.2 88.2 \n",
+       "\" clip-path=\"url(#pdedc3736d2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_6\">\n",
-       "    <path d=\"M 43.2 133.2 \n",
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-       "\" clip-path=\"url(#p40884e8298)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 79.2 101.7 \n",
+       "Q 79.2 128.7 79.2 128.7 \n",
+       "\" clip-path=\"url(#pdedc3736d2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_7\">\n",
-       "    <path d=\"M 43.2 205.2 \n",
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-       "\" clip-path=\"url(#p40884e8298)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 79.2 155.7 \n",
+       "Q 79.2 182.7 79.2 182.7 \n",
+       "\" clip-path=\"url(#pdedc3736d2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_8\">\n",
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+       "\" clip-path=\"url(#pdedc3736d2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_9\">\n",
-       "    <path d=\"M 43.2 241.2 \n",
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-       "\" clip-path=\"url(#p40884e8298)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 79.2 182.7 \n",
+       "Q 79.2 196.2 79.2 196.2 \n",
+       "\" clip-path=\"url(#pdedc3736d2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_10\">\n",
-       "    <path d=\"M 43.2 277.2 \n",
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-       "\" clip-path=\"url(#p40884e8298)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 79.2 209.7 \n",
+       "Q 79.2 223.2 79.2 223.2 \n",
+       "\" clip-path=\"url(#pdedc3736d2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_11\">\n",
-       "    <path d=\"M 25.2 61.2 \n",
-       "L 25.2 25.2 \n",
-       "L 61.2 25.2 \n",
-       "L 61.2 61.2 \n",
+       "    <path d=\"M 43.2 47.7 \n",
+       "L 43.2 20.7 \n",
+       "L 115.2 20.7 \n",
+       "L 115.2 47.7 \n",
        "z\n",
-       "\" clip-path=\"url(#p40884e8298)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pdedc3736d2)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_12\">\n",
-       "    <path d=\"M 25.2 205.2 \n",
-       "L 25.2 169.2 \n",
-       "L 61.2 169.2 \n",
-       "L 61.2 205.2 \n",
+       "    <path d=\"M 43.2 155.7 \n",
+       "L 43.2 128.7 \n",
+       "L 115.2 128.7 \n",
+       "L 115.2 155.7 \n",
        "z\n",
-       "\" clip-path=\"url(#p40884e8298)\" style=\"fill: #f7f700; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pdedc3736d2)\" style=\"fill: #f7f700; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_1\">\n",
        "    <defs>\n",
-       "     <path id=\"C0_0_4dd71d944e\" d=\"M 0 6.123724 \n",
+       "     <path id=\"C0_0_064463dd6a\" d=\"M 0 6.123724 \n",
        "C 1.624031 6.123724 3.181764 5.47849 4.330127 4.330127 \n",
        "C 5.47849 3.181764 6.123724 1.624031 6.123724 -0 \n",
        "C 6.123724 -1.624031 5.47849 -3.181764 4.330127 -4.330127 \n",
@@ -1220,16 +1236,16 @@
        "z\n",
        "\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#p40884e8298)\">\n",
-       "     <use xlink:href=\"#C0_0_4dd71d944e\" x=\"43.2\" y=\"115.2\" style=\"fill: #e8a5a5; stroke: #e8a5a5\"/>\n",
+       "    <g clip-path=\"url(#pdedc3736d2)\">\n",
+       "     <use xlink:href=\"#C0_0_064463dd6a\" x=\"79.2\" y=\"196.2\" style=\"fill: #d8f8d8; stroke: #d8f8d8\"/>\n",
        "    </g>\n",
-       "    <g clip-path=\"url(#p40884e8298)\">\n",
-       "     <use xlink:href=\"#C0_0_4dd71d944e\" x=\"43.2\" y=\"259.2\" style=\"fill: #d8f8d8; stroke: #d8f8d8\"/>\n",
+       "    <g clip-path=\"url(#pdedc3736d2)\">\n",
+       "     <use xlink:href=\"#C0_0_064463dd6a\" x=\"79.2\" y=\"88.2\" style=\"fill: #e8a5a5; stroke: #e8a5a5\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(47.7 73.298437) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(88.2 58.673438) scale(0.1 -0.1)\">\n",
        "     <defs>\n",
        "      <path id=\"DejaVuSans-71\" d=\"M 947 1747 \n",
        "Q 947 1113 1208 752 \n",
@@ -1349,7 +1365,7 @@
        "   </g>\n",
        "   <g id=\"text_2\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(47.7 145.298437) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(88.2 112.673438) scale(0.1 -0.1)\">\n",
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-    "diagram.draw()"
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-   "execution_count": 12,
+   "execution_count": 11,
    "id": "f7f0cf81",
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+     "execution_count": 11,
      "metadata": {},
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+   "id": "06cf6718",
+   "metadata": {},
+   "source": [
+    " ![classical_generators](./classical_generators.png \"Classical Generators\")"
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    "source": [
-    "measured_diagram.draw()"
+    "measured_diagram.draw(figsize=(2, 3))"
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-   "execution_count": 16,
+   "execution_count": 15,
    "id": "be987eb1",
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    "outputs": [
@@ -2194,7 +2218,7 @@
      "traceback": [
       "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
       "\u001b[31mTypeError\u001b[39m                                 Traceback (most recent call last)",
-      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[16]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[43mmeasured_diagram\u001b[49m\u001b[43m.\u001b[49m\u001b[43meval\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mamplitudes\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
+      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[15]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[43mmeasured_diagram\u001b[49m\u001b[43m.\u001b[49m\u001b[43meval\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mamplitudes\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
       "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/optyx/optyx/core/backends.py:144\u001b[39m, in \u001b[36mEvalResult.amplitudes\u001b[39m\u001b[34m(self, normalise)\u001b[39m\n\u001b[32m    137\u001b[39m \u001b[38;5;250m\u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    138\u001b[39m \u001b[33;03mGet the amplitudes from the result tensor.\u001b[39;00m\n\u001b[32m    139\u001b[39m \u001b[33;03mReturns:\u001b[39;00m\n\u001b[32m    140\u001b[39m \u001b[33;03m    dict: A dictionary mapping occupation\u001b[39;00m\n\u001b[32m    141\u001b[39m \u001b[33;03mconfigurations to amplitudes.\u001b[39;00m\n\u001b[32m    142\u001b[39m \u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    143\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m.state_type != StateType.AMP:\n\u001b[32m--> \u001b[39m\u001b[32m144\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\n\u001b[32m    145\u001b[39m         (\u001b[33m\"\u001b[39m\u001b[33mCannot get amplitudes from density \u001b[39m\u001b[33m\"\u001b[39m +\n\u001b[32m    146\u001b[39m          \u001b[33m\"\u001b[39m\u001b[33mmatrix or probability distribution.\u001b[39m\u001b[33m\"\u001b[39m)\n\u001b[32m    147\u001b[39m     )\n\u001b[32m    148\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m.tensor.dom) != \u001b[32m0\u001b[39m:\n\u001b[32m    149\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[32m    150\u001b[39m         \u001b[33m\"\u001b[39m\u001b[33mResult tensor must represent a state with inputs.\u001b[39m\u001b[33m\"\u001b[39m\n\u001b[32m    151\u001b[39m     )\n",
       "\u001b[31mTypeError\u001b[39m: Cannot get amplitudes from density matrix or probability distribution."
      ]
@@ -2206,7 +2230,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 16,
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@@ -2216,7 +2240,7 @@
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-     "execution_count": 17,
+     "execution_count": 16,
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@@ -2227,7 +2251,7 @@
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+   "execution_count": 17,
    "id": "14fff50d",
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    "outputs": [],
@@ -2242,7 +2266,7 @@
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   {
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+   "execution_count": 18,
    "id": "6d735aae",
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@@ -2698,7 +2722,7 @@
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-       "    <g transform=\"translate(119.7 721.298437) scale(0.1 -0.1)\">\n",
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@@ -3072,14 +3096,14 @@
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        "</svg>\n"
       ],
       "text/plain": [
-       "<Figure size 200x1100 with 1 Axes>"
+       "<Figure size 400x400 with 1 Axes>"
       ]
      },
      "metadata": {},
@@ -3087,12 +3111,12 @@
     }
    ],
    "source": [
-    "circuit.draw()"
+    "circuit.foliation().draw(figsize=(4, 4))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 19,
    "id": "d77483b2",
    "metadata": {},
    "outputs": [
@@ -3103,7 +3127,7 @@
        " (1,): (0.25+2.0526832973508108e-48j)}"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3120,9 +3144,17 @@
     "### Qubit teleportation - function syntax and backends"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "668cadf7",
+   "metadata": {},
+   "source": [
+    "<img src=\"teleport.svg\" alt=\"Teleportation Protocol\" width=\"800\" style=\"max-width:100%;\">\n"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 20,
    "id": "47e64a7d",
    "metadata": {},
    "outputs": [],
@@ -3135,7 +3167,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 21,
    "id": "2049d62b",
    "metadata": {},
    "outputs": [],
@@ -3156,7 +3188,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 22,
    "id": "cae3c5a8",
    "metadata": {},
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+   "execution_count": 23,
    "id": "393f7c4a",
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       "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
       "\u001b[31mValueError\u001b[39m                                Traceback (most recent call last)",
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+      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[23]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[43mteleportation\u001b[49m\u001b[43m.\u001b[49m\u001b[43meval\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mprob_dist\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
       "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/optyx/optyx/core/backends.py:169\u001b[39m, in \u001b[36mEvalResult.prob_dist\u001b[39m\u001b[34m(self, round_digits)\u001b[39m\n\u001b[32m    161\u001b[39m \u001b[38;5;250m\u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    162\u001b[39m \u001b[33;03mGet the probability distribution from the result tensor.\u001b[39;00m\n\u001b[32m    163\u001b[39m \n\u001b[32m   (...)\u001b[39m\u001b[32m    166\u001b[39m \u001b[33;03m      configurations to probabilities.\u001b[39;00m\n\u001b[32m    167\u001b[39m \u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    168\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m.tensor.dom) != \u001b[32m0\u001b[39m:\n\u001b[32m--> \u001b[39m\u001b[32m169\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[32m    170\u001b[39m         \u001b[33m\"\u001b[39m\u001b[33mResult tensor must represent a state with inputs.\u001b[39m\u001b[33m\"\u001b[39m\n\u001b[32m    171\u001b[39m     )\n\u001b[32m    172\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m.state_type \u001b[38;5;129;01mis\u001b[39;00m StateType.AMP:\n\u001b[32m    173\u001b[39m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m._prob_dist_pure(round_digits)\n",
       "\u001b[31mValueError\u001b[39m: Result tensor must represent a state with inputs."
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+   "execution_count": 24,
    "id": "c8dc0076",
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@@ -4539,7 +4458,7 @@
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+     "execution_count": 25,
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      "output_type": "execute_result"
     }
@@ -4555,7 +4474,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 26,
    "id": "8c0301af",
    "metadata": {},
    "outputs": [],
@@ -4569,11 +4488,17 @@
     "  b = (\n",
     "    Z(1, 2) @ Z(0, 2)\n",
     "  )(a)\n",
+    "\n",
     "  d = X(2, 1)(b[1], b[2])\n",
-    "  e = (Measure(1) @ Measure(1))(H()(b[0]), d)\n",
+    "\n",
+    "  e = (\n",
+    "    Measure(1) @ Measure(1)\n",
+    "  )(H()(b[0]), d)\n",
+    "\n",
     "  f = BitControlledGate(\n",
     "    X(1, 1, 0.5)\n",
     "  )(e[1], b[3])\n",
+    "\n",
     "  return BitControlledGate(\n",
     "    Z(1, 1, 0.5)\n",
     "  )(e[0], f)"
@@ -4581,7 +4506,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 27,
    "id": "7925be20",
    "metadata": {},
    "outputs": [
@@ -4591,12 +4516,12 @@
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        "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
-       "<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"382.26875pt\" height=\"446.4pt\" viewBox=\"0 0 382.26875 446.4\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
+       "<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"374.4pt\" height=\"446.4pt\" viewBox=\"0 0 374.4 446.4\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
        " <metadata>\n",
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-16T12:02:06.752830</dc:date>\n",
+       "    <dc:date>2025-09-16T19:38:30.063428</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -4612,8 +4537,8 @@
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-       "L 382.26875 446.4 \n",
-       "L 382.26875 0 \n",
+       "L 374.4 446.4 \n",
+       "L 374.4 0 \n",
        "L 0 0 \n",
        "z\n",
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@@ -4625,162 +4550,162 @@
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        "z\n",
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@@ -4788,7 +4713,7 @@
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        "z\n",
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@@ -4796,17 +4721,17 @@
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@@ -4817,7 +4742,7 @@
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@@ -4825,17 +4750,17 @@
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@@ -4846,7 +4771,7 @@
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@@ -4862,11 +4787,11 @@
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        "   <g id=\"PathCollection_1\">\n",
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-       "    <g clip-path=\"url(#pe52c7721f9)\">\n",
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-       "     <g transform=\"translate(282.590625 46.51125) scale(0.12 -0.12)\">\n",
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        "   <g id=\"text_25\">\n",
-       "    <g clip-path=\"url(#pe52c7721f9)\">\n",
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-       "     <g transform=\"translate(210.590625 262.51125) scale(0.12 -0.12)\">\n",
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@@ -5703,7 +5547,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 28,
    "id": "499fe3f9",
    "metadata": {},
    "outputs": [],
@@ -5716,7 +5560,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 29,
    "id": "936fd7d2",
    "metadata": {},
    "outputs": [
@@ -5737,7 +5581,7 @@
        "         [ 0.+0.j,  1.+0.j]]]])"
       ]
      },
-     "execution_count": 31,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5748,7 +5592,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 30,
    "id": "a1feb431",
    "metadata": {},
    "outputs": [],
@@ -5761,28 +5605,50 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 31,
    "id": "5139ef70",
    "metadata": {},
    "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n"
+     ]
+    },
     {
      "data": {
       "text/plain": [
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-       "         [-0.04264946+0.j,  0.04264946-0.j]],\n",
+       "array([[[[0.06248093+0.j, 0.06248093-0.j],\n",
+       "         [0.06248093+0.j, 0.06248093+0.j]],\n",
        "\n",
-       "        [[ 0.04264946+0.j, -0.04264946-0.j],\n",
-       "         [-0.04264946+0.j,  0.04264946-0.j]]],\n",
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        "\n",
        "\n",
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-       "         [-0.04264946+0.j,  0.04264946-0.j]],\n",
+       "       [[[0.06248093+0.j, 0.06248093-0.j],\n",
+       "         [0.06248093+0.j, 0.06248093+0.j]],\n",
        "\n",
-       "        [[ 0.04264946+0.j, -0.04264946-0.j],\n",
-       "         [-0.04264946+0.j,  0.04264946-0.j]]]])"
+       "        [[0.06248093+0.j, 0.06248093-0.j],\n",
+       "         [0.06248093+0.j, 0.06248093+0.j]]]])"
       ]
      },
-     "execution_count": 40,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5793,7 +5659,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 32,
    "id": "6113a332",
    "metadata": {},
    "outputs": [],
@@ -5805,7 +5671,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": 33,
    "id": "f24413ca",
    "metadata": {},
    "outputs": [
@@ -5826,7 +5692,7 @@
        "         [0.-0.j, 1.-0.j]]]])"
       ]
      },
-     "execution_count": 42,
+     "execution_count": 33,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5840,7 +5706,7 @@
    "id": "a727d58e",
    "metadata": {},
    "source": [
-    "# Interfacing with external libraries"
+    "## Interfacing with external libraries"
    ]
   },
   {
@@ -5848,12 +5714,12 @@
    "id": "5086ad32",
    "metadata": {},
    "source": [
-    "## Graphix graphs"
+    "### Graphix graphs"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
+   "execution_count": 34,
    "id": "eaaced50",
    "metadata": {},
    "outputs": [],
@@ -5876,7 +5742,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 35,
    "id": "d921eb1a",
    "metadata": {},
    "outputs": [
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-       "    <dc:date>2025-09-16T12:34:35.690505</dc:date>\n",
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        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8369,7 +8235,7 @@
        "   </g>\n",
        "   <g id=\"text_12\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(195.415625 505.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(499.2 201.65558) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8379,7 +8245,7 @@
        "   </g>\n",
        "   <g id=\"text_13\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(195.415625 577.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(499.2 229.084152) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8389,7 +8255,7 @@
        "   </g>\n",
        "   <g id=\"text_14\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(51.415625 649.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(115.2 256.512723) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8399,7 +8265,7 @@
        "   </g>\n",
        "   <g id=\"text_15\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(123.415625 649.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(307.2 256.512723) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8409,7 +8275,7 @@
        "   </g>\n",
        "   <g id=\"text_16\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(195.415625 649.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(499.2 256.512723) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8419,7 +8285,7 @@
        "   </g>\n",
        "   <g id=\"text_17\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(123.415625 721.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(307.2 283.941295) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8429,7 +8295,7 @@
        "   </g>\n",
        "   <g id=\"text_18\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(87.415625 793.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(211.2 311.369866) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8439,7 +8305,7 @@
        "   </g>\n",
        "   <g id=\"text_19\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(87.415625 865.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(211.2 338.798437) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8449,7 +8315,7 @@
        "   </g>\n",
        "   <g id=\"text_20\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(51.415625 937.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(115.2 366.227009) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8459,7 +8325,7 @@
        "   </g>\n",
        "   <g id=\"text_21\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(123.415625 937.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(307.2 366.227009) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8469,7 +8335,7 @@
        "   </g>\n",
        "   <g id=\"text_22\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(195.415625 937.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(499.2 366.227009) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8479,7 +8345,7 @@
        "   </g>\n",
        "   <g id=\"text_23\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(195.415625 1009.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(499.2 393.65558) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8489,7 +8355,7 @@
        "   </g>\n",
        "   <g id=\"text_24\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(195.415625 1081.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(499.2 421.084152) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8499,7 +8365,7 @@
        "   </g>\n",
        "   <g id=\"text_25\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(195.415625 1153.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(499.2 448.512723) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8509,7 +8375,7 @@
        "   </g>\n",
        "   <g id=\"text_26\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(51.415625 1225.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(115.2 475.941295) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8519,7 +8385,7 @@
        "   </g>\n",
        "   <g id=\"text_27\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(123.415625 1225.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(307.2 475.941295) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8529,7 +8395,7 @@
        "   </g>\n",
        "   <g id=\"text_28\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(195.415625 1225.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(499.2 475.941295) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8539,7 +8405,7 @@
        "   </g>\n",
        "   <g id=\"text_29\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(123.415625 1297.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(307.2 503.369866) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8549,7 +8415,7 @@
        "   </g>\n",
        "   <g id=\"text_30\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(87.415625 1369.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(211.2 530.798437) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8559,7 +8425,7 @@
        "   </g>\n",
        "   <g id=\"text_31\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(87.415625 1441.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(211.2 558.227009) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8569,7 +8435,7 @@
        "   </g>\n",
        "   <g id=\"text_32\">\n",
        "    <!-- qubit -->\n",
-       "    <g transform=\"translate(87.415625 1513.298438) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(211.2 585.65558) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-75\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-62\" transform=\"translate(126.855469 0)\"/>\n",
@@ -8579,7 +8445,7 @@
        "   </g>\n",
        "   <g id=\"text_33\">\n",
        "    <!-- Z(1, 1, 0.9204225284540524) -->\n",
-       "    <g transform=\"translate(7.2 45.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(123.484375 23.673661) scale(0.1 -0.1)\">\n",
        "     <defs>\n",
        "      <path id=\"DejaVuSans-5a\" d=\"M 359 4666 \n",
        "L 4025 4666 \n",
@@ -8841,7 +8707,7 @@
        "   </g>\n",
        "   <g id=\"text_34\">\n",
        "    <!-- Z(1, 1, 0.9204225284540524) -->\n",
-       "    <g transform=\"translate(115.2 45.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(411.484375 23.673661) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(107.519531 0)\"/>\n",
@@ -8873,7 +8739,7 @@
        "   </g>\n",
        "   <g id=\"text_35\">\n",
        "    <!-- H -->\n",
-       "    <g transform=\"translate(79.155469 117.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(195.439844 51.102232) scale(0.1 -0.1)\">\n",
        "     <defs>\n",
        "      <path id=\"DejaVuSans-48\" d=\"M 628 4666 \n",
        "L 1259 4666 \n",
@@ -8896,7 +8762,7 @@
        "   </g>\n",
        "   <g id=\"text_36\">\n",
        "    <!-- Z(1, 1) -->\n",
-       "    <g transform=\"translate(66.048438 189.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(182.332812 78.530804) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(107.519531 0)\"/>\n",
@@ -8908,13 +8774,13 @@
        "   </g>\n",
        "   <g id=\"text_37\">\n",
        "    <!-- H -->\n",
-       "    <g transform=\"translate(79.155469 261.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(195.439844 105.959375) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_38\">\n",
        "    <!-- Z(1, 2, 0.75) -->\n",
-       "    <g transform=\"translate(51.7375 333.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(168.021875 133.387946) scale(0.1 -0.1)\">\n",
        "     <defs>\n",
        "      <path id=\"DejaVuSans-37\" d=\"M 525 4666 \n",
        "L 3525 4666 \n",
@@ -8944,13 +8810,13 @@
        "   </g>\n",
        "   <g id=\"text_39\">\n",
        "    <!-- H -->\n",
-       "    <g transform=\"translate(187.155469 333.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(483.439844 133.387946) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_40\">\n",
        "    <!-- Z(1, 1) -->\n",
-       "    <g transform=\"translate(174.048438 405.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(470.332812 160.816518) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(107.519531 0)\"/>\n",
@@ -8962,13 +8828,13 @@
        "   </g>\n",
        "   <g id=\"text_41\">\n",
        "    <!-- H -->\n",
-       "    <g transform=\"translate(187.155469 477.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(483.439844 188.245089) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_42\">\n",
        "    <!-- Z(1, 1) -->\n",
-       "    <g transform=\"translate(174.048438 549.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(470.332812 215.673661) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(107.519531 0)\"/>\n",
@@ -8980,13 +8846,13 @@
        "   </g>\n",
        "   <g id=\"text_43\">\n",
        "    <!-- H -->\n",
-       "    <g transform=\"translate(43.155469 621.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(99.439844 243.102232) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_44\">\n",
        "    <!-- Swap(bit, bit) -->\n",
-       "    <g transform=\"translate(121.2875 621.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(357.571875 243.102232) scale(0.1 -0.1)\">\n",
        "     <defs>\n",
        "      <path id=\"DejaVuSans-53\" d=\"M 3425 4513 \n",
        "L 3425 3897 \n",
@@ -9113,13 +8979,13 @@
        "   </g>\n",
        "   <g id=\"text_45\">\n",
        "    <!-- H -->\n",
-       "    <g transform=\"translate(115.155469 693.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(291.439844 270.530804) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_46\">\n",
        "    <!-- Z(2, 1) -->\n",
-       "    <g transform=\"translate(66.048438 765.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(182.332812 297.959375) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-32\" transform=\"translate(107.519531 0)\"/>\n",
@@ -9131,13 +8997,13 @@
        "   </g>\n",
        "   <g id=\"text_47\">\n",
        "    <!-- H -->\n",
-       "    <g transform=\"translate(79.155469 837.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(195.439844 325.387946) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_48\">\n",
        "    <!-- Z(1, 2) -->\n",
-       "    <g transform=\"translate(66.048438 909.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(182.332812 352.816518) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(107.519531 0)\"/>\n",
@@ -9149,13 +9015,13 @@
        "   </g>\n",
        "   <g id=\"text_49\">\n",
        "    <!-- H -->\n",
-       "    <g transform=\"translate(187.155469 909.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(483.439844 352.816518) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_50\">\n",
        "    <!-- Z(1, 1) -->\n",
-       "    <g transform=\"translate(174.048438 981.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(470.332812 380.245089) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(107.519531 0)\"/>\n",
@@ -9167,13 +9033,13 @@
        "   </g>\n",
        "   <g id=\"text_51\">\n",
        "    <!-- H -->\n",
-       "    <g transform=\"translate(187.155469 1053.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(483.439844 407.673661) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_52\">\n",
        "    <!-- Z(1, 1) -->\n",
-       "    <g transform=\"translate(174.048438 1125.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(470.332812 435.102232) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(107.519531 0)\"/>\n",
@@ -9185,13 +9051,13 @@
        "   </g>\n",
        "   <g id=\"text_53\">\n",
        "    <!-- H -->\n",
-       "    <g transform=\"translate(43.155469 1197.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(99.439844 462.530804) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-48\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_54\">\n",
        "    <!-- Swap(bit, bit) -->\n",
-       "    <g transform=\"translate(121.2875 1197.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(357.571875 462.530804) scale(0.1 -0.1)\">\n",
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        "     <use xlink:href=\"#DejaVuSans-77\" transform=\"translate(63.476562 0)\"/>\n",
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@@ -9210,13 +9076,13 @@
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        "    <!-- H -->\n",
-       "    <g transform=\"translate(115.155469 1269.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(291.439844 489.959375) scale(0.1 -0.1)\">\n",
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        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_56\">\n",
        "    <!-- Z(2, 1) -->\n",
-       "    <g transform=\"translate(66.048438 1341.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(182.332812 517.387946) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-5a\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
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@@ -9228,13 +9094,13 @@
        "   </g>\n",
        "   <g id=\"text_57\">\n",
        "    <!-- H -->\n",
-       "    <g transform=\"translate(79.155469 1413.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(195.439844 544.816518) scale(0.1 -0.1)\">\n",
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        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_58\">\n",
        "    <!-- Z(1, 1) -->\n",
-       "    <g transform=\"translate(66.048438 1485.959375) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(182.332812 572.245089) scale(0.1 -0.1)\">\n",
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@@ -9247,14 +9113,14 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p496af50a44\">\n",
-       "   <rect x=\"10.915625\" y=\"7.2\" width=\"216\" height=\"1512\"/>\n",
+       "  <clipPath id=\"p71b54b3c1b\">\n",
+       "   <rect x=\"7.2\" y=\"7.2\" width=\"576\" height=\"576\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
        "</svg>\n"
       ],
       "text/plain": [
-       "<Figure size 300x2100 with 1 Axes>"
+       "<Figure size 800x800 with 1 Axes>"
       ]
      },
      "metadata": {},
@@ -9262,7 +9128,7 @@
     }
    ],
    "source": [
-    "optyx_zx.foliation().draw()"
+    "optyx_zx.foliation().draw(figsize=(8, 8))"
    ]
   },
   {
@@ -9270,12 +9136,12 @@
    "id": "4870dd44",
    "metadata": {},
    "source": [
-    "## Perceval circuits and processors"
+    "### Perceval circuits and processors"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 37,
    "id": "3f1613ed",
    "metadata": {},
    "outputs": [],
@@ -9286,10 +9152,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 38,
    "id": "1f07af00",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<perceval.components.processor.Processor at 0x75cce0301400>"
+      ]
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "p = pcvl.Processor(\"SLOS\", 6)\n",
     "p.add(0, pcvl.catalog[\"postprocessed cnot\"].build_processor())\n",
@@ -9322,7 +9199,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
+   "execution_count": 39,
    "id": "3b4867c9",
    "metadata": {},
    "outputs": [
@@ -9531,10 +9408,10 @@
        "</svg>"
       ],
       "text/plain": [
-       "<drawsvg.drawing.Drawing at 0x7207798b9ee0>"
+       "<drawsvg.drawing.Drawing at 0x75cce11cc650>"
       ]
      },
-     "execution_count": 56,
+     "execution_count": 39,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -9545,7 +9422,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 69,
+   "execution_count": 40,
    "id": "22342f65",
    "metadata": {},
    "outputs": [],
@@ -9556,7 +9433,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 70,
+   "execution_count": 42,
    "id": "8b7699cf",
    "metadata": {},
    "outputs": [
@@ -9566,12 +9443,12 @@
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-       "<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"902.413861pt\" height=\"1818.259159pt\" viewBox=\"0 0 902.413861 1818.259159\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
+       "<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"608.85131pt\" height=\"1814.435268pt\" viewBox=\"0 0 608.85131 1814.435268\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-16T12:45:41.985074</dc:date>\n",
+       "    <dc:date>2025-09-16T19:39:04.579249</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
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@@ -9586,9 +9463,9 @@
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@@ -9596,1582 +9473,1557 @@
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        "z\n",
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        "     <use xlink:href=\"#DejaVuSans-6d\"/>\n",
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@@ -11775,7 +11627,7 @@
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        "     <use xlink:href=\"#DejaVuSans-6d\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-6f\" transform=\"translate(97.412109 0)\"/>\n",
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@@ -11784,7 +11636,7 @@
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        "     <use xlink:href=\"#DejaVuSans-6d\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-6f\" transform=\"translate(97.412109 0)\"/>\n",
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@@ -11793,7 +11645,7 @@
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@@ -11803,7 +11655,7 @@
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        "   </g>\n",
        "   <g id=\"text_57\">\n",
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-       "     <use xlink:href=\"#DejaVuSans-29\" transform=\"translate(3531.148438 0)\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_135\">\n",
        "    <!-- Select((0,)) -->\n",
-       "    <g transform=\"translate(629.523362 1018.580065) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(499.458846 1012.816518) scale(0.1 -0.1)\">\n",
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@@ -13600,7 +12976,7 @@
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        "    <!-- Select((0,)) -->\n",
-       "    <g transform=\"translate(675.974975 1049.614547) scale(0.1 -0.1)\">\n",
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@@ -13617,22 +12993,13 @@
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        "    <!-- F -->\n",
-       "    <g transform=\"translate(143.679057 1763.407651) scale(0.1 -0.1)\">\n",
+       "    <g transform=\"translate(115.80809 1732.816518) scale(0.1 -0.1)\">\n",
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        "   </g>\n",
        "   <g id=\"text_138\">\n",
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-       "    <g transform=\"translate(136.016784 1794.442134) scale(0.1 -0.1)\">\n",
-       "     <defs>\n",
-       "      <path id=\"DejaVuSans-49\" d=\"M 628 4666 \n",
-       "L 1259 4666 \n",
-       "L 1259 0 \n",
-       "L 628 0 \n",
-       "L 628 4666 \n",
-       "z\n",
-       "\" transform=\"scale(0.015625)\"/>\n",
-       "     </defs>\n",
+       "    <!-- BitControlledGate -->\n",
+       "    <g transform=\"translate(241.444052 1784.245089) scale(0.1 -0.1)\">\n",
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        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"pf977e97080\">\n",
-       "   <rect x=\"7.2\" y=\"7.2\" width=\"720\" height=\"1800\"/>\n",
+       "  <clipPath id=\"p2293b2adcf\">\n",
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        "  </clipPath>\n",
        " </defs>\n",
        "</svg>\n"
       ],
       "text/plain": [
-       "<Figure size 1000x2500 with 1 Axes>"
+       "<Figure size 800x2500 with 1 Axes>"
       ]
      },
      "metadata": {},
@@ -13730,17 +13037,18 @@
     }
    ],
    "source": [
-    "optyx_diagram.draw(figsize=(10, 25))"
+    "optyx_diagram.foliation().draw(figsize=(8, 25))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 73,
+   "execution_count": 43,
    "id": "af82f2ef",
    "metadata": {},
    "outputs": [],
    "source": [
-    "to_transmit = (0.7071067811865476+0j)*pcvl.BasicState([1, 0]) + (-0.21850801222441052+0.6724985119639574j)*pcvl.BasicState([0, 1])\n",
+    "to_transmit = ((0.7071067811865476+0j)*pcvl.BasicState([1, 0]) +\n",
+    "               (-0.21850801222441052+0.6724985119639574j)*pcvl.BasicState([0, 1]))\n",
     "to_transmit.normalize()\n",
     "\n",
     "sg = pcvl.StateGenerator(pcvl.Encoding.DUAL_RAIL)\n",
@@ -13756,7 +13064,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 75,
+   "execution_count": 44,
    "id": "4cc23c53",
    "metadata": {},
    "outputs": [],
@@ -13766,7 +13074,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 76,
+   "execution_count": 45,
    "id": "d9bc5f3b",
    "metadata": {},
    "outputs": [],
@@ -13786,7 +13094,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 77,
+   "execution_count": 46,
    "id": "ad7fe8c0",
    "metadata": {},
    "outputs": [],
@@ -13796,7 +13104,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 78,
+   "execution_count": 47,
    "id": "e787f65b",
    "metadata": {},
    "outputs": [],
@@ -13812,7 +13120,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 48,
    "id": "e433baf1",
    "metadata": {},
    "outputs": [],
@@ -13828,7 +13136,7 @@
    "id": "36241fe2",
    "metadata": {},
    "source": [
-    "# Fusion teleportation"
+    "## Fusion teleportation"
    ]
   },
   {
@@ -13851,7 +13159,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 81,
+   "execution_count": 49,
    "id": "5b0a58bb",
    "metadata": {},
    "outputs": [],
@@ -13876,7 +13184,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 82,
+   "execution_count": 50,
    "id": "f7998428",
    "metadata": {},
    "outputs": [
@@ -13891,7 +13199,7 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-16T14:24:01.625617</dc:date>\n",
+       "    <dc:date>2025-09-16T19:39:45.505830</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
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@@ -13920,152 +13228,152 @@
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@@ -14073,7 +13381,7 @@
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@@ -14081,7 +13389,7 @@
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@@ -14089,7 +13397,7 @@
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@@ -14097,7 +13405,7 @@
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-       "\" clip-path=\"url(#pd1e3729155)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -14602,7 +13910,7 @@
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@@ -14635,7 +13943,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 84,
+   "execution_count": 51,
    "id": "0ce269cb",
    "metadata": {},
    "outputs": [],
@@ -14668,7 +13976,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 85,
+   "execution_count": 52,
    "id": "a1764edb",
    "metadata": {},
    "outputs": [],
@@ -14680,7 +13988,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 86,
+   "execution_count": 53,
    "id": "08e9fc37",
    "metadata": {},
    "outputs": [],
@@ -14698,7 +14006,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 87,
+   "execution_count": 54,
    "id": "76f472af",
    "metadata": {},
    "outputs": [
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-16T14:24:42.083969</dc:date>\n",
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@@ -14742,127 +14050,127 @@
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-       "\" clip-path=\"url(#p7959831e85)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -14870,7 +14178,7 @@
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@@ -14878,7 +14186,7 @@
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@@ -14886,11 +14194,11 @@
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@@ -14902,17 +14210,17 @@
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@@ -15757,9 +14837,9 @@
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        "   <g id=\"text_19\">\n",
-       "    <g clip-path=\"url(#p7959831e85)\">\n",
+       "    <g clip-path=\"url(#p826096f03f)\">\n",
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-       "     <g transform=\"translate(102.590625 190.51125) scale(0.12 -0.12)\">\n",
+       "     <g transform=\"translate(138.590625 46.51125) scale(0.12 -0.12)\">\n",
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        "      <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
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@@ -15768,9 +14848,9 @@
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        "   </g>\n",
        "   <g id=\"text_20\">\n",
-       "    <g clip-path=\"url(#p7959831e85)\">\n",
+       "    <g clip-path=\"url(#p826096f03f)\">\n",
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-       "     <g transform=\"translate(30.590625 478.51125) scale(0.12 -0.12)\">\n",
+       "     <g transform=\"translate(66.590625 334.51125) scale(0.12 -0.12)\">\n",
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@@ -15779,9 +14859,9 @@
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        "   </g>\n",
        "   <g id=\"text_21\">\n",
-       "    <g clip-path=\"url(#p7959831e85)\">\n",
+       "    <g clip-path=\"url(#p826096f03f)\">\n",
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-       "     <g transform=\"translate(138.590625 46.51125) scale(0.12 -0.12)\">\n",
+       "     <g transform=\"translate(30.590625 478.51125) scale(0.12 -0.12)\">\n",
        "      <use xlink:href=\"#DejaVuSans-5a\"/>\n",
        "      <use xlink:href=\"#DejaVuSans-28\" transform=\"translate(68.505859 0)\"/>\n",
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@@ -15792,7 +14872,7 @@
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        " <defs>\n",
-       "  <clipPath id=\"p7959831e85\">\n",
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@@ -15812,7 +14892,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 88,
+   "execution_count": 55,
    "id": "c557c4b8",
    "metadata": {},
    "outputs": [],
@@ -15829,7 +14909,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 89,
+   "execution_count": 56,
    "id": "4b5ee771",
    "metadata": {},
    "outputs": [],
@@ -15848,7 +14928,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 90,
+   "execution_count": 58,
    "id": "12531eea",
    "metadata": {},
    "outputs": [
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-       "    <dc:date>2025-09-16T14:25:06.777764</dc:date>\n",
+       "    <dc:date>2025-09-16T19:40:04.737240</dc:date>\n",
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@@ -15878,8 +14958,8 @@
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@@ -15887,477 +14967,477 @@
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        "   </g>\n",
        "   <g id=\"text_19\">\n",
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@@ -16791,7 +15871,7 @@
        "   </g>\n",
        "   <g id=\"text_20\">\n",
        "    <!-- qmode -->\n",
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+       "    <g transform=\"translate(119.7 276.398437) scale(0.1 -0.1)\">\n",
        "     <use xlink:href=\"#DejaVuSans-71\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-6d\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-6f\" transform=\"translate(160.888672 0)\"/>\n",
@@ -16801,7 +15881,7 @@
        "   </g>\n",
        "   <g id=\"text_21\">\n",
        "    <!-- qmode -->\n",
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        "     <use xlink:href=\"#DejaVuSans-6f\" transform=\"translate(160.888672 0)\"/>\n",
@@ -16811,7 +15891,7 @@
        "   </g>\n",
        "   <g id=\"text_22\">\n",
        "    <!-- qmode -->\n",
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        "     <use xlink:href=\"#DejaVuSans-6d\" transform=\"translate(63.476562 0)\"/>\n",
        "     <use xlink:href=\"#DejaVuSans-6f\" transform=\"translate(160.888672 0)\"/>\n",
@@ -16821,7 +15901,7 @@
        "   </g>\n",
        "   <g id=\"text_23\">\n",
        "    <!-- qmode -->\n",
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@@ -16831,7 +15911,7 @@
        "   </g>\n",
        "   <g id=\"text_24\">\n",
        "    <!-- mode -->\n",
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        "</svg>\n"
       ],
       "text/plain": [
-       "<Figure size 800x1500 with 1 Axes>"
+       "<Figure size 800x800 with 1 Axes>"
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      "metadata": {},
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     }
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    "source": [
-    "teleportation.foliation().draw()"
+    "teleportation.foliation().draw(figsize=(8, 8))"
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   {
    "cell_type": "code",
-   "execution_count": 91,
+   "execution_count": 59,
    "id": "c8c49c91",
    "metadata": {},
    "outputs": [],
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   {
    "cell_type": "code",
-   "execution_count": 92,
+   "execution_count": 60,
    "id": "5017fe5a",
    "metadata": {},
    "outputs": [],
@@ -18028,7 +17019,7 @@
   },
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    "cell_type": "code",
-   "execution_count": 93,
+   "execution_count": 61,
    "id": "c19354d7",
    "metadata": {},
    "outputs": [
@@ -18038,7 +17029,7 @@
        "True"
       ]
      },
-     "execution_count": 93,
+     "execution_count": 61,
      "metadata": {},
      "output_type": "execute_result"
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    "id": "07c143a0",
    "metadata": {},
    "source": [
-    "## Fusion with distinguishable photons"
+    "### Fusion with distinguishable photons"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 97,
+   "execution_count": 62,
    "id": "74e3f64e",
    "metadata": {},
    "outputs": [
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-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_23\">\n",
        "    <path d=\"M 61.2 247.2 \n",
        "Q 61.2 355.2 61.2 355.2 \n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_24\">\n",
        "    <path d=\"M 223.2 271.2 \n",
        "Q 169.2 271.2 169.2 295.2 \n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_25\">\n",
        "    <path d=\"M 223.2 271.2 \n",
        "Q 277.2 271.2 277.2 295.2 \n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "    <path d=\"M 169.2 247.2 \n",
        "Q 169.2 271.2 223.2 271.2 \n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_27\">\n",
        "    <path d=\"M 277.2 247.2 \n",
        "Q 277.2 271.2 223.2 271.2 \n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "    <path d=\"M 169.2 295.2 \n",
        "Q 169.2 355.2 169.2 355.2 \n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "Q 277.2 355.2 277.2 355.2 \n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_33\">\n",
        "    <path d=\"M 169.2 379.2 \n",
        "Q 169.2 403.2 169.2 403.2 \n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_34\">\n",
        "    <path d=\"M 277.2 379.2 \n",
        "Q 277.2 403.2 277.2 403.2 \n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_35\">\n",
        "    <path d=\"M 385.2 379.2 \n",
        "Q 385.2 403.2 385.2 403.2 \n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_36\">\n",
        "    <path d=\"M 169.2 427.2 \n",
        "Q 169.2 439.2 169.2 439.2 \n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_37\">\n",
        "    <path d=\"M 277.2 427.2 \n",
        "Q 277.2 439.2 277.2 439.2 \n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_38\">\n",
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@@ -18286,7 +17277,7 @@
        "L 196.2 19.2 \n",
        "L 196.2 43.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_39\">\n",
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@@ -18294,7 +17285,7 @@
        "L 412.2 67.2 \n",
        "L 412.2 91.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_40\">\n",
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@@ -18302,7 +17293,7 @@
        "L 304.2 163.2 \n",
        "L 304.2 187.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -18310,7 +17301,7 @@
        "L 412.2 307.2 \n",
        "L 412.2 331.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -18318,17 +17309,17 @@
        "L 412.2 355.2 \n",
        "L 412.2 379.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_43\">\n",
        "    <path d=\"M 207 372 \n",
        "Q 207 362.4 223.2 362.4 \n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_44\">\n",
        "    <path d=\"M 223.2 362.4 \n",
        "Q 239.4 362.4 239.4 372 \n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_45\">\n",
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@@ -18339,7 +17330,7 @@
        "L 228.547049 359.995293 \n",
        "L 227.540973 359.905864 \n",
        "z\n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_46\">\n",
        "    <path d=\"M 34.2 427.2 \n",
@@ -18347,7 +17338,7 @@
        "L 412.2 403.2 \n",
        "L 412.2 427.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p2d4f7e4122)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p76bd758808)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
        "    <!-- qmode -->\n",
@@ -18987,7 +17978,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p2d4f7e4122\">\n",
+       "  <clipPath id=\"p76bd758808\">\n",
        "   <rect x=\"7.2\" y=\"7.2\" width=\"432\" height=\"432\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -19008,7 +17999,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 98,
+   "execution_count": null,
    "id": "fcbe90b6",
    "metadata": {},
    "outputs": [
@@ -19016,14 +18007,13 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[1, 0] [1. 0.]\n"
+      "[1, 0] [0. 1.]\n"
      ]
     }
    ],
    "source": [
-    "amp = 0.1\n",
     "internal_state_1 = [1, 0]\n",
-    "internal_state_2 = [1, 0]\n",
+    "internal_state_2 = [0, 1]\n",
     "internal_state_2 = internal_state_2 / np.linalg.norm(internal_state_2)\n",
     "\n",
     "print(internal_state_1, internal_state_2)"
@@ -19031,7 +18021,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 99,
+   "execution_count": 70,
    "id": "bdb9611d",
    "metadata": {},
    "outputs": [
@@ -19046,7 +18036,7 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-16T14:45:43.979798</dc:date>\n",
+       "    <dc:date>2025-09-16T19:40:29.920521</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -19075,262 +18065,262 @@
        "L 583.2 7.2 \n",
        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
        "    <path d=\"M 72.654545 23.2 \n",
        "Q 33.381818 23.2 33.381818 31.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 72.654545 23.2 \n",
        "Q 111.927273 23.2 111.927273 31.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
        "    <path d=\"M 33.381818 31.2 \n",
        "Q 33.381818 559.2 33.381818 559.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_6\">\n",
        "    <path d=\"M 111.927273 31.2 \n",
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-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "Q 216.654545 87.2 216.654545 95.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "    <path d=\"M 255.927273 87.2 \n",
        "Q 295.2 87.2 295.2 95.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_9\">\n",
        "    <path d=\"M 216.654545 95.2 \n",
        "Q 216.654545 175.2 216.654545 175.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "Q 295.2 559.2 295.2 559.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "Q 85.745455 207.2 85.745455 207.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_12\">\n",
        "    <path d=\"M 138.109091 159.2 \n",
        "Q 138.109091 207.2 138.109091 207.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_13\">\n",
        "    <path d=\"M 190.472727 191.2 \n",
        "Q 190.472727 239.2 190.472727 239.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_14\">\n",
        "    <path d=\"M 242.836364 191.2 \n",
        "Q 242.836364 239.2 242.836364 239.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_15\">\n",
        "    <path d=\"M 85.745455 223.2 \n",
        "Q 85.745455 327.2 85.745455 327.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_16\">\n",
        "    <path d=\"M 138.109091 223.2 \n",
        "Q 138.109091 263.2 138.109091 263.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_17\">\n",
        "    <path d=\"M 190.472727 255.2 \n",
        "Q 190.472727 263.2 190.472727 263.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_18\">\n",
        "    <path d=\"M 242.836364 255.2 \n",
        "Q 242.836364 399.2 242.836364 399.2 \n",
-       "\" clip-path=\"url(#p060b7d29fe)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pb0db694e32)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
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   },
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   },
   {
    "cell_type": "code",
-   "execution_count": 106,
+   "execution_count": 76,
+   "id": "14a649ed",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fidelity = (experiment >> bell_state.dagger())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 77,
    "id": "aa3042f9",
    "metadata": {},
    "outputs": [],
    "source": [
-    "fidelity = (experiment >> bell_state.dagger())\n",
-    "\n",
-    "normalisation = (experiment >> Discard(2)).inflate(2).double().to_tensor().to_quimb()^..."
+    "normalisation = (experiment >> Discard(2)).inflate(2).eval().tensor.array"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 108,
+   "execution_count": 78,
    "id": "c83b686e",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "(1.0000000000000002-1.8369701987210297e-16j)"
+       "(0.5000000000000001-3.061616997868383e-17j)"
       ]
      },
-     "execution_count": 108,
+     "execution_count": 78,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "f = fidelity.inflate(2).double().to_tensor().to_quimb()^...\n",
+    "f = fidelity.inflate(2).eval().tensor.array\n",
     "f/normalisation"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 79,
    "id": "9e5c4078",
    "metadata": {},
    "outputs": [],
+   "source": [
+    "import math\n",
+    "\n",
+    "def rotated_unit_vectors(n: int = 10):\n",
+    "    for i in range(n):\n",
+    "        theta = i * (math.pi / 2) / (n - 1)\n",
+    "        yield (math.cos(theta), math.sin(theta))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 80,
+   "id": "83a32908",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "unit_vectors = list(rotated_unit_vectors(30))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 81,
+   "id": "30b96ad0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "inner_product_states = []\n",
+    "inner_product_bell_states = []\n",
+    "\n",
+    "result_bell = bell_state.eval().tensor.array.flatten()\n",
+    "result_bell = result_bell / np.linalg.norm(result_bell)\n",
+    "\n",
+    "for vector in unit_vectors:\n",
+    "    encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(vector)\n",
+    "    experiment = bell_state @ bell_state >> Id(1) @ (encoding_layer >> fusion_channel\n",
+    "                                                                                >> post_select) @ Id(1)\n",
+    "\n",
+    "    f = (experiment >> bell_state.dagger()).inflate(2).eval().tensor.array\n",
+    "    normalisation = (experiment >> Discard(2)).inflate(2).eval().tensor.array\n",
+    "\n",
+    "    inner_product_states.append(np.inner(vector, internal_state_1))\n",
+    "    inner_product_bell_states.append(f/normalisation)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 82,
+   "id": "1c50f388",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part\n",
+      "  return math.isfinite(val)\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part\n",
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+      ],
+      "text/plain": [
+       "<Figure size 600x400 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "plt.figure(figsize=(6, 4))\n",
+    "plt.plot(inner_product_states, inner_product_bell_states, marker='o')\n",
+    "plt.xlabel('<Internal state 1 | Internal state 2>')\n",
+    "plt.ylabel('<Result | Bell State> (fidelity)')\n",
+    "plt.title('Fidelity of the resulting state with the perfect Bell state')\n",
+    "plt.grid(True)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 83,
+   "id": "06b9a545",
+   "metadata": {},
+   "outputs": [
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+       "    </g>\n",
+       "   </g>\n",
+       "  </g>\n",
+       " </g>\n",
+       " <defs>\n",
+       "  <clipPath id=\"pcd8cb14f14\">\n",
+       "   <rect x=\"50.465625\" y=\"22.318125\" width=\"334.8\" height=\"221.76\"/>\n",
+       "  </clipPath>\n",
+       " </defs>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 600x400 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "plt.figure(figsize=(6, 4))\n",
+    "plt.plot(inner_product_states, inner_product_bell_states, marker='o')\n",
+    "plt.xlabel('<Internal state 1 | Internal state 2>')\n",
+    "plt.ylabel('<Result | Bell State> (fidelity)')\n",
+    "plt.title('Fidelity of the resulting state with the perfect Bell state')\n",
+    "plt.xlim(0.9, 1)\n",
+    "plt.ylim(0.9, 1)\n",
+    "plt.grid(True)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2f2a52e7",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d316d264",
+   "metadata": {},
+   "outputs": [],
    "source": []
   }
  ],
diff --git a/docs/notebooks/photonic_generators.png b/docs/notebooks/photonic_generators.png
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diff --git a/optyx/classical.py b/optyx/classical.py
index 0faa558e..382ab4c7 100644
--- a/optyx/classical.py
+++ b/optyx/classical.py
@@ -192,7 +192,7 @@ def __init__(
             )
 
             super().__init__(
-                f"BitControlledGate({control_gate}, {default_gate})",
+                f"BitControlledGate",
                 kraus,
                 bit @ tp**len(control_gate_single.dom),
                 tp**len(control_gate_single.cod)

From 4de42bb599e160fd9c9c1f8625b15a77e2d2ef47 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Fri, 19 Sep 2025 11:23:35 +0100
Subject: [PATCH 14/59] readme as graphix workshop notebook

---
 docs/notebooks/graphix_workshop.ipynb | 26962 +++++++-----------------
 1 file changed, 7975 insertions(+), 18987 deletions(-)

diff --git a/docs/notebooks/graphix_workshop.ipynb b/docs/notebooks/graphix_workshop.ipynb
index 912bdcde..b8c99a85 100644
--- a/docs/notebooks/graphix_workshop.ipynb
+++ b/docs/notebooks/graphix_workshop.ipynb
@@ -8,59 +8,25 @@
     "# Optyx: A ZX-based Python library for networked quantum architectures"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "9ab492f0",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "markdown",
-   "id": "22456298",
-   "metadata": {},
-   "source": [
-    "## Building blocks"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b362a4dc",
-   "metadata": {},
-   "source": [
-    " ![generators](./generators.png \"Optyx Generators\")"
-   ]
-  },
   {
    "cell_type": "markdown",
-   "id": "36f0ed2d",
+   "id": "b1adf8d9",
    "metadata": {},
    "source": [
-    "### Photonic generators and syntax"
+    "## Hong-Ou-Mandel effect"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "a62bf012",
-   "metadata": {},
-   "source": [
-    " ![photonic_generators](./photonic_generators.png \"Photonic Generators\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "id": "66790776",
+   "id": "6f3dab5d",
    "metadata": {},
-   "outputs": [],
    "source": [
-    "from optyx.photonic import BBS"
+    "### Experiment definition"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 42,
    "id": "13dbbb3a",
    "metadata": {},
    "outputs": [
@@ -75,7 +41,7 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-16T19:38:12.041220</dc:date>\n",
+       "    <dc:date>2025-09-19T10:18:42.709571</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -104,27 +70,27 @@
        "L 151.2 7.2 \n",
        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p1423168275)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pc4955cc6d1)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
        "    <path d=\"M 43.2 7.2 \n",
        "Q 43.2 25.2 43.2 25.2 \n",
-       "\" clip-path=\"url(#p1423168275)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pc4955cc6d1)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 115.2 7.2 \n",
        "Q 115.2 25.2 115.2 25.2 \n",
-       "\" clip-path=\"url(#p1423168275)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pc4955cc6d1)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
        "    <path d=\"M 43.2 61.2 \n",
        "Q 43.2 79.2 43.2 79.2 \n",
-       "\" clip-path=\"url(#p1423168275)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pc4955cc6d1)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_6\">\n",
        "    <path d=\"M 115.2 61.2 \n",
        "Q 115.2 79.2 115.2 79.2 \n",
-       "\" clip-path=\"url(#p1423168275)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pc4955cc6d1)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_7\">\n",
        "    <path d=\"M 25.2 61.2 \n",
@@ -132,7 +98,7 @@
        "L 133.2 25.2 \n",
        "L 133.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p1423168275)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pc4955cc6d1)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
        "    <!-- qmode -->\n",
@@ -430,7 +396,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p1423168275\">\n",
+       "  <clipPath id=\"pc4955cc6d1\">\n",
        "   <rect x=\"7.2\" y=\"7.2\" width=\"144\" height=\"72\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -445,38 +411,17 @@
     }
    ],
    "source": [
+    "from optyx.photonic import BBS\n",
+    "\n",
     "beam_splitter = BBS(0)\n",
     "beam_splitter.draw()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
-   "id": "5623660f",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.photonic import Create"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 43,
    "id": "79ab4b08",
    "metadata": {},
-   "outputs": [],
-   "source": [
-    "hong_ou_mandel = (\n",
-    "    Create(1) @ Create(1) >>\n",
-    "    beam_splitter\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "id": "cc4724df",
-   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -489,7 +434,7 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-16T19:38:12.158722</dc:date>\n",
+       "    <dc:date>2025-09-19T10:18:43.207236</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -518,27 +463,27 @@
        "L 151.2 7.2 \n",
        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p9153d3b25a)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"text_1\">\n",
        "    <!-- qmode -->\n",
@@ -1011,7 +956,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p9153d3b25a\">\n",
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        " </defs>\n",
@@ -1026,6 +971,13 @@
     }
    ],
    "source": [
+    "from optyx.photonic import Create\n",
+    "\n",
+    "hong_ou_mandel = (\n",
+    "    Create(1) @ Create(1) >>\n",
+    "    beam_splitter\n",
+    ")\n",
+    "\n",
     "hong_ou_mandel.draw()"
    ]
   },
@@ -1037,9 +989,41 @@
     " ![HOM](./hom.png \"Hong-Ou-Mandel Effect\")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "94bfc225",
+   "metadata": {},
+   "source": [
+    "### Diagram evaluation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "id": "f1478f68",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array(-0.+0.j)"
+      ]
+     },
+     "execution_count": 44,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from optyx.classical import Select\n",
+    "(\n",
+    "    hong_ou_mandel >> Select(1, 1)\n",
+    ").eval().tensor.array"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 45,
    "id": "801f0884",
    "metadata": {},
    "outputs": [
@@ -1049,79 +1033,279 @@
        "{(0, 2): 0.5, (1, 1): 4.9303806576313227e-32, (2, 0): 0.5}"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 45,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "# evaluation => the semantics of the diagram\n",
     "hong_ou_mandel.eval().prob_dist()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "b1f34bd2",
+   "metadata": {},
+   "source": [
+    "## Qubit teleportation - function syntax and backends"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 7,
-   "id": "f1478f68",
+   "execution_count": 8,
+   "id": "47e64a7d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx import qubit, bit\n",
+    "from optyx.qubits import Scalar\n",
+    "\n",
+    "from optyx import Channel\n",
+    "from optyx.qubits import Z, X, H, Measure, Scalar, qubit, bit\n",
+    "from optyx.classical import BitControlledGate"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "748d7e3d",
+   "metadata": {},
+   "source": [
+    "### Define the protocol"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "8fa3a149",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "@Channel.from_callable(\n",
+    "  dom=qubit @ qubit, cod=qubit @ qubit\n",
+    ")\n",
+    "def cnot(a, b):\n",
+    "  c, d = Z(1, 2)(a)\n",
+    "  Scalar(2 ** 0.5)()\n",
+    "  return X(2, 1)(c, b), d"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "668cadf7",
+   "metadata": {},
+   "source": [
+    "<img src=\"teleport.svg\" alt=\"Teleportation Protocol\" width=\"800\" style=\"max-width:100%;\">\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "8c0301af",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "bell = Scalar(0.5 ** 0.5) @ Z(0, 2)\n",
+    "\n",
+    "@Channel.from_callable(\n",
+    "  dom=qubit, cod=qubit\n",
+    ")\n",
+    "def teleportation(c):\n",
+    "  a, b = bell()\n",
+    "  aa, cc = cnot(a, c)\n",
+    "  c_ = Measure(1)(H()(cc))\n",
+    "  a_ = Measure(1)(aa)\n",
+    "  bb = BitControlledGate(X(1, 1, 0.5))(a_, b)\n",
+    "  return BitControlledGate(Z(1, 1, 0.5))(c_, bb)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "174c4713",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "teleportation_monoidal_syntax = (\n",
+    "    qubit @ bell >>\n",
+    "    cnot @ qubit >>\n",
+    "    H() @ qubit ** 2 >>\n",
+    "    Measure(1) @ Measure(1) @ qubit >>\n",
+    "    bit @ BitControlledGate(X(1, 1, 0.5)) >>\n",
+    "    BitControlledGate(Z(1, 1, 0.5))\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7fcce92a",
+   "metadata": {},
+   "source": [
+    "### Verify the protocol"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "bb29783a",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array(-0.+0.j)"
+       "True"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "from optyx.classical import Select\n",
-    "(hong_ou_mandel >> Select(1, 1)).eval().tensor.array"
+    "import numpy as np\n",
+    "from optyx.qubits import Id\n",
+    "\n",
+    "np.allclose(\n",
+    "    teleportation.eval().tensor.array,\n",
+    "    Id(1).double().to_tensor().eval().array,\n",
+    "    teleportation_monoidal_syntax.eval().tensor.array\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "25af2db6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from optyx.core.backends import (\n",
+    "    DiscopyBackend,\n",
+    "    QuimbBackend\n",
+    ")\n",
+    "\n",
+    "np.allclose(\n",
+    "    teleportation.eval(DiscopyBackend()).tensor.array,\n",
+    "    teleportation.eval(QuimbBackend()).tensor.array\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "36241fe2",
+   "metadata": {},
+   "source": [
+    "## Fusion teleportation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5721aeab",
+   "metadata": {},
+   "source": [
+    "Graphically, the fusion measurement we would like to use, takes the following form:\n",
+    "\n",
+    "![Fusion II](./fusion_ii.png \"Fusion measurement implementing a Bell measurement in dual rail encoding\")\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1ab1655b",
+   "metadata": {},
+   "source": [
+    "where $\\underline{a}, \\underline{b}, \\underline{c}, \\underline{d}$ are the measurement outcomes as the measured photon numbers. "
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "aa602937",
+   "id": "ea1f931a",
    "metadata": {},
    "source": [
-    "### Qubit and classical generators"
+    "$\\underline{s} = \\underline{a} \\oplus \\underline{b}$\n",
+    "\n",
+    "$\\underline{k} = \\underline{s} (\\underline{b} + \\underline{d}) + \\neg \\underline s (1 - \\frac{\\underline{a} + \\underline{b}}{2})$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "d1116b59",
+   "id": "515133cf",
    "metadata": {},
    "source": [
-    " ![qubit_generators](./qubit_generators.png \"Qubit Generators\")"
+    "### Define the protocol"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
-   "id": "8d45cf0f",
+   "execution_count": 14,
+   "id": "a1764edb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.classical import PostselectBit, BitControlledGate\n",
+    "from optyx.photonic import Phase\n",
+    "from optyx.photonic import HadamardBS, qmode\n",
+    "\n",
+    "# postselect on fusion success\n",
+    "fusion_failure_processing = PostselectBit(1)\n",
+    "\n",
+    "# apply the box if the control bit is 1, otherwise apply an identity channel\n",
+    "correction = BitControlledGate(\n",
+    "    HadamardBS() >>\n",
+    "    (Phase(0.5) @ qmode) >>\n",
+    "    HadamardBS()\n",
+    ") @ Scalar(2 ** 0.5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "c557c4b8",
    "metadata": {},
    "outputs": [],
    "source": [
-    "# ZX-calculus\n",
-    "from optyx.qubits import Ket, Z, X, H"
+    "from optyx.photonic import DualRail\n",
+    "\n",
+    "dual_rail_encoded_bell = (\n",
+    "    bell >>\n",
+    "    DualRail(1) @ DualRail(1)\n",
+    ")"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
-   "id": "c4999dab",
+   "execution_count": 16,
+   "id": "7bb5e46f",
    "metadata": {},
    "outputs": [],
    "source": [
-    "diagram = Ket(1) >> X(1, 1, 0.5) >> H() >> Z(1, 1, 0.5)"
+    "from optyx.photonic import FusionTypeII\n",
+    "\n",
+    "@Channel.from_callable(\n",
+    "    dom=qubit, cod=qubit\n",
+    ")\n",
+    "def fusion_teleportation(a):\n",
+    "    dual_rail_encoded_input = DualRail(1)(a)\n",
+    "    b, c, d, e = dual_rail_encoded_bell()\n",
+    "    s, k = FusionTypeII()(*dual_rail_encoded_input, b, c)\n",
+    "    fusion_failure_processing(s)\n",
+    "    output_rail_1, output_rail = correction(k, d, e)\n",
+    "    return DualRail(1).dagger()(output_rail_1, output_rail)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
-   "id": "83c7f83a",
+   "execution_count": 17,
+   "id": "4b5ee771",
    "metadata": {},
    "outputs": [
     {
@@ -1130,12 +1314,12 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-16T19:38:12.951413</dc:date>\n",
+       "    <dc:date>2025-09-19T10:14:02.215469</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -1150,102 +1334,395 @@
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        "  <g id=\"axes_1\">\n",
        "   <g id=\"patch_2\">\n",
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-   "source": [
-    "diagram.draw(figsize=(2, 3))"
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-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "id": "f7f0cf81",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "{(0,): (0.7071067811865476+0j),\n",
-       " (1,): (-0.7071067811865476+2.5978681687064796e-16j)}"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
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-    "diagram.eval().amplitudes()"
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-  {
-   "cell_type": "markdown",
-   "id": "06cf6718",
-   "metadata": {},
-   "source": [
-    " ![classical_generators](./classical_generators.png \"Classical Generators\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "id": "7c1af845",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# measurement\n",
-    "from optyx.qubits import Measure"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "id": "e43b8f77",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "measured_diagram = diagram >> Measure(1)"
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-   "execution_count": 14,
-   "id": "4e217d96",
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-    "measured_diagram.draw(figsize=(2, 3))"
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-   "execution_count": 15,
-   "id": "be987eb1",
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "TypeError",
-     "evalue": "Cannot get amplitudes from density matrix or probability distribution.",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
-      "\u001b[31mTypeError\u001b[39m                                 Traceback (most recent call last)",
-      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[15]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[43mmeasured_diagram\u001b[49m\u001b[43m.\u001b[49m\u001b[43meval\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mamplitudes\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
-      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/optyx/optyx/core/backends.py:144\u001b[39m, in \u001b[36mEvalResult.amplitudes\u001b[39m\u001b[34m(self, normalise)\u001b[39m\n\u001b[32m    137\u001b[39m \u001b[38;5;250m\u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    138\u001b[39m \u001b[33;03mGet the amplitudes from the result tensor.\u001b[39;00m\n\u001b[32m    139\u001b[39m \u001b[33;03mReturns:\u001b[39;00m\n\u001b[32m    140\u001b[39m \u001b[33;03m    dict: A dictionary mapping occupation\u001b[39;00m\n\u001b[32m    141\u001b[39m \u001b[33;03mconfigurations to amplitudes.\u001b[39;00m\n\u001b[32m    142\u001b[39m \u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    143\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m.state_type != StateType.AMP:\n\u001b[32m--> \u001b[39m\u001b[32m144\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\n\u001b[32m    145\u001b[39m         (\u001b[33m\"\u001b[39m\u001b[33mCannot get amplitudes from density \u001b[39m\u001b[33m\"\u001b[39m +\n\u001b[32m    146\u001b[39m          \u001b[33m\"\u001b[39m\u001b[33mmatrix or probability distribution.\u001b[39m\u001b[33m\"\u001b[39m)\n\u001b[32m    147\u001b[39m     )\n\u001b[32m    148\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m.tensor.dom) != \u001b[32m0\u001b[39m:\n\u001b[32m    149\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[32m    150\u001b[39m         \u001b[33m\"\u001b[39m\u001b[33mResult tensor must represent a state with inputs.\u001b[39m\u001b[33m\"\u001b[39m\n\u001b[32m    151\u001b[39m     )\n",
-      "\u001b[31mTypeError\u001b[39m: Cannot get amplitudes from density matrix or probability distribution."
-     ]
-    }
-   ],
-   "source": [
-    "measured_diagram.eval().amplitudes()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "id": "f02f6b44",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "{(0,): (0.5+0j), (1,): (0.5+0j)}"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
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-   ],
-   "source": [
-    "measured_diagram.eval().prob_dist()"
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-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "id": "14fff50d",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.classical import AndBit\n",
-    "\n",
-    "circuit = (\n",
-    "    measured_diagram @ measured_diagram >>\n",
-    "    AndBit()\n",
-    ")"
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-  {
-   "cell_type": "code",
-   "execution_count": 18,
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        " </defs>\n",
        "</svg>\n"
       ],
       "text/plain": [
-       "<Figure size 400x400 with 1 Axes>"
+       "<Figure size 800x800 with 1 Axes>"
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      },
      "metadata": {},
@@ -3111,99 +3217,113 @@
     }
    ],
    "source": [
-    "circuit.foliation().draw(figsize=(4, 4))"
+    "from optyx.photonic import FusionTypeII\n",
+    "\n",
+    "fusion_teleportation_monoidal_syntax = (\n",
+    "    DualRail(1) @ dual_rail_encoded_bell >>\n",
+    "    FusionTypeII() @ qmode**2 >>\n",
+    "    fusion_failure_processing @ correction >>\n",
+    "    DualRail(1).dagger()\n",
+    ")\n",
+    "\n",
+    "array_teleportation = fusion_teleportation.eval().tensor.array\n",
+    "\n",
+    "fusion_teleportation_monoidal_syntax.foliation().draw(figsize=(8, 8))\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5017fe5a",
+   "metadata": {},
+   "source": [
+    "### Verify the protocol"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
-   "id": "d77483b2",
+   "execution_count": 18,
+   "id": "c19354d7",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{(0,): (0.7500000000000001-2.0526832973508108e-48j),\n",
-       " (1,): (0.25+2.0526832973508108e-48j)}"
+       "True"
       ]
      },
-     "execution_count": 19,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "circuit.eval().prob_dist()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b1f34bd2",
-   "metadata": {},
-   "source": [
-    "### Qubit teleportation - function syntax and backends"
+    "import numpy as np\n",
+    "from optyx.photonic import Id\n",
+    "\n",
+    "array_id = Id(1).double().to_tensor().eval().array\n",
+    "np.allclose(array_teleportation, array_id)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "668cadf7",
-   "metadata": {},
-   "source": [
-    "<img src=\"teleport.svg\" alt=\"Teleportation Protocol\" width=\"800\" style=\"max-width:100%;\">\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "id": "47e64a7d",
+   "id": "6e6b4039",
    "metadata": {},
-   "outputs": [],
    "source": [
-    "from optyx.classical import (\n",
-    "  BitControlledGate\n",
-    ")\n",
-    "from optyx import qubit, bit"
+    "### Approximate contraction with Quimb and Cotengra"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
-   "id": "2049d62b",
+   "execution_count": null,
+   "id": "51acb733",
    "metadata": {},
    "outputs": [],
    "source": [
-    "teleportation = (\n",
-    "    Z(1, 2) @ Z(0, 2) >>\n",
-    "    qubit @ X(2, 1) @ qubit >>\n",
-    "    H() @ qubit @ qubit >>\n",
-    "    Measure(1) @ Measure(1) @ qubit >>\n",
-    "    bit @ BitControlledGate(\n",
-    "                X(1, 1, 0.5)\n",
-    "    ) >>\n",
-    "    BitControlledGate(\n",
-    "        Z(1, 1, 0.5)\n",
-    "    )\n",
-    ")"
+    "# process fidelity\n",
+    "\n",
+    "def _flat(x):\n",
+    "    return np.asarray(x, dtype=complex).ravel()\n",
+    "\n",
+    "# cosine similarity of pure unitary channels as superoperators\n",
+    "def process_fidelity(SU, SV):\n",
+    "    a, b = _flat(SU), _flat(SV)\n",
+    "    num = abs(np.vdot(a, b))\n",
+    "    den = np.linalg.norm(a) * np.linalg.norm(b)\n",
+    "    return float(num / den)\n",
+    "\n",
+    "def average_fidelity(SU, SV, d):\n",
+    "    Fp = process_fidelity(SU, SV)\n",
+    "    return float((d * Fp + 1) / (d + 1))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
-   "id": "cae3c5a8",
+   "execution_count": 110,
+   "id": "fb497580",
    "metadata": {},
    "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0.5, 1.0, 'Fusion-based Teleportation Fidelity vs Contraction Chi')"
+      ]
+     },
+     "execution_count": 110,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
     {
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       "text/plain": [
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+       "<Figure size 640x480 with 1 Axes>"
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      },
      "metadata": {},
@@ -4224,50 +4584,92 @@
     }
    ],
    "source": [
-    "teleportation.foliation().draw()"
+    "from cotengra import HyperCompressedOptimizer\n",
+    "\n",
+    "errors = []\n",
+    "for chi in range(1, 6):\n",
+    "    optimiser = HyperCompressedOptimizer(\n",
+    "        chi=chi\n",
+    "    )\n",
+    "    error_for_chi = []\n",
+    "    for _ in range(10):\n",
+    "         error_for_chi.append(\n",
+    "             average_fidelity(\n",
+    "                 fusion_teleportation.eval(QuimbBackend(optimiser)).tensor.array,\n",
+    "                 array_teleportation,\n",
+    "                 d=2\n",
+    "             )\n",
+    "         )\n",
+    "    errors.append(np.median(error_for_chi))\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "plt.plot(range(1, 6), errors, marker='o')\n",
+    "plt.grid()\n",
+    "plt.xlabel('Chi')\n",
+    "plt.ylabel('Average Gate Fidelity')\n",
+    "plt.title('Fusion-based Teleportation Fidelity vs Contraction Chi')\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "351608f0",
+   "metadata": {},
+   "source": [
+    "### Photon loss and channel fidelity"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
-   "id": "393f7c4a",
+   "execution_count": 21,
+   "id": "ac439493",
    "metadata": {},
-   "outputs": [
-    {
-     "ename": "ValueError",
-     "evalue": "Result tensor must represent a state with inputs.",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
-      "\u001b[31mValueError\u001b[39m                                Traceback (most recent call last)",
-      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[23]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[43mteleportation\u001b[49m\u001b[43m.\u001b[49m\u001b[43meval\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mprob_dist\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
-      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/optyx/optyx/core/backends.py:169\u001b[39m, in \u001b[36mEvalResult.prob_dist\u001b[39m\u001b[34m(self, round_digits)\u001b[39m\n\u001b[32m    161\u001b[39m \u001b[38;5;250m\u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    162\u001b[39m \u001b[33;03mGet the probability distribution from the result tensor.\u001b[39;00m\n\u001b[32m    163\u001b[39m \n\u001b[32m   (...)\u001b[39m\u001b[32m    166\u001b[39m \u001b[33;03m      configurations to probabilities.\u001b[39;00m\n\u001b[32m    167\u001b[39m \u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    168\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m.tensor.dom) != \u001b[32m0\u001b[39m:\n\u001b[32m--> \u001b[39m\u001b[32m169\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[32m    170\u001b[39m         \u001b[33m\"\u001b[39m\u001b[33mResult tensor must represent a state with inputs.\u001b[39m\u001b[33m\"\u001b[39m\n\u001b[32m    171\u001b[39m     )\n\u001b[32m    172\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m.state_type \u001b[38;5;129;01mis\u001b[39;00m StateType.AMP:\n\u001b[32m    173\u001b[39m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m._prob_dist_pure(round_digits)\n",
-      "\u001b[31mValueError\u001b[39m: Result tensor must represent a state with inputs."
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "teleportation.eval().prob_dist()"
+    "from optyx.photonic import FusionTypeII, PhotonLoss\n",
+    "\n",
+    "def fusion_teleportation_with_photon_loss(p):\n",
+    "    @Channel.from_callable(\n",
+    "        dom=qubit, cod=qubit\n",
+    "    )\n",
+    "    def fusion_teleportation(a):\n",
+    "        dr_input_1, dr_input_2 = DualRail(1)(a)\n",
+    "        b, c, d, e = dual_rail_encoded_bell()\n",
+    "        dr_input_2_loss, c_loss, e_loss = PhotonLoss(p)(dr_input_2), PhotonLoss(p)(c), PhotonLoss(p)(e)\n",
+    "        s, k = FusionTypeII()(dr_input_1, dr_input_2_loss, b, c_loss)\n",
+    "        fusion_failure_processing(s)\n",
+    "        output_rail_1, output_rail = correction(k, d, e_loss)\n",
+    "        return DualRail(1).dagger()(output_rail_1, output_rail)\n",
+    "    return fusion_teleportation"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
-   "id": "c8dc0076",
+   "execution_count": null,
+   "id": "ea619cd4",
    "metadata": {},
    "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0.5, 1.0, 'Fusion-based Teleportation Fidelity vs Photon Survival Probability (p)')"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
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-       "<Figure size 50x100 with 1 Axes>"
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-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "from optyx.qubits import Id\n",
-    "\n",
-    "Id(1).draw()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "id": "bb29783a",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
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-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "import numpy as np\n",
-    "\n",
-    "np.allclose(\n",
-    "    teleportation.eval().tensor.array,\n",
-    "    Id(1).double().to_tensor().eval().array\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "id": "8c0301af",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx import Diagram\n",
-    "\n",
-    "@Diagram.from_callable(\n",
-    "  dom=qubit, cod=qubit\n",
-    ")\n",
-    "def teleportation(a):\n",
-    "  b = (\n",
-    "    Z(1, 2) @ Z(0, 2)\n",
-    "  )(a)\n",
-    "\n",
-    "  d = X(2, 1)(b[1], b[2])\n",
-    "\n",
-    "  e = (\n",
-    "    Measure(1) @ Measure(1)\n",
-    "  )(H()(b[0]), d)\n",
-    "\n",
-    "  f = BitControlledGate(\n",
-    "    X(1, 1, 0.5)\n",
-    "  )(e[1], b[3])\n",
-    "\n",
-    "  return BitControlledGate(\n",
-    "    Z(1, 1, 0.5)\n",
-    "  )(e[0], f)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "id": "7925be20",
-   "metadata": {},
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-      ],
-      "text/plain": [
-       "<Figure size 500x600 with 1 Axes>"
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-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "teleportation.foliation().draw()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "id": "499fe3f9",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.core.backends import (\n",
-    "    DiscopyBackend,\n",
-    "    QuimbBackend\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "id": "936fd7d2",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[[[ 1.+0.j, -0.+0.j],\n",
-       "         [-0.+0.j,  0.+0.j]],\n",
-       "\n",
-       "        [[ 0.+0.j,  1.+0.j],\n",
-       "         [ 0.-0.j,  0.+0.j]]],\n",
-       "\n",
-       "\n",
-       "       [[[ 0.+0.j,  0.+0.j],\n",
-       "         [ 1.-0.j, -0.+0.j]],\n",
-       "\n",
-       "        [[ 0.+0.j,  0.+0.j],\n",
-       "         [ 0.+0.j,  1.+0.j]]]])"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "teleportation.eval(DiscopyBackend()).tensor.array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "id": "a1feb431",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from cotengra import HyperCompressedOptimizer\n",
-    "optimiser = HyperCompressedOptimizer(\n",
-    "    chi=1\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "id": "5139ef70",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "array([[[[0.06248093+0.j, 0.06248093-0.j],\n",
-       "         [0.06248093+0.j, 0.06248093+0.j]],\n",
-       "\n",
-       "        [[0.06248093+0.j, 0.06248093-0.j],\n",
-       "         [0.06248093+0.j, 0.06248093+0.j]]],\n",
-       "\n",
-       "\n",
-       "       [[[0.06248093+0.j, 0.06248093-0.j],\n",
-       "         [0.06248093+0.j, 0.06248093+0.j]],\n",
-       "\n",
-       "        [[0.06248093+0.j, 0.06248093-0.j],\n",
-       "         [0.06248093+0.j, 0.06248093+0.j]]]])"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "teleportation.eval(QuimbBackend(optimiser)).tensor.array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "id": "6113a332",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "optimiser = HyperCompressedOptimizer(\n",
-    "    chi=2\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "id": "f24413ca",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[[[1.-0.j, 0.-0.j],\n",
-       "         [0.+0.j, 0.-0.j]],\n",
-       "\n",
-       "        [[0.+0.j, 1.+0.j],\n",
-       "         [0.+0.j, 0.+0.j]]],\n",
-       "\n",
-       "\n",
-       "       [[[0.-0.j, 0.-0.j],\n",
-       "         [1.-0.j, 0.-0.j]],\n",
-       "\n",
-       "        [[0.+0.j, 0.+0.j],\n",
-       "         [0.-0.j, 1.-0.j]]]])"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "teleportation.eval(QuimbBackend(optimiser)).tensor.array"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "a727d58e",
-   "metadata": {},
-   "source": [
-    "## Interfacing with external libraries"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "5086ad32",
-   "metadata": {},
-   "source": [
-    "### Graphix graphs"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "id": "eaaced50",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import graphix\n",
-    "from optyx import qubits\n",
-    "\n",
-    "circuit = graphix.Circuit(2)\n",
-    "circuit.rz(0, 0.5)\n",
-    "circuit.rz(1, 0.5)\n",
-    "circuit.cnot(0, 1)\n",
-    "circuit.s(0)\n",
-    "circuit.cnot(1, 0)\n",
-    "\n",
-    "pattern = circuit.transpile().pattern\n",
-    "\n",
-    "# open graph zx diagram\n",
-    "optyx_zx = qubits.Circuit(pattern)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "id": "d921eb1a",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The pattern is not consistent with flow or gflow structure.\n"
-     ]
-    },
-    {
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-       "L 172 3500 \n",
-       "L 594 3500 \n",
-       "L 594 4494 \n",
-       "L 1172 4494 \n",
-       "z\n",
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-       "<Figure size 800x800 with 1 Axes>"
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-    "optyx_zx.foliation().draw(figsize=(8, 8))"
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-  {
-   "cell_type": "markdown",
-   "id": "4870dd44",
-   "metadata": {},
-   "source": [
-    "### Perceval circuits and processors"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "id": "3f1613ed",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import perceval as pcvl\n",
-    "from optyx import Channel"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "id": "1f07af00",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<perceval.components.processor.Processor at 0x75cce0301400>"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "p = pcvl.Processor(\"SLOS\", 6)\n",
-    "p.add(0, pcvl.catalog[\"postprocessed cnot\"].build_processor())\n",
-    "\n",
-    "p.add(0, pcvl.BS.H())\n",
-    "p.add(0, pcvl.Detector.pnr())\n",
-    "p.add(1, pcvl.Detector.pnr())\n",
-    "p.add(2, pcvl.Detector.pnr())\n",
-    "p.add(3, pcvl.Detector.pnr())\n",
-    "\n",
-    "ff_X = pcvl.FFCircuitProvider(\n",
-    "  2, 0, pcvl.Circuit(2)\n",
-    ")\n",
-    "ff_X.add_configuration(\n",
-    "  [0, 1], pcvl.PERM([1, 0])\n",
-    ")\n",
-    "p.add(2, ff_X)\n",
-    "\n",
-    "phi = pcvl.P(\"phi\")\n",
-    "ff_Z = pcvl.FFConfigurator(\n",
-    "  2, 3,\n",
-    "  pcvl.PS(phi),\n",
-    "  {\"phi\": 0}\n",
-    ").add_configuration(\n",
-    "  [0, 1],\n",
-    "  {\"phi\": np.pi}\n",
-    ")\n",
-    "p.add(0, ff_Z)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "id": "3b4867c9",
-   "metadata": {},
-   "outputs": [
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-       "<path d=\"M25,225 L28,225 L72,325 L75,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M28,275 L72,375\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M25,275 L28,275 L72,375 L75,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M77,2 L473,2 L473,298 L77,298 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"79\" y=\"305\" font-size=\"8\" text-anchor=\"start\">POSTPROCESSED CNOT</text>\n",
-       "<path d=\"M25,125 L53,125 L72,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M78,144 L97,125 L125,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M25,175 L53,175 L72,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M78,156 L97,175 L125,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M50,143 L100,143 L100,157 L50,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"75\" y=\"185\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<text x=\"75\" y=\"126\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<path d=\"M50,143 L100,143 L100,147 L50,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M93,150 L103,150 L103,160 L93,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"98\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
-       "<path d=\"M25,75.0 L125,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M128,75 L172,175\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M125,75 L128,75 L172,175 L175,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M128,125 L172,125\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M125,125 L128,125 L172,125 L175,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M128,175 L172,225\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M125,175 L128,175 L172,225 L175,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M25,25.0 L175,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M175,25 L203,25 L222,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M228,44 L247,25 L275,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M175,75 L203,75 L222,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M228,56 L247,75 L275,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M200,43 L250,43 L250,57 L200,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"225\" y=\"80\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<text x=\"225\" y=\"26\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
-       "<path d=\"M200,43 L250,43 L250,47 L200,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M243,50 L253,50 L253,60 L243,60 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"248\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
-       "<path d=\"M175,125 L203,125 L222,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M228,144 L247,125 L275,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M175,175 L203,175 L222,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M228,156 L247,175 L275,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M200,143 L250,143 L250,157 L200,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"225\" y=\"180\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<text x=\"225\" y=\"126\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
-       "<path d=\"M200,143 L250,143 L250,147 L200,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M243,150 L253,150 L253,160 L243,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"248\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
-       "<path d=\"M175,225 L203,225 L222,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M228,244 L247,225 L275,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M175,275 L203,275 L222,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M228,256 L247,275 L275,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M200,243 L250,243 L250,257 L200,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"225\" y=\"280\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<text x=\"225\" y=\"226\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
-       "<path d=\"M200,243 L250,243 L250,247 L200,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M243,250 L253,250 L253,260 L243,260 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"248\" y=\"257\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
-       "<path d=\"M278,125 L322,125\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M275,125 L278,125 L322,125 L325,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M278,175 L322,75\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M275,175 L278,175 L322,75 L325,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M278,225 L322,175\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M275,225 L278,225 L322,175 L325,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M325,125 L353,125 L372,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M378,144 L397,125 L425,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M325,175 L353,175 L372,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M378,156 L397,175 L425,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M350,143 L400,143 L400,157 L350,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"375\" y=\"185\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<text x=\"375\" y=\"126\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<path d=\"M350,143 L400,143 L400,147 L350,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M393,150 L403,150 L403,160 L393,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"398\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
-       "<path d=\"M275,25.0 L425,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M325,75.0 L425,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M75,325.0 L425,325.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M75,375.0 L425,375.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M428,325 L472,225\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M425,325 L428,325 L472,225 L475,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M428,375 L472,275\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M425,375 L428,375 L472,275 L475,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M425,25 L453,25 L472,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M478,44 L497,25 L525,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M425,75 L453,75 L472,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M478,56 L497,75 L525,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M450,43 L500,43 L500,57 L450,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"475\" y=\"85\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<text x=\"475\" y=\"26\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<path d=\"M450,43 L500,43 L500,47 L450,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M493,50 L503,50 L503,60 L493,60 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"498\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
-       "<path d=\"M425,125.0 L525,125.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M425,175.0 L525,175.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M475,225.0 L525,225.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M475,275.0 L525,275.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M525,25 L575,25\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M525,75 L575,75\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M549,10 L551,10 L551,90 L549,90 Z\" stroke=\"dimgrey\" fill=\"dimgrey\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M525,225 L575,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M525,275 L575,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M549,210 L551,210 L551,290 L549,290 Z\" stroke=\"dimgrey\" fill=\"dimgrey\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M525,125 L550,125\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M550,125 L575,125\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M545,135 L537,135 L537,115 L545,115 C545,115,555,115,555,125 C555,135,545,135,545,135 L545,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
-       "<text x=\"537\" y=\"112\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
-       "<path d=\"M525,175 L550,175\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M550,175 L575,175\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M545,185 L537,185 L537,165 L545,165 C545,165,555,165,555,175 C555,185,545,185,545,185 L545,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
-       "<text x=\"537\" y=\"162\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
-       "<path d=\"M575,125 L675,125\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M575,175 L675,175\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M625,190.0 L625,205.0\" stroke=\"white\" stroke-width=\"5\" fill=\"none\" />\n",
-       "<path d=\"M625,190.0 L625,205.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" stroke-dasharray=\"4,4\" />\n",
-       "<path d=\"M625,198.0 L622,195.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M625,198.0 L628,195.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M580,110 L670,110 L670,190 L580,190 Z\" stroke=\"black\" fill=\"lightgreen\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"625\" y=\"155.0\" font-size=\"10\" text-anchor=\"middle\">FFC</text>\n",
-       "<path d=\"M575,225 L675,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M575,275 L675,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M580,205 L670,205 L670,295 L580,295 Z\" stroke=\"black\" fill=\"lightyellow\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"625\" y=\"250\" font-size=\"10\" text-anchor=\"middle\">U(FFC)</text>\n",
-       "<path d=\"M575,25.0 L675,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M575,75.0 L675,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M675,125 L725,125\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M675,175 L725,175\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M675,225 L725,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M675,275 L725,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M699,110 L701,110 L701,290 L699,290 Z\" stroke=\"dimgrey\" fill=\"dimgrey\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M675,25.0 L725,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M675,75.0 L725,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M725,25 L750,25\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M750,25 L775,25\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M745,35 L737,35 L737,15 L745,15 C745,15,755,15,755,25 C755,35,745,35,745,35 L745,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
-       "<text x=\"737\" y=\"12\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
-       "<path d=\"M725,75 L750,75\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M750,75 L775,75\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M745,85 L737,85 L737,65 L745,65 C745,65,755,65,755,75 C755,85,745,85,745,85 L745,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
-       "<text x=\"737\" y=\"62\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
-       "<path d=\"M775,25 L825,25\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M775,75 L825,75\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M800,90.0 L800,255.0\" stroke=\"white\" stroke-width=\"5\" fill=\"none\" />\n",
-       "<path d=\"M800,90.0 L800,255.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" stroke-dasharray=\"4,4\" />\n",
-       "<path d=\"M800,98.0 L797,95.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M800,98.0 L803,95.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M780,10 L820,10 L820,90 L780,90 Z\" stroke=\"black\" fill=\"lightgreen\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"800\" y=\"55.0\" font-size=\"10\" text-anchor=\"middle\">FFC</text>\n",
-       "<path d=\"M725,275 L775,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M730,290 L739,290 L753,260 L744,260 L730,290 L739,290 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"747\" y=\"288\" font-size=\"7\" text-anchor=\"start\">Φ=phi</text>\n",
-       "<path d=\"M725,125.0 L825,125.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M725,175.0 L825,175.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M725,225.0 L825,225.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M775,275.0 L825,275.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M825,25.0 L840,25.0\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M825,75.0 L840,75.0\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M825,125.0 L840,125.0\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M825,175.0 L840,175.0\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M825,225.0 L840,225.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M825,275.0 L840,275.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M157,75 C157,75,157,65,167,65 L175,65 L175,85 L167,85 C157,85,157,75,157,75 L157,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n",
-       "<text x=\"163\" y=\"91\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\">[herald0]</text>\n",
-       "<text x=\"167\" y=\"78\" font-size=\"7\" text-anchor=\"middle\">0</text>\n",
-       "<path d=\"M157,275 C157,275,157,265,167,265 L175,265 L175,285 L167,285 C157,285,157,275,157,275 L157,275\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n",
-       "<text x=\"163\" y=\"291\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\">[herald1]</text>\n",
-       "<text x=\"167\" y=\"278\" font-size=\"7\" text-anchor=\"middle\">0</text>\n",
-       "<path d=\"M-2,15 L10,15 L10,85 L-2,85 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"-2\" y=\"91\" font-size=\"6\" text-anchor=\"start\" font-style=\"italic\">[ctrl]</text>\n",
-       "<path d=\"M-2,115 L10,115 L10,185 L-2,185 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"-2\" y=\"191\" font-size=\"6\" text-anchor=\"start\" font-style=\"italic\">[data]</text>\n",
-       "<path d=\"M840,15 L852,15 L852,85 L840,85 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"852\" y=\"91\" font-size=\"6\" text-anchor=\"end\" font-style=\"italic\">[ctrl]</text>\n",
-       "<path d=\"M840,115 L852,115 L852,185 L840,185 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"852\" y=\"191\" font-size=\"6\" text-anchor=\"end\" font-style=\"italic\">[data]</text>\n",
-       "<path d=\"M283,85 L275,85 L275,65 L283,65 C283,65,293,65,293,75 C293,85,283,85,283,85 L283,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n",
-       "<text x=\"288\" y=\"61\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\">[herald0]</text>\n",
-       "<text x=\"283\" y=\"78\" font-size=\"7\" text-anchor=\"middle\">0</text>\n",
-       "<path d=\"M283,285 L275,285 L275,265 L283,265 C283,265,293,265,293,275 C293,285,283,285,283,285 L283,285\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n",
-       "<text x=\"288\" y=\"261\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\">[herald1]</text>\n",
-       "<text x=\"283\" y=\"278\" font-size=\"7\" text-anchor=\"middle\">0</text>\n",
-       "<text x=\"850\" y=\"28.0\" font-size=\"9\" text-anchor=\"end\">0</text>\n",
-       "<text x=\"850\" y=\"78.0\" font-size=\"9\" text-anchor=\"end\">1</text>\n",
-       "<text x=\"850\" y=\"128.0\" font-size=\"9\" text-anchor=\"end\">2</text>\n",
-       "<text x=\"850\" y=\"178.0\" font-size=\"9\" text-anchor=\"end\">3</text>\n",
-       "<text x=\"850\" y=\"228.0\" font-size=\"9\" text-anchor=\"end\">4</text>\n",
-       "<text x=\"850\" y=\"278.0\" font-size=\"9\" text-anchor=\"end\">5</text>\n",
-       "<text x=\"0\" y=\"28.0\" font-size=\"9\" text-anchor=\"start\">0</text>\n",
-       "<text x=\"0\" y=\"78.0\" font-size=\"9\" text-anchor=\"start\">1</text>\n",
-       "<text x=\"0\" y=\"128.0\" font-size=\"9\" text-anchor=\"start\">2</text>\n",
-       "<text x=\"0\" y=\"178.0\" font-size=\"9\" text-anchor=\"start\">3</text>\n",
-       "<text x=\"0\" y=\"228.0\" font-size=\"9\" text-anchor=\"start\">4</text>\n",
-       "<text x=\"0\" y=\"278.0\" font-size=\"9\" text-anchor=\"start\">5</text>\n",
-       "</svg>"
-      ],
-      "text/plain": [
-       "<drawsvg.drawing.Drawing at 0x75cce11cc650>"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "pcvl.pdisplay(p, recursive=True)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "id": "22342f65",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# convert to Optyx\n",
-    "optyx_diagram = Channel.from_perceval(p)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "id": "8b7699cf",
-   "metadata": {},
-   "outputs": [
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-   "source": [
-    "optyx_diagram.foliation().draw(figsize=(8, 25))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "id": "af82f2ef",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "to_transmit = ((0.7071067811865476+0j)*pcvl.BasicState([1, 0]) +\n",
-    "               (-0.21850801222441052+0.6724985119639574j)*pcvl.BasicState([0, 1]))\n",
-    "to_transmit.normalize()\n",
-    "\n",
-    "sg = pcvl.StateGenerator(pcvl.Encoding.DUAL_RAIL)\n",
-    "bell_state = sg.bell_state(\"phi+\")\n",
-    "\n",
-    "input_state = to_transmit * bell_state\n",
-    "p.min_detected_photons_filter(2)\n",
-    "\n",
-    "input_state *= pcvl.BasicState([0, 0])\n",
-    "\n",
-    "p.with_input(input_state)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "id": "4cc23c53",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "result_perceval = p.probs()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "id": "d9bc5f3b",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.qubits import Scalar\n",
-    "from optyx.photonic import DualRail\n",
-    "\n",
-    "bell_state = Z(0, 2) @ Scalar(0.5**0.5)\n",
-    "transmit = Ket(\"+\") >> Z(1, 1, 0.3)\n",
-    "\n",
-    "protocol = (\n",
-    "    transmit @ bell_state >>\n",
-    "    DualRail(3) >>\n",
-    "    Channel.from_perceval(p)\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "id": "ad7fe8c0",
-   "metadata": {},
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-   "source": [
-    "result_optyx = protocol.eval().prob_dist()"
-   ]
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-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "id": "e787f65b",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def check_dict_agreement(d1, d2, rtol=1e-5, atol=1e-8):\n",
-    "    for key in d1.keys() - d2.keys():\n",
-    "        assert np.isclose(d1[key], 0, rtol=rtol, atol=atol)\n",
-    "    for key in d2.keys() - d1.keys():\n",
-    "        assert np.isclose(d2[key], 0, rtol=rtol, atol=atol)\n",
-    "    for key in d1.keys() & d2.keys():\n",
-    "        assert np.isclose(d1[key], d2[key], rtol=rtol, atol=atol)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "id": "e433baf1",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "check_dict_agreement(\n",
-    "    {tuple(k): v for k, v in dict(result_perceval[\"results\"]).items()},\n",
-    "    result_optyx\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "36241fe2",
-   "metadata": {},
-   "source": [
-    "## Fusion teleportation"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "5721aeab",
-   "metadata": {},
-   "source": [
-    "Graphically, the fusion measurement we would like to use, takes the following form:\n",
-    "\n",
-    "![Fusion II](./fusion_ii.png \"Fusion measurement implementing a Bell measurement in dual rail encoding\")\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1ab1655b",
-   "metadata": {},
-   "source": [
-    "where $\\underline{a}, \\underline{b}, \\underline{c}, \\underline{d}$ are the measurement outcomes as the measured photon numbers. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "id": "5b0a58bb",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx import qmode\n",
-    "\n",
-    "from optyx.photonic import (\n",
-    "    DualRail,\n",
-    "    Swap,\n",
-    "    HadamardBS\n",
-    ")\n",
-    "\n",
-    "fusion = (\n",
-    "    HadamardBS() @ HadamardBS() >>\n",
-    "    qmode @ Swap(1, 1) @ qmode >>\n",
-    "    qmode @ HadamardBS() @ qmode >>\n",
-    "    Swap(1, 1) @ qmode @ qmode >>\n",
-    "    qmode @ Swap(1, 1) @ qmode >>\n",
-    "    qmode @ qmode @ HadamardBS()\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "id": "f7998428",
-   "metadata": {},
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-    "As we are dealing with dual-rail encoding, we will restrict ourselves to the outcome results where the total measured number of photons is 4. We have that $\\underline{s} = \\underline{a} \\oplus \\underline{b}$ is the Boolean value of success (whether an entangling operation succeeded) and $\\underline{k} = \\underline{s} (\\underline{b} + \\underline{d}) + \\neg \\underline s (1 - \\frac{\\underline{a} + \\underline{b}}{2})$ is the Pauli error.\n",
-    "This means that the error is $\\underline{b} + \\underline{d}$ in case of success and $1 - \\frac{\\underline{a} + \\underline{b}}{2}$ in case of failure.\n",
-    "\n",
-    "We interpret this diagram as a CP-map which means that the sums represent classical mixing and not quantum superposition. We obtain different protocols conditioned on the value of $\\underline{s}$ and $\\underline{k}$.\n",
-    "\n",
-    "In our analysis we will ignore the case when the fusion fails."
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-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "id": "0ce269cb",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.classical import (\n",
-    "    ClassicalFunction\n",
-    ")\n",
-    "\n",
-    "from optyx import mode, bit\n",
-    "\n",
-    "def fusion_function(x):\n",
-    "    \"\"\"\n",
-    "    A classical function that returns two bits based on an input x,\n",
-    "    based on the classical logical for the Fusion type II circuit.\n",
-    "    \"\"\"\n",
-    "    a = x[0]\n",
-    "    b = x[1]\n",
-    "    c = x[2]\n",
-    "    d = x[3]\n",
-    "    s = (a % 2) ^ (b % 2)\n",
-    "    k = int(s*(b + d) + (1-s)*(1 - (a + b)/2))%2\n",
-    "    return [s, k]\n",
-    "\n",
-    "classical_function = ClassicalFunction(\n",
-    "    fusion_function,\n",
-    "    mode**4,\n",
-    "    bit**2\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "id": "a1764edb",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.classical import PostselectBit\n",
-    "\n",
-    "fusion_failure_processing = PostselectBit(1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "id": "08e9fc37",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.photonic import Phase\n",
-    "from optyx.classical import BitControlledGate\n",
-    "\n",
-    "# apply the box if the control bit is 1, otherwise apply an identity channel\n",
-    "correction = BitControlledGate(\n",
-    "    HadamardBS() >>\n",
-    "    (Phase(0.5) @ qmode) >>\n",
-    "    HadamardBS()\n",
-    ")"
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-   "execution_count": 54,
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-  {
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-   "execution_count": 55,
-   "id": "c557c4b8",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.qubits import Z\n",
-    "from optyx.photonic import Scalar\n",
-    "\n",
-    "channel_bell = (\n",
-    "    Z(0, 2) @ Scalar(0.5**0.5) >> DualRail(1) @ DualRail(1)\n",
-    ")\n",
-    "\n",
-    "dual_rail_input = DualRail(1)"
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-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "id": "4b5ee771",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.photonic import NumberResolvingMeasurement\n",
-    "\n",
-    "teleportation = (\n",
-    "    dual_rail_input @ channel_bell >>\n",
-    "    fusion @ qmode**2 >>\n",
-    "    NumberResolvingMeasurement(4) @ qmode**2 >>\n",
-    "    classical_function @ qmode**2 >>\n",
-    "    fusion_failure_processing @ correction >>\n",
-    "    DualRail(1).dagger()\n",
-    ")"
-   ]
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-  {
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-   "execution_count": 58,
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-   "source": [
-    "teleportation.foliation().draw(figsize=(8, 8))"
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-  {
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-   "execution_count": 59,
-   "id": "c8c49c91",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "array_teleportation = teleportation.eval().tensor.array"
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-   "execution_count": 60,
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-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.photonic import Id\n",
-    "\n",
-    "array_id = (\n",
-    "    Id(1) @ Scalar(0.5**0.5)\n",
-    ").double().to_tensor().eval().array"
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-  {
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-   "execution_count": 61,
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-   "source": [
-    "import numpy as np\n",
-    "\n",
-    "np.allclose(array_teleportation, array_id)"
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-   "id": "07c143a0",
-   "metadata": {},
-   "source": [
-    "### Fusion with distinguishable photons"
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-   "execution_count": 62,
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        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p76bd758808\">\n",
-       "   <rect x=\"7.2\" y=\"7.2\" width=\"432\" height=\"432\"/>\n",
+       "  <clipPath id=\"p98c73b8fc3\">\n",
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        " </defs>\n",
        "</svg>\n"
       ],
       "text/plain": [
-       "<Figure size 600x600 with 1 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
      "metadata": {},
@@ -17993,8 +5952,47 @@
     }
    ],
    "source": [
-    "fusion_channel = fusion >> NumberResolvingMeasurement(4) >> classical_function\n",
-    "fusion_channel.draw(figsize=(6, 6))"
+    "\n",
+    "ps = np.linspace(0, 1, 20)\n",
+    "errors_with_loss = []\n",
+    "for p in ps:\n",
+    "    errors_with_loss.append(\n",
+    "        average_fidelity(\n",
+    "            fusion_teleportation_with_photon_loss(p).eval().tensor.array,\n",
+    "            array_teleportation,\n",
+    "            d=2\n",
+    "        )\n",
+    "    )\n",
+    "\n",
+    "plt.plot(ps, errors_with_loss, marker='o')\n",
+    "plt.grid()\n",
+    "plt.xlabel('Photon Survival Probability (p)')\n",
+    "plt.ylabel('Average Gate Fidelity')\n",
+    "plt.title('Fusion-based Teleportation Fidelity vs Photon Survival Probability (p)')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "07c143a0",
+   "metadata": {},
+   "source": [
+    "## Distributed entanglement generation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e20c30a8",
+   "metadata": {},
+   "source": [
+    "### Fusion and photon distinguishability"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "18ab5a86",
+   "metadata": {},
+   "source": [
+    "#### Define the protocol"
    ]
   },
   {
@@ -18014,14 +6012,13 @@
    "source": [
     "internal_state_1 = [1, 0]\n",
     "internal_state_2 = [0, 1]\n",
-    "internal_state_2 = internal_state_2 / np.linalg.norm(internal_state_2)\n",
     "\n",
     "print(internal_state_1, internal_state_2)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 70,
+   "execution_count": 24,
    "id": "bdb9611d",
    "metadata": {},
    "outputs": [
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+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from optyx.qubits import Z, Scalar, Id, Measure\n",
+    "from optyx.photonic import DualRail\n",
+    "from optyx.classical import PostselectBit\n",
+    "from discopy.drawing import Equation\n",
+    "\n",
+    "bell_state = Z(0, 2) @ Scalar(0.5 ** 0.5)\n",
+    "dual_rail_encoding = lambda state: DualRail(1, internal_states=[state])\n",
+    "encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(internal_state_2)\n",
+    "\n",
+    "post_select = PostselectBit(1) @ PostselectBit(0)\n",
+    "\n",
+    "protocol = (\n",
+    "    bell_state @ bell_state >>\n",
+    "    Id(1) @ (encoding_layer >> FusionTypeII() >> post_select) @ Id(1)\n",
+    ")\n",
+    "measure = Measure(2)\n",
+    "\n",
+    "Equation(protocol >> measure, bell_state >> measure).draw(figsize=(8, 8))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eb9f34b3",
+   "metadata": {},
+   "source": [
+    "#### Define a set of internal states with varying degrees of distinguishability"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "9e5c4078",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import math\n",
+    "\n",
+    "def rotated_unit_vectors(n: int = 10):\n",
+    "    for i in range(n):\n",
+    "        theta = i * (math.pi / 2) / (n - 1)\n",
+    "        yield (math.cos(theta), math.sin(theta))\n",
+    "\n",
+    "unit_vectors = list(rotated_unit_vectors(15))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "945ace07",
+   "metadata": {},
+   "source": [
+    "#### Run the experiments"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "30b96ad0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.qubits import Discard\n",
+    "\n",
+    "inner_product_states = []\n",
+    "inner_product_bell_states = []\n",
+    "\n",
+    "result_bell = bell_state.eval().tensor.array.flatten()\n",
+    "result_bell = result_bell / np.linalg.norm(result_bell)\n",
+    "\n",
+    "for vector in unit_vectors:\n",
+    "    encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(vector)\n",
+    "    experiment = bell_state @ bell_state >> Id(1) @ (encoding_layer >> FusionTypeII()\n",
+    "                                                                                >> post_select) @ Id(1)\n",
+    "\n",
+    "    f = (experiment >> bell_state.dagger()).inflate(2).eval().tensor.array\n",
+    "    normalisation = (experiment >> Discard(2)).inflate(2).eval().tensor.array\n",
+    "\n",
+    "    inner_product_states.append(np.inner(vector, internal_state_1))\n",
+    "    inner_product_bell_states.append(f/normalisation)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "1c50f388",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part\n",
+      "  return math.isfinite(val)\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part\n",
+      "  return np.asarray(x, float)\n"
+     ]
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-   "source": [
-    "from optyx.qubits import Z, Scalar, Id, Measure\n",
-    "from optyx.photonic import DualRail\n",
-    "from optyx.classical import PostselectBit\n",
-    "from discopy.drawing import Equation\n",
-    "\n",
-    "bell_state = Z(0, 2) @ Scalar(0.5 ** 0.5)\n",
-    "dual_rail_encoding = lambda state: DualRail(1, internal_states=[state])\n",
-    "encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(internal_state_2)\n",
-    "post_select = PostselectBit(1) @ PostselectBit(0)\n",
-    "experiment = bell_state @ bell_state >> Id(1) @ (encoding_layer >> fusion_channel >> post_select) @ Id(1)\n",
-    "measure = Measure(2)\n",
-    "Equation(experiment >> measure, bell_state >> measure).draw(figsize=(8, 8))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 75,
-   "id": "2fbb6c45",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.qubits import Discard"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 76,
-   "id": "14a649ed",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "fidelity = (experiment >> bell_state.dagger())"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 77,
-   "id": "aa3042f9",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "normalisation = (experiment >> Discard(2)).inflate(2).eval().tensor.array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 78,
-   "id": "c83b686e",
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-       "(0.5000000000000001-3.061616997868383e-17j)"
+       "<Figure size 600x400 with 1 Axes>"
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      },
-     "execution_count": 78,
      "metadata": {},
-     "output_type": "execute_result"
+     "output_type": "display_data"
     }
    ],
    "source": [
-    "f = fidelity.inflate(2).eval().tensor.array\n",
-    "f/normalisation"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 79,
-   "id": "9e5c4078",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import math\n",
-    "\n",
-    "def rotated_unit_vectors(n: int = 10):\n",
-    "    for i in range(n):\n",
-    "        theta = i * (math.pi / 2) / (n - 1)\n",
-    "        yield (math.cos(theta), math.sin(theta))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 80,
-   "id": "83a32908",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "unit_vectors = list(rotated_unit_vectors(30))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 81,
-   "id": "30b96ad0",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "inner_product_states = []\n",
-    "inner_product_bell_states = []\n",
-    "\n",
-    "result_bell = bell_state.eval().tensor.array.flatten()\n",
-    "result_bell = result_bell / np.linalg.norm(result_bell)\n",
-    "\n",
-    "for vector in unit_vectors:\n",
-    "    encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(vector)\n",
-    "    experiment = bell_state @ bell_state >> Id(1) @ (encoding_layer >> fusion_channel\n",
-    "                                                                                >> post_select) @ Id(1)\n",
-    "\n",
-    "    f = (experiment >> bell_state.dagger()).inflate(2).eval().tensor.array\n",
-    "    normalisation = (experiment >> Discard(2)).inflate(2).eval().tensor.array\n",
+    "import matplotlib.pyplot as plt\n",
     "\n",
-    "    inner_product_states.append(np.inner(vector, internal_state_1))\n",
-    "    inner_product_bell_states.append(f/normalisation)"
+    "plt.figure(figsize=(6, 4))\n",
+    "plt.plot(inner_product_states, inner_product_bell_states, marker='o')\n",
+    "plt.xlabel('<Internal state 1 | Internal state 2>')\n",
+    "plt.ylabel('<Result | Bell State> (fidelity)')\n",
+    "plt.title('Fidelity of the resulting state with the perfect Bell state')\n",
+    "plt.grid(True)\n",
+    "plt.show()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 82,
-   "id": "1c50f388",
+   "execution_count": 28,
+   "id": "06b9a545",
    "metadata": {},
    "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part\n",
-      "  return math.isfinite(val)\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part\n",
-      "  return np.asarray(x, float)\n"
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     "plt.xlabel('<Internal state 1 | Internal state 2>')\n",
     "plt.ylabel('<Result | Bell State> (fidelity)')\n",
     "plt.title('Fidelity of the resulting state with the perfect Bell state')\n",
+    "plt.xlim(0.9, 1)\n",
+    "plt.ylim(0.9, 1)\n",
     "plt.grid(True)\n",
     "plt.show()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "7aa6a1d2",
+   "metadata": {},
+   "source": [
+    "## Interfacing with external libraries"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e4b64d36",
+   "metadata": {},
+   "source": [
+    "### Graphix"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 83,
-   "id": "06b9a545",
+   "execution_count": 65,
+   "id": "79f358ae",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import graphix\n",
+    "from optyx import qubits\n",
+    "\n",
+    "circuit = graphix.Circuit(2)\n",
+    "circuit.cnot(0, 1)\n",
+    "\n",
+    "pattern = circuit.transpile().pattern"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 66,
+   "id": "4888034c",
    "metadata": {},
    "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The pattern is not consistent with flow or gflow structure.\n"
+     ]
+    },
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        "   </g>\n",
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"pcd8cb14f14\">\n",
-       "   <rect x=\"50.465625\" y=\"22.318125\" width=\"334.8\" height=\"221.76\"/>\n",
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        " </defs>\n",
        "</svg>\n"
       ],
       "text/plain": [
-       "<Figure size 600x400 with 1 Axes>"
+       "<Figure size 620x200 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "pattern.draw_graph()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 67,
+   "id": "bff50dee",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "simulator = graphix.simulator.PatternSimulator(pattern, backend=\"statevector\")\n",
+    "graphix_result = simulator.run().psi.conj()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 68,
+   "id": "bf2d9106",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "optyx_zx = qubits.Circuit(pattern)\n",
+    "\n",
+    "optyx_res = (\n",
+    "    qubits.Ket(\"+\")**2 >> optyx_zx\n",
+    ").eval().amplitudes()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 69,
+   "id": "908e477d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "for keys in optyx_res.keys():\n",
+    "    assert np.isclose(optyx_res[keys], graphix_result[keys], atol=1e-6)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "598ab8dc",
+   "metadata": {},
+   "source": [
+    "### Perceval circuits and processors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 70,
+   "id": "07f5f7ba",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import perceval as pcvl"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7d106d80",
+   "metadata": {},
+   "source": [
+    "#### Define the protocol in Perceval"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 71,
+   "id": "988c9618",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/svg+xml": [
+       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
+       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
+       "     width=\"1175.0\" height=\"531.25\" viewBox=\"-45.0 0 940.0 425.0\">\n",
+       "<defs>\n",
+       "</defs>\n",
+       "<path d=\"M10,25.0 L25,25.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
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+       "<path d=\"M25,225 L28,225 L72,325 L75,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
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+       "<path d=\"M25,275 L28,275 L72,375 L75,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
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+       "<text x=\"79\" y=\"305\" font-size=\"8\" text-anchor=\"start\">POSTPROCESSED CNOT</text>\n",
+       "<path d=\"M25,125 L53,125 L72,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M78,144 L97,125 L125,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M25,175 L53,175 L72,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M78,156 L97,175 L125,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M50,143 L100,143 L100,157 L50,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"75\" y=\"185\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"75\" y=\"126\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<path d=\"M50,143 L100,143 L100,147 L50,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M93,150 L103,150 L103,160 L93,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"98\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M25,75.0 L125,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M128,75 L172,175\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M125,75 L128,75 L172,175 L175,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M128,125 L172,125\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M125,125 L128,125 L172,125 L175,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M128,175 L172,225\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M125,175 L128,175 L172,225 L175,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M25,25.0 L175,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M175,25 L203,25 L222,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,44 L247,25 L275,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M175,75 L203,75 L222,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,56 L247,75 L275,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M200,43 L250,43 L250,57 L200,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"225\" y=\"80\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"225\" y=\"26\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
+       "<path d=\"M200,43 L250,43 L250,47 L200,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M243,50 L253,50 L253,60 L243,60 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"248\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M175,125 L203,125 L222,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,144 L247,125 L275,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M175,175 L203,175 L222,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,156 L247,175 L275,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M200,143 L250,143 L250,157 L200,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"225\" y=\"180\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"225\" y=\"126\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
+       "<path d=\"M200,143 L250,143 L250,147 L200,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M243,150 L253,150 L253,160 L243,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"248\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M175,225 L203,225 L222,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,244 L247,225 L275,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M175,275 L203,275 L222,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,256 L247,275 L275,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M200,243 L250,243 L250,257 L200,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"225\" y=\"280\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"225\" y=\"226\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
+       "<path d=\"M200,243 L250,243 L250,247 L200,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M243,250 L253,250 L253,260 L243,260 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"248\" y=\"257\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M278,125 L322,125\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M275,125 L278,125 L322,125 L325,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M278,175 L322,75\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M275,175 L278,175 L322,75 L325,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M278,225 L322,175\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M275,225 L278,225 L322,175 L325,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M325,125 L353,125 L372,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M378,144 L397,125 L425,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M325,175 L353,175 L372,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M378,156 L397,175 L425,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M350,143 L400,143 L400,157 L350,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"375\" y=\"185\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"375\" y=\"126\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<path d=\"M350,143 L400,143 L400,147 L350,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M393,150 L403,150 L403,160 L393,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"398\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M275,25.0 L425,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M325,75.0 L425,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M75,325.0 L425,325.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M75,375.0 L425,375.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M428,325 L472,225\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M425,325 L428,325 L472,225 L475,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M428,375 L472,275\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M425,375 L428,375 L472,275 L475,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M425,25 L453,25 L472,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M478,44 L497,25 L525,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M425,75 L453,75 L472,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M478,56 L497,75 L525,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M450,43 L500,43 L500,57 L450,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"475\" y=\"85\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"475\" y=\"26\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<path d=\"M450,43 L500,43 L500,47 L450,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M493,50 L503,50 L503,60 L493,60 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"498\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M425,125.0 L525,125.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M425,175.0 L525,175.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M475,225.0 L525,225.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M475,275.0 L525,275.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M525,25 L575,25\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M525,75 L575,75\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M549,10 L551,10 L551,90 L549,90 Z\" stroke=\"dimgrey\" fill=\"dimgrey\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M525,225 L575,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M525,275 L575,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M549,210 L551,210 L551,290 L549,290 Z\" stroke=\"dimgrey\" fill=\"dimgrey\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M525,125 L550,125\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M550,125 L575,125\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M545,135 L537,135 L537,115 L545,115 C545,115,555,115,555,125 C555,135,545,135,545,135 L545,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
+       "<text x=\"537\" y=\"112\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
+       "<path d=\"M525,175 L550,175\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M550,175 L575,175\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M545,185 L537,185 L537,165 L545,165 C545,165,555,165,555,175 C555,185,545,185,545,185 L545,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
+       "<text x=\"537\" y=\"162\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
+       "<path d=\"M575,125 L675,125\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M575,175 L675,175\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M625,190.0 L625,205.0\" stroke=\"white\" stroke-width=\"5\" fill=\"none\" />\n",
+       "<path d=\"M625,190.0 L625,205.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" stroke-dasharray=\"4,4\" />\n",
+       "<path d=\"M625,198.0 L622,195.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M625,198.0 L628,195.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M580,110 L670,110 L670,190 L580,190 Z\" stroke=\"black\" fill=\"lightgreen\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"625\" y=\"155.0\" font-size=\"10\" text-anchor=\"middle\">FFC</text>\n",
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+       "<text x=\"800\" y=\"55.0\" font-size=\"10\" text-anchor=\"middle\">FFC</text>\n",
+       "<path d=\"M725,275 L775,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M730,290 L739,290 L753,260 L744,260 L730,290 L739,290 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"747\" y=\"288\" font-size=\"7\" text-anchor=\"start\">Φ=phi</text>\n",
+       "<path d=\"M725,125.0 L825,125.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M725,175.0 L825,175.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
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+       "<text x=\"163\" y=\"91\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\">[herald0]</text>\n",
+       "<text x=\"167\" y=\"78\" font-size=\"7\" text-anchor=\"middle\">0</text>\n",
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+       "<text x=\"-2\" y=\"91\" font-size=\"6\" text-anchor=\"start\" font-style=\"italic\">[ctrl]</text>\n",
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+       "</svg>"
+      ],
+      "text/plain": [
+       "<drawsvg.drawing.Drawing at 0x7f37cbefa1b0>"
       ]
      },
+     "execution_count": 71,
      "metadata": {},
-     "output_type": "display_data"
+     "output_type": "execute_result"
     }
    ],
    "source": [
-    "import matplotlib.pyplot as plt\n",
+    "p = pcvl.Processor(\"SLOS\", 6)\n",
+    "p.add(0, pcvl.catalog[\"postprocessed cnot\"].build_processor())\n",
     "\n",
-    "plt.figure(figsize=(6, 4))\n",
-    "plt.plot(inner_product_states, inner_product_bell_states, marker='o')\n",
-    "plt.xlabel('<Internal state 1 | Internal state 2>')\n",
-    "plt.ylabel('<Result | Bell State> (fidelity)')\n",
-    "plt.title('Fidelity of the resulting state with the perfect Bell state')\n",
-    "plt.xlim(0.9, 1)\n",
-    "plt.ylim(0.9, 1)\n",
-    "plt.grid(True)\n",
-    "plt.show()"
+    "p.add(0, pcvl.BS.H())\n",
+    "p.add(0, pcvl.Detector.pnr())\n",
+    "p.add(1, pcvl.Detector.pnr())\n",
+    "p.add(2, pcvl.Detector.pnr())\n",
+    "p.add(3, pcvl.Detector.pnr())\n",
+    "\n",
+    "ff_X = pcvl.FFCircuitProvider(\n",
+    "  2, 0, pcvl.Circuit(2)\n",
+    ")\n",
+    "ff_X.add_configuration(\n",
+    "  [0, 1], pcvl.PERM([1, 0])\n",
+    ")\n",
+    "p.add(2, ff_X)\n",
+    "\n",
+    "phi = pcvl.P(\"phi\")\n",
+    "ff_Z = pcvl.FFConfigurator(\n",
+    "  2, 3,\n",
+    "  pcvl.PS(phi),\n",
+    "  {\"phi\": 0}\n",
+    ").add_configuration(\n",
+    "  [0, 1],\n",
+    "  {\"phi\": np.pi}\n",
+    ")\n",
+    "p.add(0, ff_Z)\n",
+    "\n",
+    "pcvl.pdisplay(p, recursive=True)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "id": "2f2a52e7",
+   "execution_count": 96,
+   "id": "96d5bf6b",
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "from optyx.qubits import Ket\n",
+    "\n",
+    "state = Ket(\"+\") >> Z(1, 1, 0.3)\n",
+    "state_array = state.eval().tensor.array\n",
+    "state_array = state_array / np.linalg.norm(state_array)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f64e6adb",
+   "metadata": {},
+   "source": [
+    "#### Evaluate the protocol in Perceval"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 97,
+   "id": "bce649df",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "to_transmit = (complex(state_array[0])*pcvl.BasicState([1, 0]) +\n",
+    "               complex(state_array[1])*pcvl.BasicState([0, 1]))\n",
+    "\n",
+    "sg = pcvl.StateGenerator(pcvl.Encoding.DUAL_RAIL)\n",
+    "bell_state = sg.bell_state(\"phi+\")\n",
+    "\n",
+    "input_state = to_transmit * bell_state\n",
+    "p.min_detected_photons_filter(2)\n",
+    "\n",
+    "input_state *= pcvl.BasicState([0, 0])\n",
+    "\n",
+    "p.with_input(input_state)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 98,
+   "id": "f0c1fbf3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "result_perceval = p.probs()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ab098b6e",
+   "metadata": {},
+   "source": [
+    "#### Convert to Optyx and simulate"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 104,
+   "id": "463bcb6f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx import Channel\n",
+    "\n",
+    "optyx_diagram = Channel.from_perceval(p)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 105,
+   "id": "3f3fca2d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.qubits import Scalar, Ket\n",
+    "from optyx.photonic import DualRail\n",
+    "\n",
+    "bell_state = Z(0, 2) @ Scalar(0.5**0.5)\n",
+    "transmit = Ket(\"+\") >> Z(1, 1, 0.3)\n",
+    "\n",
+    "input_state = transmit @ bell_state\n",
+    "\n",
+    "protocol = (\n",
+    "    input_state >>\n",
+    "    DualRail(3) >>\n",
+    "    Channel.from_perceval(p)\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 106,
+   "id": "54633b7a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "result_optyx = protocol.eval().prob_dist()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 107,
+   "id": "e019251e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def check_dict_agreement(d1, d2, rtol=1e-5, atol=1e-8):\n",
+    "    for key in d1.keys() - d2.keys():\n",
+    "        assert np.isclose(d1[key], 0, rtol=rtol, atol=atol)\n",
+    "    for key in d2.keys() - d1.keys():\n",
+    "        assert np.isclose(d2[key], 0, rtol=rtol, atol=atol)\n",
+    "    for key in d1.keys() & d2.keys():\n",
+    "        assert np.isclose(d1[key], d2[key], rtol=rtol, atol=atol)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 108,
+   "id": "ca6102c5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "check_dict_agreement(\n",
+    "    {tuple(k): v for k, v in dict(result_perceval[\"results\"]).items()},\n",
+    "    result_optyx\n",
+    ")"
+   ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d316d264",
+   "id": "419dd1dd",
    "metadata": {},
    "outputs": [],
    "source": []

From 40c666168781bedde55193fb51f22e1a83858224 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Fri, 19 Sep 2025 11:35:29 +0100
Subject: [PATCH 15/59] function syntax and cup/caps for hypergraphs

---
 optyx/core/channel.py | 60 ++++++++++++++++++++++++++++++-------------
 optyx/utils/utils.py  | 12 +++------
 2 files changed, 46 insertions(+), 26 deletions(-)

diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index e839231e..eed7812d 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -118,7 +118,7 @@
 from optyx.utils.utils import explode_channel
 
 
-class Ob(symmetric.Ob):
+class Ob(frobenius.Ob):
     """Basic object: bit, mode, qubit or qmode"""
 
     _classical = {
@@ -156,7 +156,7 @@ def double(self):
 
 
 @factory
-class Ty(symmetric.Ty):
+class Ty(frobenius.Ty):
     """Classical and quantum types."""
 
     ob_factory = Ob
@@ -213,10 +213,10 @@ def inflate(self, d):
         assert isinstance(d, int), "Dimension must be an integer"
         assert d > 0, "Dimension must be positive"
 
-        dom = symmetric.Category(Ty, Diagram)
-        cod = symmetric.Category(Ty, Diagram)
+        dom = frobenius.Category(Ty, Diagram)
+        cod = frobenius.Category(Ty, Diagram)
 
-        return symmetric.Functor(
+        return frobenius.Functor(
             lambda x: x.inflate(d),
             lambda f: f.inflate(d),
             dom,
@@ -227,9 +227,9 @@ def double(self):
         """Returns the diagram.Diagram obtained by
         doubling every quantum dimension
         and building the completely positive map."""
-        dom = symmetric.Category(Ty, Diagram)
-        cod = symmetric.Category(diagram.Ty, diagram.Diagram)
-        return symmetric.Functor(
+        dom = frobenius.Category(Ty, Diagram)
+        cod = frobenius.Category(diagram.Ty, diagram.Diagram)
+        return frobenius.Functor(
             lambda x: x.double(), lambda f: f.double(), dom, cod
         )(self)
 
@@ -289,19 +289,19 @@ def to_path(self, dtype: type = complex):
 
         assert self.is_pure, "Diagram must be pure to convert to path."
 
-        return symmetric.Functor(
+        return frobenius.Functor(
             ob=len,
             ar=lambda f: f.get_kraus().to_path(dtype),
-            cod=symmetric.Category(int, path.Matrix[dtype]),
+            cod=frobenius.Category(int, path.Matrix[dtype]),
         )(self)
 
     def _decomp(self):
 
         # pylint: disable=protected-access
-        return symmetric.Functor(
+        return frobenius.Functor(
             ob=lambda x: qubit**len(x),
             ar=lambda arr: arr._decomp(),
-            cod=symmetric.Category(Ty, Diagram),
+            cod=frobenius.Category(Ty, Diagram),
         )(self)
 
     def to_dual_rail(self):
@@ -309,10 +309,10 @@ def to_dual_rail(self):
 
         assert self.is_pure, "Diagram must be pure to convert to dual rail."
 
-        return symmetric.Functor(
+        return frobenius.Functor(
             ob=lambda x: qmode**(2*len(x)),
             ar=lambda arr: arr.to_dual_rail(),
-            cod=symmetric.Category(Ty, Diagram),
+            cod=frobenius.Category(Ty, Diagram),
         )(self._decomp())
 
     def to_tket(self):
@@ -474,7 +474,7 @@ def eval(self, backend=None, **kwargs):
         return backend.eval(self, **kwargs)
 
 
-class Channel(symmetric.Box, Diagram):
+class Channel(frobenius.Box, Diagram):
     """
     Channel initialised by its Kraus map.
     """
@@ -628,7 +628,7 @@ def eval(self, n_photons=0, permanent=None, dtype=complex):
         )
 
 
-class CQMap(symmetric.Box, Diagram):
+class CQMap(frobenius.Box, Diagram):
     """
     Channel initialised by its Density matrix.
     """
@@ -675,7 +675,7 @@ def __pow__(self, n):
         return self @ self ** (n - 1)
 
 
-class Swap(symmetric.Swap, Channel):
+class Swap(frobenius.Swap, Channel):
     def dagger(self):
         return self
 
@@ -835,11 +835,35 @@ def __call__(self, other):
         return frobenius.Functor.__call__(self, other)
 
 
+class Cup(frobenius.Cup, Channel):
+    """
+    A frobenius cup is a compact cup in a frobenius diagram.
+
+    Parameters:
+        left (Ty) : The atomic type.
+        right (Ty) : Its adjoint.
+    """
+    __ambiguous_inheritance__ = (frobenius.Cup, )
+
+
+class Cap(frobenius.Cap, Channel):
+    """
+    A frobenius cap is a compact cap in a frobenius diagram.
+
+    Parameters:
+        left (Ty) : The atomic type.
+        right (Ty) : Its adjoint.
+    """
+    __ambiguous_inheritance__ = (frobenius.Cap, )
+
+
 class Hypergraph(hypergraph.Hypergraph):  # pragma: no cover
     category, functor = Category, Functor
 
-
+Hypergraph.ty_factory = Ty
 Diagram.spider_factory = Spider
+Diagram.cup_factory = Cup
+Diagram.cap_factory = Cap
 Diagram.hypergraph_factory = Hypergraph
 Diagram.braid_factory = Swap
 Diagram.sum_factory = Sum
diff --git a/optyx/utils/utils.py b/optyx/utils/utils.py
index bf3f04a8..31c9e300 100644
--- a/optyx/utils/utils.py
+++ b/optyx/utils/utils.py
@@ -519,25 +519,24 @@ def get_max_dim_for_box(
     from optyx.core.diagram import Swap, DualRail
     from optyx.core.zw import Create, Endo
 
-    # Boxes with no inputs (or a pure Swap) don't constrain the bound here.
     if len(box.dom) == 0 or isinstance(box, (Swap, Endo)):
         return 1e20
 
     dim_for_box = 0
 
-    # Light-cone at the current layer inputs
+    # light-cone at the current layer inputs
     wires_in_light_cone: List[bool] = (
         [False] * left_offset
         + [True] * len(box.dom)
         + [False] * right_offset
     )
-    # Walk previous layers from nearest to farthest
+    # walk previous layers from nearest to farthest
     for previous_left_offset, previous_box in prev_layers[::-1]:
         total = len(wires_in_light_cone)
         cod_len = len(previous_box.cod)
 
-        # Clamp the left offset so the (left, cod_len) span fits this frame.
-        # This guarantees previous_right_offset >= 0 and len(mask) == total.
+        # Clamp the left offset so the (left, cod_len) span fits this frame
+        # this guarantees previous_right_offset>= 0 and len(mask) == total
         max_left = max(0, total - cod_len)
         adj_left = previous_left_offset
         if adj_left < 0:
@@ -547,7 +546,6 @@ def get_max_dim_for_box(
 
         previous_right_offset = calculate_right_offset(total, adj_left, cod_len)
 
-        # If connected, count created photons that lie on LC wires.
         if is_previous_box_connected_to_current_box(
             wires_in_light_cone,
             adj_left,
@@ -567,9 +565,7 @@ def get_max_dim_for_box(
             if isinstance(previous_box, DualRail):
                 dim_for_box += 1
 
-        # Pull the LC back through this box (use the same clamped offsets)
         if isinstance(previous_box, Swap):
-            # Swaps always connect all their wires
             wires_in_light_cone = (
                 wires_in_light_cone[:adj_left]
                 + [wires_in_light_cone[adj_left + 1]]

From 1b6c5f74f4fa18cfac9634ce1fdb14f7386c40c6 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Sat, 20 Sep 2025 14:25:00 +0100
Subject: [PATCH 16/59] workshop_notebook

---
 docs/notebooks/graphix_workshop.ipynb | 2275 ++++++++++++-------------
 optyx/core/diagram.py                 |    7 +-
 optyx/utils/utils.py                  |    6 +
 3 files changed, 1065 insertions(+), 1223 deletions(-)

diff --git a/docs/notebooks/graphix_workshop.ipynb b/docs/notebooks/graphix_workshop.ipynb
index b8c99a85..aea2c944 100644
--- a/docs/notebooks/graphix_workshop.ipynb
+++ b/docs/notebooks/graphix_workshop.ipynb
@@ -26,7 +26,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": 1,
    "id": "13dbbb3a",
    "metadata": {},
    "outputs": [
@@ -41,7 +41,7 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-19T10:18:42.709571</dc:date>\n",
+       "    <dc:date>2025-09-20T14:16:32.451481</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -70,27 +70,27 @@
        "L 151.2 7.2 \n",
        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pc4955cc6d1)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pa284aa0791)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
        "    <path d=\"M 43.2 7.2 \n",
        "Q 43.2 25.2 43.2 25.2 \n",
-       "\" clip-path=\"url(#pc4955cc6d1)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pa284aa0791)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 115.2 7.2 \n",
        "Q 115.2 25.2 115.2 25.2 \n",
-       "\" clip-path=\"url(#pc4955cc6d1)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pa284aa0791)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
        "    <path d=\"M 43.2 61.2 \n",
        "Q 43.2 79.2 43.2 79.2 \n",
-       "\" clip-path=\"url(#pc4955cc6d1)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pa284aa0791)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_6\">\n",
        "    <path d=\"M 115.2 61.2 \n",
        "Q 115.2 79.2 115.2 79.2 \n",
-       "\" clip-path=\"url(#pc4955cc6d1)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pa284aa0791)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_7\">\n",
        "    <path d=\"M 25.2 61.2 \n",
@@ -98,7 +98,7 @@
        "L 133.2 25.2 \n",
        "L 133.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pc4955cc6d1)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pa284aa0791)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
        "    <!-- qmode -->\n",
@@ -396,7 +396,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"pc4955cc6d1\">\n",
+       "  <clipPath id=\"pa284aa0791\">\n",
        "   <rect x=\"7.2\" y=\"7.2\" width=\"144\" height=\"72\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -414,12 +414,13 @@
     "from optyx.photonic import BBS\n",
     "\n",
     "beam_splitter = BBS(0)\n",
+    "\n",
     "beam_splitter.draw()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": 2,
    "id": "79ab4b08",
    "metadata": {},
    "outputs": [
@@ -434,7 +435,7 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-19T10:18:43.207236</dc:date>\n",
+       "    <dc:date>2025-09-20T14:16:32.484953</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -463,27 +464,27 @@
        "L 151.2 7.2 \n",
        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p8c63707856)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
        "    <path d=\"M 43.2 61.2 \n",
        "Q 43.2 169.2 43.2 169.2 \n",
-       "\" clip-path=\"url(#p8c63707856)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 115.2 133.2 \n",
        "Q 115.2 169.2 115.2 169.2 \n",
-       "\" clip-path=\"url(#p8c63707856)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
        "    <path d=\"M 43.2 205.2 \n",
        "Q 43.2 223.2 43.2 223.2 \n",
-       "\" clip-path=\"url(#p8c63707856)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_6\">\n",
        "    <path d=\"M 115.2 205.2 \n",
        "Q 115.2 223.2 115.2 223.2 \n",
-       "\" clip-path=\"url(#p8c63707856)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_7\">\n",
        "    <path d=\"M 25.2 61.2 \n",
@@ -491,7 +492,7 @@
        "L 61.2 25.2 \n",
        "L 61.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p8c63707856)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_8\">\n",
        "    <path d=\"M 97.2 133.2 \n",
@@ -499,7 +500,7 @@
        "L 133.2 97.2 \n",
        "L 133.2 133.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p8c63707856)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_9\">\n",
        "    <path d=\"M 25.2 205.2 \n",
@@ -507,7 +508,7 @@
        "L 133.2 169.2 \n",
        "L 133.2 205.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p8c63707856)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
        "    <!-- qmode -->\n",
@@ -956,7 +957,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p8c63707856\">\n",
+       "  <clipPath id=\"p7c1f3775ff\">\n",
        "   <rect x=\"7.2\" y=\"7.2\" width=\"144\" height=\"216\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -999,7 +1000,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 3,
    "id": "f1478f68",
    "metadata": {},
    "outputs": [
@@ -1009,7 +1010,7 @@
        "array(-0.+0.j)"
       ]
      },
-     "execution_count": 44,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1023,7 +1024,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 4,
    "id": "801f0884",
    "metadata": {},
    "outputs": [
@@ -1033,7 +1034,7 @@
        "{(0, 2): 0.5, (1, 1): 4.9303806576313227e-32, (2, 0): 0.5}"
       ]
      },
-     "execution_count": 45,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1052,7 +1053,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 5,
    "id": "47e64a7d",
    "metadata": {},
    "outputs": [],
@@ -1075,7 +1076,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 6,
    "id": "8fa3a149",
    "metadata": {},
    "outputs": [],
@@ -1099,7 +1100,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 7,
    "id": "8c0301af",
    "metadata": {},
    "outputs": [],
@@ -1120,7 +1121,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 8,
    "id": "174c4713",
    "metadata": {},
    "outputs": [],
@@ -1145,7 +1146,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 9,
    "id": "bb29783a",
    "metadata": {},
    "outputs": [
@@ -1155,7 +1156,7 @@
        "True"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1173,7 +1174,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 10,
    "id": "25af2db6",
    "metadata": {},
    "outputs": [
@@ -1183,7 +1184,7 @@
        "True"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1246,7 +1247,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 11,
    "id": "a1764edb",
    "metadata": {},
    "outputs": [],
@@ -1263,12 +1264,12 @@
     "    HadamardBS() >>\n",
     "    (Phase(0.5) @ qmode) >>\n",
     "    HadamardBS()\n",
-    ") @ Scalar(2 ** 0.5)"
+    ")"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 12,
    "id": "c557c4b8",
    "metadata": {},
    "outputs": [],
@@ -1283,7 +1284,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 13,
    "id": "7bb5e46f",
    "metadata": {},
    "outputs": [],
@@ -1291,20 +1292,20 @@
     "from optyx.photonic import FusionTypeII\n",
     "\n",
     "@Channel.from_callable(\n",
-    "    dom=qubit, cod=qubit\n",
+    "    dom=qubit, cod=qmode @ qmode\n",
     ")\n",
     "def fusion_teleportation(a):\n",
     "    dual_rail_encoded_input = DualRail(1)(a)\n",
     "    b, c, d, e = dual_rail_encoded_bell()\n",
     "    s, k = FusionTypeII()(*dual_rail_encoded_input, b, c)\n",
     "    fusion_failure_processing(s)\n",
-    "    output_rail_1, output_rail = correction(k, d, e)\n",
-    "    return DualRail(1).dagger()(output_rail_1, output_rail)"
+    "    dr_output_1, dr_output_2 = correction(k, d, e)\n",
+    "    return dr_output_1, dr_output_2"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": null,
    "id": "4b5ee771",
    "metadata": {},
    "outputs": [
@@ -1319,7 +1320,7 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-19T10:14:02.215469</dc:date>\n",
+       "    <dc:date>2025-09-20T14:16:34.796782</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -1348,381 +1349,360 @@
        "L 583.2 7.2 \n",
        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pc684b033d8)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p4bcf70933b)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
        "    <path d=\"M 79.2 7.2 \n",
-       "Q 79.2 21.6 79.2 21.6 \n",
-       "\" clip-path=\"url(#pc684b033d8)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "Q 79.2 23.2 79.2 23.2 \n",
+       "\" clip-path=\"url(#p4bcf70933b)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
-       "    <path d=\"M 43.2 50.4 \n",
-       "Q 43.2 136.8 43.2 136.8 \n",
-       "\" clip-path=\"url(#pc684b033d8)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 43.2 55.2 \n",
+       "Q 43.2 151.2 43.2 151.2 \n",
+       "\" clip-path=\"url(#p4bcf70933b)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
-       "    <path d=\"M 115.2 50.4 \n",
-       "Q 115.2 136.8 115.2 136.8 \n",
-       "\" clip-path=\"url(#pc684b033d8)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 115.2 55.2 \n",
+       "Q 115.2 151.2 115.2 151.2 \n",
+       "\" clip-path=\"url(#p4bcf70933b)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_6\">\n",
-       "    <path d=\"M 403.2 36 \n",
-       "Q 331.2 36 331.2 50.4 \n",
-       "\" clip-path=\"url(#pc684b033d8)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 403.2 39.2 \n",
+       "Q 331.2 39.2 331.2 55.2 \n",
+       "\" clip-path=\"url(#p4bcf70933b)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_7\">\n",
-       "    <path d=\"M 403.2 36 \n",
-       "Q 475.2 36 475.2 50.4 \n",
-       "\" clip-path=\"url(#pc684b033d8)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 403.2 39.2 \n",
+       "Q 475.2 39.2 475.2 55.2 \n",
+       "\" clip-path=\"url(#p4bcf70933b)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_8\">\n",
-       "    <path d=\"M 331.2 50.4 \n",
-       "Q 331.2 79.2 331.2 79.2 \n",
-       "\" clip-path=\"url(#pc684b033d8)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 331.2 55.2 \n",
+       "Q 331.2 87.2 331.2 87.2 \n",
+       "\" clip-path=\"url(#p4bcf70933b)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_9\">\n",
-       "    <path d=\"M 475.2 50.4 \n",
-       "Q 475.2 79.2 475.2 79.2 \n",
-       "\" clip-path=\"url(#pc684b033d8)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 475.2 55.2 \n",
+       "Q 475.2 87.2 475.2 87.2 \n",
+       "\" clip-path=\"url(#p4bcf70933b)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_10\">\n",
-       "    <path d=\"M 259.2 108 \n",
-       "Q 259.2 136.8 259.2 136.8 \n",
-       "\" clip-path=\"url(#pc684b033d8)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 259.2 119.2 \n",
+       "Q 259.2 151.2 259.2 151.2 \n",
+       "\" clip-path=\"url(#p4bcf70933b)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_11\">\n",
-       "    <path d=\"M 367.2 108 \n",
-       "Q 367.2 136.8 367.2 136.8 \n",
-       "\" clip-path=\"url(#pc684b033d8)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 367.2 119.2 \n",
+       "Q 367.2 151.2 367.2 151.2 \n",
+       "\" clip-path=\"url(#p4bcf70933b)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_12\">\n",
-       "    <path d=\"M 439.2 108 \n",
-       "Q 439.2 367.2 439.2 367.2 \n",
-       "\" clip-path=\"url(#pc684b033d8)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 439.2 119.2 \n",
+       "Q 439.2 407.2 439.2 407.2 \n",
+       "\" clip-path=\"url(#p4bcf70933b)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_13\">\n",
-       "    <path d=\"M 511.2 108 \n",
-       "Q 511.2 367.2 511.2 367.2 \n",
-       "\" clip-path=\"url(#pc684b033d8)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 511.2 119.2 \n",
+       "Q 511.2 407.2 511.2 407.2 \n",
+       "\" clip-path=\"url(#p4bcf70933b)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_14\">\n",
-       "    <path d=\"M 43.2 165.6 \n",
-       "Q 43.2 194.4 43.2 194.4 \n",
-       "\" clip-path=\"url(#pc684b033d8)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "    <path d=\"M 43.2 183.2 \n",
+       "Q 43.2 215.2 43.2 215.2 \n",
+       "\" clip-path=\"url(#p4bcf70933b)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_15\">\n",
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@@ -3222,11 +3012,10 @@
     "fusion_teleportation_monoidal_syntax = (\n",
     "    DualRail(1) @ dual_rail_encoded_bell >>\n",
     "    FusionTypeII() @ qmode**2 >>\n",
-    "    fusion_failure_processing @ correction >>\n",
-    "    DualRail(1).dagger()\n",
+    "    fusion_failure_processing @ correction\n",
     ")\n",
     "\n",
-    "array_teleportation = fusion_teleportation.eval().tensor.array\n",
+    "array_teleportation = fusion_teleportation_monoidal_syntax.eval().tensor.array\n",
     "\n",
     "fusion_teleportation_monoidal_syntax.foliation().draw(figsize=(8, 8))\n"
    ]
@@ -3241,7 +3030,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 15,
    "id": "c19354d7",
    "metadata": {},
    "outputs": [
@@ -3251,7 +3040,7 @@
        "True"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3260,8 +3049,8 @@
     "import numpy as np\n",
     "from optyx.photonic import Id\n",
     "\n",
-    "array_id = Id(1).double().to_tensor().eval().array\n",
-    "np.allclose(array_teleportation, array_id)"
+    "array_dr = (DualRail(1) @ Scalar(0.5**0.5)).double().to_tensor().eval().array\n",
+    "np.allclose(array_teleportation[:, :, :2, :2, :2, :2], array_dr)\n"
    ]
   },
   {
@@ -3274,7 +3063,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 16,
    "id": "51acb733",
    "metadata": {},
    "outputs": [],
@@ -3289,6 +3078,8 @@
     "    a, b = _flat(SU), _flat(SV)\n",
     "    num = abs(np.vdot(a, b))\n",
     "    den = np.linalg.norm(a) * np.linalg.norm(b)\n",
+    "    if den == 0:\n",
+    "        return 0.0\n",
     "    return float(num / den)\n",
     "\n",
     "def average_fidelity(SU, SV, d):\n",
@@ -3298,17 +3089,39 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 110,
+   "execution_count": 17,
    "id": "fb497580",
    "metadata": {},
    "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n"
+     ]
+    },
     {
      "data": {
       "text/plain": [
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-     "execution_count": 110,
+     "execution_count": 17,
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        "    </g>\n",
-       "    <g id=\"text_17\">\n",
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@@ -4594,10 +4343,9 @@
     "    error_for_chi = []\n",
     "    for _ in range(10):\n",
     "         error_for_chi.append(\n",
-    "             average_fidelity(\n",
+    "             process_fidelity(\n",
     "                 fusion_teleportation.eval(QuimbBackend(optimiser)).tensor.array,\n",
-    "                 array_teleportation,\n",
-    "                 d=2\n",
+    "                 array_teleportation\n",
     "             )\n",
     "         )\n",
     "    errors.append(np.median(error_for_chi))\n",
@@ -4620,7 +4368,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 18,
    "id": "ac439493",
    "metadata": {},
    "outputs": [],
@@ -4629,32 +4377,34 @@
     "\n",
     "def fusion_teleportation_with_photon_loss(p):\n",
     "    @Channel.from_callable(\n",
-    "        dom=qubit, cod=qubit\n",
+    "        dom=qubit, cod=qmode**2\n",
     "    )\n",
     "    def fusion_teleportation(a):\n",
     "        dr_input_1, dr_input_2 = DualRail(1)(a)\n",
     "        b, c, d, e = dual_rail_encoded_bell()\n",
-    "        dr_input_2_loss, c_loss, e_loss = PhotonLoss(p)(dr_input_2), PhotonLoss(p)(c), PhotonLoss(p)(e)\n",
-    "        s, k = FusionTypeII()(dr_input_1, dr_input_2_loss, b, c_loss)\n",
+    "        dr_input_1_loss, dr_input_2_loss, b_loss, c_loss, d_loss, e_loss = (\n",
+    "            PhotonLoss(p)(dr_input_1), PhotonLoss(p)(dr_input_2), PhotonLoss(p)(b), PhotonLoss(p)(c), PhotonLoss(p)(d), PhotonLoss(p)(e)\n",
+    "        )\n",
+    "        s, k = FusionTypeII()(dr_input_1_loss, dr_input_2_loss, b_loss, c_loss)\n",
     "        fusion_failure_processing(s)\n",
-    "        output_rail_1, output_rail = correction(k, d, e_loss)\n",
-    "        return DualRail(1).dagger()(output_rail_1, output_rail)\n",
+    "        output_rail_1, output_rail = correction(k, d_loss, e_loss)\n",
+    "        return output_rail_1, output_rail\n",
     "    return fusion_teleportation"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "id": "ea619cd4",
+   "execution_count": 41,
+   "id": "7e1a2957",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Text(0.5, 1.0, 'Fusion-based Teleportation Fidelity vs Photon Survival Probability (p)')"
+       "Text(0.5, 1.0, 'Fusion-based Teleportation: Success Probability vs Average Fidelity')"
       ]
      },
-     "execution_count": 22,
+     "execution_count": 41,
      "metadata": {},
      "output_type": "execute_result"
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     }
    ],
    "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "ps = np.linspace(0.0, 1.0, 20)\n",
     "\n",
-    "ps = np.linspace(0, 1, 20)\n",
-    "errors_with_loss = []\n",
+    "F_avg_vals = []\n",
+    "succ_probs = []\n",
     "for p in ps:\n",
-    "    errors_with_loss.append(\n",
-    "        average_fidelity(\n",
-    "            fusion_teleportation_with_photon_loss(p).eval().tensor.array,\n",
-    "            array_teleportation,\n",
-    "            d=2\n",
-    "        )\n",
-    "    )\n",
+    "    S_impl = fusion_teleportation_with_photon_loss(p).eval().tensor.array\n",
+    "    S_tgt  = array_teleportation\n",
+    "    s = average_fidelity(S_impl, S_tgt, d=2)\n",
     "\n",
-    "plt.plot(ps, errors_with_loss, marker='o')\n",
-    "plt.grid()\n",
+    "    succ_probs.append(s)\n",
+    "\n",
+    "plt.figure()\n",
+    "plt.plot(ps, succ_probs, marker='o')\n",
+    "plt.grid(True)\n",
     "plt.xlabel('Photon Survival Probability (p)')\n",
-    "plt.ylabel('Average Gate Fidelity')\n",
-    "plt.title('Fusion-based Teleportation Fidelity vs Photon Survival Probability (p)')"
+    "plt.ylabel('Average fidelity')\n",
+    "plt.title('Fusion-based Teleportation: Success Probability vs Average Fidelity')\n"
    ]
   },
   {
@@ -5997,7 +5842,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 20,
    "id": "fcbe90b6",
    "metadata": {},
    "outputs": [
@@ -6005,7 +5850,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[1, 0] [0. 1.]\n"
+      "[1, 0] [0, 1]\n"
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    ],
@@ -6018,7 +5863,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 21,
    "id": "bdb9611d",
    "metadata": {},
    "outputs": [
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@@ -7568,10 +7390,33 @@
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@@ -7638,7 +7483,7 @@
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   {
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-   "execution_count": 25,
+   "execution_count": 22,
    "id": "9e5c4078",
    "metadata": {},
    "outputs": [],
@@ -7663,7 +7508,7 @@
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   {
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-   "execution_count": 26,
+   "execution_count": 23,
    "id": "30b96ad0",
    "metadata": {},
    "outputs": [],
@@ -7690,7 +7535,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 24,
    "id": "1c50f388",
    "metadata": {},
    "outputs": [
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        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-19T10:17:16.103446</dc:date>\n",
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@@ -8006,11 +7851,11 @@
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@@ -8276,16 +8121,16 @@
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@@ -8328,11 +8173,11 @@
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@@ -8380,11 +8225,11 @@
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@@ -8400,11 +8245,11 @@
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@@ -8452,11 +8297,11 @@
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@@ -8754,22 +8599,22 @@
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+       "     <use xlink:href=\"#m01cfbd2c3c\" x=\"93.399222\" y=\"231.470859\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
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@@ -9011,7 +8856,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p6d9b947ed2\">\n",
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@@ -9039,7 +8884,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 25,
    "id": "06b9a545",
    "metadata": {},
    "outputs": [
@@ -9054,7 +8899,7 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-19T10:17:16.172772</dc:date>\n",
+       "    <dc:date>2025-09-20T14:19:37.254559</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -9090,16 +8935,16 @@
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@@ -9223,11 +9068,11 @@
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-       "\" clip-path=\"url(#pbb4c0ea47e)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
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@@ -9265,11 +9110,11 @@
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-       "\" clip-path=\"url(#pbb4c0ea47e)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
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        "     </g>\n",
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-       "       <use xlink:href=\"#md57850eaee\" x=\"251.345625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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@@ -9318,11 +9163,11 @@
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-       "\" clip-path=\"url(#pbb4c0ea47e)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
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        "     </g>\n",
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-       "       <use xlink:href=\"#md57850eaee\" x=\"318.305625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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@@ -9380,11 +9225,11 @@
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@@ -9651,16 +9496,16 @@
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        "     <g id=\"line2d_14\">\n",
        "      <defs>\n",
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@@ -9677,11 +9522,11 @@
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@@ -9698,11 +9543,11 @@
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-       "\" clip-path=\"url(#pbb4c0ea47e)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p7534fc087b)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
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@@ -9719,11 +9564,11 @@
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-       "\" clip-path=\"url(#pbb4c0ea47e)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p7534fc087b)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
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@@ -9740,11 +9585,11 @@
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@@ -9761,11 +9606,11 @@
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@@ -10041,9 +9886,9 @@
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        "L -1 262.721498 \n",
-       "\" clip-path=\"url(#pbb4c0ea47e)\" style=\"fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p7534fc087b)\" style=\"fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square\"/>\n",
        "    <defs>\n",
-       "     <path id=\"m0ccf231872\" d=\"M 0 3 \n",
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@@ -10055,13 +9900,13 @@
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-       "     <use xlink:href=\"#m0ccf231872\" x=\"-1\" y=\"262.721498\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "    <g clip-path=\"url(#p7534fc087b)\">\n",
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+       "     <use xlink:href=\"#mca84f504d1\" x=\"197.387015\" y=\"143.270751\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "     <use xlink:href=\"#mca84f504d1\" x=\"53.709395\" y=\"231.055379\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
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@@ -10303,7 +10148,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"pbb4c0ea47e\">\n",
+       "  <clipPath id=\"p7534fc087b\">\n",
        "   <rect x=\"50.465625\" y=\"22.318125\" width=\"334.8\" height=\"221.76\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -10349,7 +10194,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 65,
+   "execution_count": 26,
    "id": "79f358ae",
    "metadata": {},
    "outputs": [],
@@ -10365,7 +10210,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 66,
+   "execution_count": 27,
    "id": "4888034c",
    "metadata": {},
    "outputs": [
@@ -10387,7 +10232,7 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-19T10:50:29.636857</dc:date>\n",
+       "    <dc:date>2025-09-20T14:19:37.414832</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -10421,35 +10266,35 @@
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        "Q 106.042743 90.36 170.400086 90.36 \n",
-       "\" clip-path=\"url(#p738f5004be)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
+       "\" clip-path=\"url(#pdc0410589b)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
        "    <path d=\"M 166.400086 88.36 \n",
        "L 170.400086 90.36 \n",
        "L 166.400086 92.36 \n",
-       "\" clip-path=\"url(#p738f5004be)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
+       "\" clip-path=\"url(#pdc0410589b)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 40.024391 87.326433 \n",
        "Q 106.045262 62.640169 171.018913 38.345478 \n",
-       "\" clip-path=\"url(#p738f5004be)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
+       "\" clip-path=\"url(#pdc0410589b)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
        "    <path d=\"M 166.571796 37.873085 \n",
        "L 171.018913 38.345478 \n",
        "L 167.972729 41.619735 \n",
-       "\" clip-path=\"url(#p738f5004be)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
+       "\" clip-path=\"url(#pdc0410589b)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
        "   </g>\n",
        "   <g id=\"matplotlib.axis_1\">\n",
        "    <g id=\"xtick_1\"/>\n",
@@ -10568,11 +10413,11 @@
        "L 167.778687 33.07423 \n",
        "L 169.081412 33.262286 \n",
        "L 170.382137 33.454569 \n",
-       "\" clip-path=\"url(#p738f5004be)\" style=\"fill: none; stroke: #d62728; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#pdc0410589b)\" style=\"fill: none; stroke: #d62728; stroke-linecap: square\"/>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_1\">\n",
        "    <defs>\n",
-       "     <path id=\"m6a225ba081\" d=\"M 0 9.354143 \n",
+       "     <path id=\"m2a3cbc8ba2\" d=\"M 0 9.354143 \n",
        "C 2.480748 9.354143 4.860225 8.368532 6.614378 6.614378 \n",
        "C 8.368532 4.860225 9.354143 2.480748 9.354143 0 \n",
        "C 9.354143 -2.480748 8.368532 -4.860225 6.614378 -6.614378 \n",
@@ -10584,13 +10429,13 @@
        "z\n",
        "\" style=\"stroke: #ff0000\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#p738f5004be)\">\n",
-       "     <use xlink:href=\"#m6a225ba081\" x=\"180.18\" y=\"90.36\" style=\"fill: #d3d3d3; stroke: #ff0000\"/>\n",
+       "    <g clip-path=\"url(#pdc0410589b)\">\n",
+       "     <use xlink:href=\"#m2a3cbc8ba2\" x=\"180.18\" y=\"90.36\" style=\"fill: #d3d3d3; stroke: #ff0000\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_2\">\n",
        "    <defs>\n",
-       "     <path id=\"mdfb9ad8fde\" d=\"M 0 9.354143 \n",
+       "     <path id=\"m99067599b2\" d=\"M 0 9.354143 \n",
        "C 2.480748 9.354143 4.860225 8.368532 6.614378 6.614378 \n",
        "C 8.368532 4.860225 9.354143 2.480748 9.354143 0 \n",
        "C 9.354143 -2.480748 8.368532 -4.860225 6.614378 -6.614378 \n",
@@ -10602,13 +10447,13 @@
        "z\n",
        "\" style=\"stroke: #ff0000\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#p738f5004be)\">\n",
-       "     <use xlink:href=\"#mdfb9ad8fde\" x=\"31.911429\" y=\"90.36\" style=\"fill: #add8e6; stroke: #ff0000\"/>\n",
+       "    <g clip-path=\"url(#pdc0410589b)\">\n",
+       "     <use xlink:href=\"#m99067599b2\" x=\"31.911429\" y=\"90.36\" style=\"fill: #add8e6; stroke: #ff0000\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_3\">\n",
        "    <defs>\n",
-       "     <path id=\"m4f56fa9f95\" d=\"M 0 9.354143 \n",
+       "     <path id=\"me2a765baa4\" d=\"M 0 9.354143 \n",
        "C 2.480748 9.354143 4.860225 8.368532 6.614378 6.614378 \n",
        "C 8.368532 4.860225 9.354143 2.480748 9.354143 0 \n",
        "C 9.354143 -2.480748 8.368532 -4.860225 6.614378 -6.614378 \n",
@@ -10620,13 +10465,13 @@
        "z\n",
        "\" style=\"stroke: #000000\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#p738f5004be)\">\n",
-       "     <use xlink:href=\"#m4f56fa9f95\" x=\"31.911429\" y=\"34.92\" style=\"fill: #add8e6; stroke: #000000\"/>\n",
+       "    <g clip-path=\"url(#pdc0410589b)\">\n",
+       "     <use xlink:href=\"#me2a765baa4\" x=\"31.911429\" y=\"34.92\" style=\"fill: #add8e6; stroke: #000000\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_4\">\n",
        "    <defs>\n",
-       "     <path id=\"m23332b100d\" d=\"M 0 9.354143 \n",
+       "     <path id=\"mc019d27685\" d=\"M 0 9.354143 \n",
        "C 2.480748 9.354143 4.860225 8.368532 6.614378 6.614378 \n",
        "C 8.368532 4.860225 9.354143 2.480748 9.354143 0 \n",
        "C 9.354143 -2.480748 8.368532 -4.860225 6.614378 -6.614378 \n",
@@ -10638,8 +10483,8 @@
        "z\n",
        "\" style=\"stroke: #000000\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#p738f5004be)\">\n",
-       "     <use xlink:href=\"#m23332b100d\" x=\"180.18\" y=\"34.92\" style=\"fill: #d3d3d3; stroke: #000000\"/>\n",
+       "    <g clip-path=\"url(#pdc0410589b)\">\n",
+       "     <use xlink:href=\"#mc019d27685\" x=\"180.18\" y=\"34.92\" style=\"fill: #d3d3d3; stroke: #000000\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"line2d_2\"/>\n",
@@ -10676,7 +10521,7 @@
        "\" style=\"fill: none; stroke: #d62728; stroke-linecap: round\"/>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
-       "    <g clip-path=\"url(#p738f5004be)\">\n",
+       "    <g clip-path=\"url(#pdc0410589b)\">\n",
        "     <!-- 0 -->\n",
        "     <g transform=\"translate(176.3625 93.67125) scale(0.12 -0.12)\">\n",
        "      <defs>\n",
@@ -10707,7 +10552,7 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_2\">\n",
-       "    <g clip-path=\"url(#p738f5004be)\">\n",
+       "    <g clip-path=\"url(#pdc0410589b)\">\n",
        "     <!-- 1 -->\n",
        "     <g transform=\"translate(28.093929 93.67125) scale(0.12 -0.12)\">\n",
        "      <defs>\n",
@@ -10731,7 +10576,7 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_3\">\n",
-       "    <g clip-path=\"url(#p738f5004be)\">\n",
+       "    <g clip-path=\"url(#pdc0410589b)\">\n",
        "     <!-- 2 -->\n",
        "     <g transform=\"translate(28.093929 38.23125) scale(0.12 -0.12)\">\n",
        "      <defs>\n",
@@ -10765,7 +10610,7 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_4\">\n",
-       "    <g clip-path=\"url(#p738f5004be)\">\n",
+       "    <g clip-path=\"url(#pdc0410589b)\">\n",
        "     <!-- 3 -->\n",
        "     <g transform=\"translate(176.3625 38.23125) scale(0.12 -0.12)\">\n",
        "      <defs>\n",
@@ -11204,7 +11049,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p738f5004be\">\n",
+       "  <clipPath id=\"pdc0410589b\">\n",
        "   <rect x=\"7.2\" y=\"7.2\" width=\"345.96\" height=\"110.88\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -11224,7 +11069,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 67,
+   "execution_count": 28,
    "id": "bff50dee",
    "metadata": {},
    "outputs": [],
@@ -11235,7 +11080,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 68,
+   "execution_count": 29,
    "id": "bf2d9106",
    "metadata": {},
    "outputs": [],
@@ -11249,7 +11094,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 69,
+   "execution_count": 30,
    "id": "908e477d",
    "metadata": {},
    "outputs": [],
@@ -11268,7 +11113,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 70,
+   "execution_count": 31,
    "id": "07f5f7ba",
    "metadata": {},
    "outputs": [],
@@ -11286,7 +11131,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 71,
+   "execution_count": 32,
    "id": "988c9618",
    "metadata": {},
    "outputs": [
@@ -11495,10 +11340,10 @@
        "</svg>"
       ],
       "text/plain": [
-       "<drawsvg.drawing.Drawing at 0x7f37cbefa1b0>"
+       "<drawsvg.drawing.Drawing at 0x7caaafa91d30>"
       ]
      },
-     "execution_count": 71,
+     "execution_count": 32,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -11537,7 +11382,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 96,
+   "execution_count": 33,
    "id": "96d5bf6b",
    "metadata": {},
    "outputs": [],
@@ -11559,7 +11404,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 97,
+   "execution_count": 34,
    "id": "bce649df",
    "metadata": {},
    "outputs": [],
@@ -11580,7 +11425,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 98,
+   "execution_count": 35,
    "id": "f0c1fbf3",
    "metadata": {},
    "outputs": [],
@@ -11598,7 +11443,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 104,
+   "execution_count": 36,
    "id": "463bcb6f",
    "metadata": {},
    "outputs": [],
@@ -11610,7 +11455,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 105,
+   "execution_count": 37,
    "id": "3f3fca2d",
    "metadata": {},
    "outputs": [],
@@ -11632,7 +11477,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 106,
+   "execution_count": 38,
    "id": "54633b7a",
    "metadata": {},
    "outputs": [],
@@ -11642,7 +11487,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 107,
+   "execution_count": 39,
    "id": "e019251e",
    "metadata": {},
    "outputs": [],
@@ -11658,7 +11503,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 108,
+   "execution_count": 40,
    "id": "ca6102c5",
    "metadata": {},
    "outputs": [],
@@ -11668,14 +11513,6 @@
     "    result_optyx\n",
     ")"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "419dd1dd",
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index d0d52299..ce40e78e 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -314,12 +314,12 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
         number_of_input_layer_wires = len(self.dom)
 
         if input_dims is None:
-            layer_dims = [2 for _ in range(len(self.dom))]
+            input_dims = [2 for _ in range(len(self.dom))]
         else:
             assert len(self.dom) == len(input_dims), (
                 f"Input dims length {len(input_dims)} does not match number of input wires {len(self.dom)}"
             )
-            layer_dims = input_dims
+        layer_dims = input_dims
 
         if len(self.boxes) == 0 and len(self.offsets) == 0:
             return tensor.Diagram.id(list_to_dim(layer_dims))
@@ -333,10 +333,9 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
                 left_offset,
                 box,
                 right_offset,
-                layer_dims,
+                input_dims,
                 prev_layers
             )
-
             dims_in = layer_dims[left_offset:left_offset + len(box.dom)]
             dims_out, _ = modify_io_dims_against_max_dim(
                 box.determine_output_dimensions(dims_in),
diff --git a/optyx/utils/utils.py b/optyx/utils/utils.py
index 31c9e300..df0e6502 100644
--- a/optyx/utils/utils.py
+++ b/optyx/utils/utils.py
@@ -518,6 +518,7 @@ def get_max_dim_for_box(
 ):
     from optyx.core.diagram import Swap, DualRail
     from optyx.core.zw import Create, Endo
+    from optyx.core.control import BitControlledBox
 
     if len(box.dom) == 0 or isinstance(box, (Swap, Endo)):
         return 1e20
@@ -529,6 +530,11 @@ def get_max_dim_for_box(
         [False] * left_offset
         + [True] * len(box.dom)
         + [False] * right_offset
+    ) if not isinstance(box, BitControlledBox) else (
+        [False] * (left_offset + 1)
+        + [True] * (len(box.dom) - 1)
+        + [False] * right_offset
+
     )
     # walk previous layers from nearest to farthest
     for previous_left_offset, previous_box in prev_layers[::-1]:

From aa8a1acdd3eb44741fd91e196c15dd4e5c476448 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Sat, 20 Sep 2025 15:44:42 +0100
Subject: [PATCH 17/59] Fixed an issue with checking if a channel diagram is
 pure

---
 docs/notebooks/graphix_workshop.ipynb | 860 +++++++++++++-------------
 optyx/core/backends.py                |   2 +-
 optyx/core/channel.py                 |  18 +
 test/test_qubit.py                    |  22 +-
 4 files changed, 467 insertions(+), 435 deletions(-)

diff --git a/docs/notebooks/graphix_workshop.ipynb b/docs/notebooks/graphix_workshop.ipynb
index aea2c944..187435cc 100644
--- a/docs/notebooks/graphix_workshop.ipynb
+++ b/docs/notebooks/graphix_workshop.ipynb
@@ -41,7 +41,7 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-20T14:16:32.451481</dc:date>\n",
+       "    <dc:date>2025-09-20T15:23:03.038095</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -70,27 +70,27 @@
        "L 151.2 7.2 \n",
        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pa284aa0791)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#peefc055285)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
        "    <path d=\"M 43.2 7.2 \n",
        "Q 43.2 25.2 43.2 25.2 \n",
-       "\" clip-path=\"url(#pa284aa0791)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#peefc055285)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 115.2 7.2 \n",
        "Q 115.2 25.2 115.2 25.2 \n",
-       "\" clip-path=\"url(#pa284aa0791)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#peefc055285)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
        "    <path d=\"M 43.2 61.2 \n",
        "Q 43.2 79.2 43.2 79.2 \n",
-       "\" clip-path=\"url(#pa284aa0791)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#peefc055285)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_6\">\n",
        "    <path d=\"M 115.2 61.2 \n",
        "Q 115.2 79.2 115.2 79.2 \n",
-       "\" clip-path=\"url(#pa284aa0791)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#peefc055285)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_7\">\n",
        "    <path d=\"M 25.2 61.2 \n",
@@ -98,7 +98,7 @@
        "L 133.2 25.2 \n",
        "L 133.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pa284aa0791)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#peefc055285)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
        "    <!-- qmode -->\n",
@@ -396,7 +396,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"pa284aa0791\">\n",
+       "  <clipPath id=\"peefc055285\">\n",
        "   <rect x=\"7.2\" y=\"7.2\" width=\"144\" height=\"72\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -435,7 +435,7 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-20T14:16:32.484953</dc:date>\n",
+       "    <dc:date>2025-09-20T15:23:03.113336</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -464,27 +464,27 @@
        "L 151.2 7.2 \n",
        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p82b0da7130)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
        "    <path d=\"M 43.2 61.2 \n",
        "Q 43.2 169.2 43.2 169.2 \n",
-       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p82b0da7130)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 115.2 133.2 \n",
        "Q 115.2 169.2 115.2 169.2 \n",
-       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p82b0da7130)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
        "    <path d=\"M 43.2 205.2 \n",
        "Q 43.2 223.2 43.2 223.2 \n",
-       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p82b0da7130)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_6\">\n",
        "    <path d=\"M 115.2 205.2 \n",
        "Q 115.2 223.2 115.2 223.2 \n",
-       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p82b0da7130)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_7\">\n",
        "    <path d=\"M 25.2 61.2 \n",
@@ -492,7 +492,7 @@
        "L 61.2 25.2 \n",
        "L 61.2 61.2 \n",
        "z\n",
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@@ -500,7 +500,7 @@
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        "z\n",
-       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -508,7 +508,7 @@
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        "z\n",
-       "\" clip-path=\"url(#p7c1f3775ff)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -957,7 +957,7 @@
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        " <defs>\n",
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@@ -1305,7 +1305,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 14,
    "id": "4b5ee771",
    "metadata": {},
    "outputs": [
@@ -1320,7 +1320,7 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-20T14:16:34.796782</dc:date>\n",
+       "    <dc:date>2025-09-20T15:23:05.418345</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
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@@ -1349,217 +1349,217 @@
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@@ -1567,7 +1567,7 @@
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@@ -1575,7 +1575,7 @@
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-       "    <g clip-path=\"url(#pdc0410589b)\">\n",
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@@ -10552,7 +10572,7 @@
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@@ -11049,7 +11069,7 @@
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        " <defs>\n",
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@@ -11340,7 +11360,7 @@
        "</svg>"
       ],
       "text/plain": [
-       "<drawsvg.drawing.Drawing at 0x7caaafa91d30>"
+       "<drawsvg.drawing.Drawing at 0x77f4e00d1400>"
       ]
      },
      "execution_count": 32,
@@ -11513,6 +11533,14 @@
     "    result_optyx\n",
     ")"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a7c85548",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
diff --git a/optyx/core/backends.py b/optyx/core/backends.py
index b87508e5..ab9e1565 100644
--- a/optyx/core/backends.py
+++ b/optyx/core/backends.py
@@ -250,7 +250,7 @@ def _prob_dist_mixed(
 
         if not any(t in {bit, mode} for t in self.output_types):
             raise ValueError(
-                "Types must contain at least one 'bit' or 'mode'."
+                "Output types must contain at least one 'bit' or 'mode'."
             )
 
         values = self._convert_array_to_dict(self.tensor.array, round_digits)
diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index eed7812d..cabf31f3 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -240,12 +240,30 @@ def is_pure(self):
         for layer in self:
             generator = layer.inside[0][1]
 
+            # if we have a discard/measure acting on quantum types, it's not pure
+            if (
+                isinstance(generator, (Discard, Measure)) and
+                any(not ty.is_classical for ty in generator.dom.inside)
+            ):
+                return False
+            if hasattr(generator, 'env') and generator.env != diagram.Ty():
+                return False
+
+            # if we prepare quantum from classical types, it's not pure
+            if (
+                isinstance(generator, Encode) and
+                any(ty.is_classical for ty in generator.cod.inside)
+            ):
+                return False
+
+            # if we're mixing classical and quantum types, it's not pure
             are_layers_pure.append(
                 any(ty.is_classical for ty in generator.cod.inside) or
                 any(ty.is_classical for ty in generator.dom.inside) or
                 isinstance(generator, Discard)
             )
 
+            # assume all classical maps are pure
             are_layers_classical.append(
                 all(ty.is_classical for ty in generator.cod.inside) and
                 all(ty.is_classical for ty in generator.dom.inside)
diff --git a/test/test_qubit.py b/test/test_qubit.py
index c6f5ca6c..003f08df 100644
--- a/test/test_qubit.py
+++ b/test/test_qubit.py
@@ -107,27 +107,13 @@ def test_discard_qubits():
 
 def test_bit_flip_error():
     prob = 0.43
-    a = (qubits.BitFlipError(prob).get_kraus().to_tensor().to_quimb() ^ ...).data
-    b = zx.X(1, 2) >> zx.Id(1) @ zx.ZBox(
-            1, 1, np.sqrt((1 - prob) / prob)
-        ) @ zx.scalar(np.sqrt(prob * 2))
-    b = (b.to_tensor().to_quimb() ^ ...).data
-
-    assert np.allclose(a, b)
+    a = (qubits.Z(0, 1) >> qubits.BitFlipError(prob)).eval().tensor.array
+    assert np.allclose(a, np.array([[-.14, -0.14], [-0.14, -0.14]]))
 
 def test_dephasingerror():
     prob = 0.43
-    a = (qubits.DephasingError(prob).get_kraus().to_tensor().to_quimb() ^ ...).data
-    b = (
-            zx.H
-            >> zx.X(1, 2)
-            >> zx.H
-            @ zx.ZBox(1, 1, np.sqrt((1 - prob) / prob))
-            @ zx.scalar(np.sqrt(prob * 2))
-        )
-    b = (b.to_tensor().to_quimb() ^ ...).data
-
-    assert np.allclose(a, b)
+    a = (qubits.Z(0, 1) >> qubits.DephasingError(prob)).eval().tensor.array
+    assert np.allclose(a,  np.array([[-.14, 1.], [1, -0.14]]))
 
 def test_ket():
     from optyx.core import diagram

From 9ebdd71f1936019fcb14fea54e70a0ba9cb10841 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Mon, 22 Sep 2025 16:13:11 +0100
Subject: [PATCH 18/59] revised readme notebook

---
 docs/notebooks/distributed_entanglement.png |  Bin 0 -> 314876 bytes
 docs/notebooks/graphix_workshop.ipynb       | 3532 ++++++-------------
 docs/notebooks/teleportation_danube.png     |  Bin 0 -> 190048 bytes
 3 files changed, 1012 insertions(+), 2520 deletions(-)
 create mode 100644 docs/notebooks/distributed_entanglement.png
 create mode 100644 docs/notebooks/teleportation_danube.png

diff --git a/docs/notebooks/distributed_entanglement.png b/docs/notebooks/distributed_entanglement.png
new file mode 100644
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     "## Fusion teleportation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "7043700a",
+   "metadata": {},
+   "source": [
+    "Ursin, R., Jennewein, T., Aspelmeyer, M. et al. Quantum teleportation across the Danube. Nature 430, 849 (2004). https://doi.org/10.1038/430849a\n",
+    "\n",
+    "<img src=\"./teleportation_danube.png\" alt=\"Fusion teleportation across the Danube\" width=\"1150px\">"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "5721aeab",
@@ -1216,7 +1226,7 @@
    "source": [
     "Graphically, the fusion measurement we would like to use, takes the following form:\n",
     "\n",
-    "![Fusion II](./fusion_ii.png \"Fusion measurement implementing a Bell measurement in dual rail encoding\")\n"
+    "<img src=\"./fusion_ii.png\" alt=\"Fusion measurement\" width=\"1200px\">\n"
    ]
   },
   {
@@ -1248,6 +1258,21 @@
   {
    "cell_type": "code",
    "execution_count": 11,
+   "id": "c557c4b8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.photonic import DualRail\n",
+    "\n",
+    "dual_rail_encoded_bell = (\n",
+    "    bell >>\n",
+    "    DualRail(1) @ DualRail(1)\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
    "id": "a1764edb",
    "metadata": {},
    "outputs": [],
@@ -1267,21 +1292,6 @@
     ")"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "id": "c557c4b8",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.photonic import DualRail\n",
-    "\n",
-    "dual_rail_encoded_bell = (\n",
-    "    bell >>\n",
-    "    DualRail(1) @ DualRail(1)\n",
-    ")"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": 13,
@@ -1320,7 +1330,7 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-20T15:23:05.418345</dc:date>\n",
+       "    <dc:date>2025-09-22T16:09:07.230615</dc:date>\n",
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        "    <dc:creator>\n",
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     "    fusion_failure_processing @ correction\n",
     ")\n",
     "\n",
-    "array_teleportation = fusion_teleportation_monoidal_syntax.eval().tensor.array\n",
-    "\n",
     "fusion_teleportation_monoidal_syntax.foliation().draw(figsize=(8, 8))\n"
    ]
   },
@@ -3049,7 +3057,9 @@
     "import numpy as np\n",
     "from optyx.photonic import Id\n",
     "\n",
+    "array_teleportation = fusion_teleportation_monoidal_syntax.eval().tensor.array\n",
     "array_dr = (DualRail(1) @ Scalar(0.5**0.5)).double().to_tensor().eval().array\n",
+    "\n",
     "np.allclose(array_teleportation[:, :, :2, :2, :2, :2], array_dr)\n"
    ]
   },
@@ -3068,8 +3078,6 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "# process fidelity\n",
-    "\n",
     "def _flat(x):\n",
     "    return np.asarray(x, dtype=complex).ravel()\n",
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     "plt.plot(range(1, 6), errors, marker='o')\n",
     "plt.grid()\n",
     "plt.xlabel('Chi')\n",
-    "plt.ylabel('Average Gate Fidelity')\n",
-    "plt.title('Fusion-based Teleportation Fidelity vs Contraction Chi')\n"
+    "plt.ylabel('Average cosine similarity')\n",
+    "plt.title('Fusion-based Teleportation similarity vs Contraction Chi')\n"
    ]
   },
   {
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   {
    "cell_type": "code",
    "execution_count": 19,
+   "id": "ccefb368",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.core.channel import Spider, Diagram\n",
+    "\n",
+    "def get_perm(n):\n",
+    "    return sorted(sorted(list(range(n))), key=lambda i: i % 2)\n",
+    "\n",
+    "def channel_fidelity(diagram_1, diagram_2):\n",
+    "    bell_1 = Channel.tensor(*[Spider(0, 2, ty) for ty in diagram_1.dom])\n",
+    "    permutation_1 = Diagram.permutation(get_perm(len(bell_1.cod)), bell_1.cod)\n",
+    "\n",
+    "    bell_2 = Channel.tensor(*[Spider(0, 2, ty) for ty in diagram_2.dom])\n",
+    "    permutation_2 = Diagram.permutation(get_perm(len(bell_2.cod)), bell_2.cod)\n",
+    "\n",
+    "    choi_1 = bell_1 >> permutation_1 >> (diagram_1 @ diagram_1.dom)\n",
+    "    choi_2 = bell_2 >> permutation_2 >> (diagram_2 @ diagram_2.dom)\n",
+    "\n",
+    "    return (choi_1 >> choi_2.dagger()).eval().tensor.array\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
    "id": "7e1a2957",
    "metadata": {},
    "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part\n",
+      "  return math.isfinite(val)\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part\n",
+      "  return np.asarray(x, float)\n"
+     ]
+    },
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@@ -5817,14 +5615,14 @@
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
     "\n",
-    "ps = np.linspace(0.0, 1.0, 20)\n",
+    "ps = np.linspace(0.05, 1.0, 20)\n",
     "\n",
     "F_avg_vals = []\n",
     "succ_probs = []\n",
     "for p in ps:\n",
-    "    S_impl = fusion_teleportation_with_photon_loss(p).eval().tensor.array\n",
-    "    S_tgt  = array_teleportation\n",
-    "    s = average_fidelity(S_impl, S_tgt, d=2)\n",
+    "    S_impl = fusion_teleportation_with_photon_loss(p)\n",
+    "    S_tgt  = fusion_teleportation_monoidal_syntax\n",
+    "    s = channel_fidelity(S_impl, S_tgt)\n",
     "\n",
     "    succ_probs.append(s)\n",
     "\n",
@@ -5832,8 +5630,8 @@
     "plt.plot(ps, succ_probs, marker='o')\n",
     "plt.grid(True)\n",
     "plt.xlabel('Photon Survival Probability (p)')\n",
-    "plt.ylabel('Average fidelity')\n",
-    "plt.title('Fusion-based Teleportation: Success Probability vs Average Fidelity')\n"
+    "plt.ylabel('Fidelity')\n",
+    "plt.title('Fusion-based Teleportation: Success Probability vs Fidelity')\n"
    ]
   },
   {
@@ -5844,6 +5642,17 @@
     "## Distributed entanglement generation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "9fa0ec11",
+   "metadata": {},
+   "source": [
+    "![Distributed entanglement](./distributed_entanglement.png \"An example of distributed entanglement generation\")\n",
+    "\n",
+    "Main, D., Drmota, P., Nadlinger, D.P. et al. Distributed quantum computing across an optical network link. Nature 638, 383–388 (2025). https://doi.org/10.1038/s41586-024-08404-x~\n",
+    "\n"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "e20c30a8",
@@ -5862,7 +5671,7 @@
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   {
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    "id": "fcbe90b6",
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    "outputs": [
@@ -5883,7 +5692,7 @@
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   {
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    "id": "bdb9611d",
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     "    normalisation = (experiment >> Discard(2)).inflate(2).eval().tensor.array\n",
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-       " </g>\n",
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-       "  </clipPath>\n",
-       " </defs>\n",
-       "</svg>\n"
-      ],
-      "text/plain": [
-       "<Figure size 600x400 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "import matplotlib.pyplot as plt\n",
-    "\n",
-    "plt.figure(figsize=(6, 4))\n",
-    "plt.plot(inner_product_states, inner_product_bell_states, marker='o')\n",
-    "plt.xlabel('<Internal state 1 | Internal state 2>')\n",
-    "plt.ylabel('<Result | Bell State> (fidelity)')\n",
-    "plt.title('Fidelity of the resulting state with the perfect Bell state')\n",
-    "plt.grid(True)\n",
-    "plt.show()"
+    "    inner_product_bell_states.append(f/normalisation)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 25,
-   "id": "06b9a545",
+   "id": "1c50f388",
    "metadata": {},
    "outputs": [
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        "    <!-- Fidelity of the resulting state with the perfect Bell state -->\n",
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@@ -10190,8 +8697,6 @@
     "plt.xlabel('<Internal state 1 | Internal state 2>')\n",
     "plt.ylabel('<Result | Bell State> (fidelity)')\n",
     "plt.title('Fidelity of the resulting state with the perfect Bell state')\n",
-    "plt.xlim(0.9, 1)\n",
-    "plt.ylim(0.9, 1)\n",
     "plt.grid(True)\n",
     "plt.show()"
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@@ -10209,7 +8714,9 @@
    "id": "e4b64d36",
    "metadata": {},
    "source": [
-    "### Graphix"
+    "### Graphix\n",
+    "\n",
+    "Open graphs only for now (graph + measurements; desire to implement deterministically - no corrections)"
    ]
   },
   {
@@ -10217,22 +8724,6 @@
    "execution_count": 26,
    "id": "79f358ae",
    "metadata": {},
-   "outputs": [],
-   "source": [
-    "import graphix\n",
-    "from optyx import qubits\n",
-    "\n",
-    "circuit = graphix.Circuit(2)\n",
-    "circuit.cnot(0, 1)\n",
-    "\n",
-    "pattern = circuit.transpile().pattern"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "id": "4888034c",
-   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
@@ -10252,7 +8743,7 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-20T15:26:10.879280</dc:date>\n",
+       "    <dc:date>2025-09-22T16:12:41.572896</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -10286,35 +8777,35 @@
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        "   </g>\n",
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@@ -10433,11 +8924,11 @@
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-       "     <path id=\"m1d741caf5e\" d=\"M 0 9.354143 \n",
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@@ -10449,13 +8940,13 @@
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        "    </g>\n",
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@@ -10467,13 +8958,13 @@
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        "    </defs>\n",
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        "    </g>\n",
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        "   <g id=\"PathCollection_3\">\n",
        "    <defs>\n",
-       "     <path id=\"mec4cf275eb\" d=\"M 0 9.354143 \n",
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@@ -10485,13 +8976,13 @@
        "z\n",
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        "    </defs>\n",
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        "   <g id=\"PathCollection_4\">\n",
        "    <defs>\n",
-       "     <path id=\"mebd4a1cc48\" d=\"M 0 9.354143 \n",
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@@ -10503,8 +8994,8 @@
        "z\n",
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        "    </defs>\n",
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@@ -10541,7 +9032,7 @@
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        "   </g>\n",
        "   <g id=\"text_1\">\n",
-       "    <g clip-path=\"url(#p2d12089205)\">\n",
+       "    <g clip-path=\"url(#pfb4929274f)\">\n",
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@@ -10572,7 +9063,7 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_2\">\n",
-       "    <g clip-path=\"url(#p2d12089205)\">\n",
+       "    <g clip-path=\"url(#pfb4929274f)\">\n",
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@@ -10596,7 +9087,7 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_3\">\n",
-       "    <g clip-path=\"url(#p2d12089205)\">\n",
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@@ -10630,7 +9121,7 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_4\">\n",
-       "    <g clip-path=\"url(#p2d12089205)\">\n",
+       "    <g clip-path=\"url(#pfb4929274f)\">\n",
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@@ -11069,7 +9560,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p2d12089205\">\n",
+       "  <clipPath id=\"pfb4929274f\">\n",
        "   <rect x=\"7.2\" y=\"7.2\" width=\"345.96\" height=\"110.88\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -11084,12 +9575,19 @@
     }
    ],
    "source": [
+    "import graphix\n",
+    "\n",
+    "circuit = graphix.Circuit(2)\n",
+    "circuit.cnot(0, 1)\n",
+    "\n",
+    "pattern = circuit.transpile().pattern\n",
+    "\n",
     "pattern.draw_graph()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 27,
    "id": "bff50dee",
    "metadata": {},
    "outputs": [],
@@ -11100,11 +9598,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 28,
    "id": "bf2d9106",
    "metadata": {},
    "outputs": [],
    "source": [
+    "from optyx import qubits\n",
+    "\n",
     "optyx_zx = qubits.Circuit(pattern)\n",
     "\n",
     "optyx_res = (\n",
@@ -11114,7 +9614,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 29,
    "id": "908e477d",
    "metadata": {},
    "outputs": [],
@@ -11131,16 +9631,6 @@
     "### Perceval circuits and processors"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "id": "07f5f7ba",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import perceval as pcvl"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "7d106d80",
@@ -11151,7 +9641,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 30,
    "id": "988c9618",
    "metadata": {},
    "outputs": [
@@ -11360,15 +9850,17 @@
        "</svg>"
       ],
       "text/plain": [
-       "<drawsvg.drawing.Drawing at 0x77f4e00d1400>"
+       "<drawsvg.drawing.Drawing at 0x796261dbd850>"
       ]
      },
-     "execution_count": 32,
+     "execution_count": 30,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
+    "import perceval as pcvl\n",
+    "\n",
     "p = pcvl.Processor(\"SLOS\", 6)\n",
     "p.add(0, pcvl.catalog[\"postprocessed cnot\"].build_processor())\n",
     "\n",
@@ -11402,7 +9894,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 31,
    "id": "96d5bf6b",
    "metadata": {},
    "outputs": [],
@@ -11424,7 +9916,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 32,
    "id": "bce649df",
    "metadata": {},
    "outputs": [],
@@ -11445,7 +9937,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 33,
    "id": "f0c1fbf3",
    "metadata": {},
    "outputs": [],
@@ -11463,7 +9955,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 34,
    "id": "463bcb6f",
    "metadata": {},
    "outputs": [],
@@ -11475,7 +9967,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 35,
    "id": "3f3fca2d",
    "metadata": {},
    "outputs": [],
@@ -11497,7 +9989,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 36,
    "id": "54633b7a",
    "metadata": {},
    "outputs": [],
@@ -11507,7 +9999,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 37,
    "id": "e019251e",
    "metadata": {},
    "outputs": [],
@@ -11523,7 +10015,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 38,
    "id": "ca6102c5",
    "metadata": {},
    "outputs": [],
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HcmV?d00001


From b983051f1144ff543493114db95e5fcdad414216 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Mon, 22 Sep 2025 17:19:40 +0100
Subject: [PATCH 19/59] fixing plot typos

---
 docs/notebooks/graphix_workshop.ipynb | 1219 ++++++++++++-------------
 1 file changed, 587 insertions(+), 632 deletions(-)

diff --git a/docs/notebooks/graphix_workshop.ipynb b/docs/notebooks/graphix_workshop.ipynb
index 37b61e36..3ffad86a 100644
--- a/docs/notebooks/graphix_workshop.ipynb
+++ b/docs/notebooks/graphix_workshop.ipynb
@@ -26,7 +26,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 41,
    "id": "13dbbb3a",
    "metadata": {},
    "outputs": [
@@ -41,7 +41,7 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-22T16:09:05.479277</dc:date>\n",
+       "    <dc:date>2025-09-22T17:00:56.423581</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -70,27 +70,27 @@
        "L 151.2 7.2 \n",
        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p65614644b3)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p82ef8c5618)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
        "    <path d=\"M 43.2 7.2 \n",
        "Q 43.2 25.2 43.2 25.2 \n",
-       "\" clip-path=\"url(#p65614644b3)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p82ef8c5618)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 115.2 7.2 \n",
        "Q 115.2 25.2 115.2 25.2 \n",
-       "\" clip-path=\"url(#p65614644b3)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p82ef8c5618)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
        "    <path d=\"M 43.2 61.2 \n",
        "Q 43.2 79.2 43.2 79.2 \n",
-       "\" clip-path=\"url(#p65614644b3)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p82ef8c5618)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_6\">\n",
        "    <path d=\"M 115.2 61.2 \n",
        "Q 115.2 79.2 115.2 79.2 \n",
-       "\" clip-path=\"url(#p65614644b3)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p82ef8c5618)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_7\">\n",
        "    <path d=\"M 25.2 61.2 \n",
@@ -98,7 +98,7 @@
        "L 133.2 25.2 \n",
        "L 133.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p65614644b3)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p82ef8c5618)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
        "    <!-- qmode -->\n",
@@ -396,7 +396,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p65614644b3\">\n",
+       "  <clipPath id=\"p82ef8c5618\">\n",
        "   <rect x=\"7.2\" y=\"7.2\" width=\"144\" height=\"72\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -420,7 +420,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 42,
    "id": "79ab4b08",
    "metadata": {},
    "outputs": [
@@ -435,7 +435,7 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-22T16:09:05.511685</dc:date>\n",
+       "    <dc:date>2025-09-22T17:00:57.109107</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -464,27 +464,27 @@
        "L 151.2 7.2 \n",
        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p12201c4d34)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p12201c4d34)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p9d6919ffad)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 115.2 133.2 \n",
        "Q 115.2 169.2 115.2 169.2 \n",
-       "\" clip-path=\"url(#p12201c4d34)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p9d6919ffad)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
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        "   </g>\n",
        "   <g id=\"patch_6\">\n",
        "    <path d=\"M 115.2 205.2 \n",
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-       "\" clip-path=\"url(#p12201c4d34)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p9d6919ffad)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -492,7 +492,7 @@
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        "z\n",
-       "\" clip-path=\"url(#p12201c4d34)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p9d6919ffad)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_8\">\n",
        "    <path d=\"M 97.2 133.2 \n",
@@ -500,7 +500,7 @@
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        "z\n",
-       "\" clip-path=\"url(#p12201c4d34)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p9d6919ffad)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_9\">\n",
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@@ -508,7 +508,7 @@
        "L 133.2 169.2 \n",
        "L 133.2 205.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p12201c4d34)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p9d6919ffad)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
        "    <!-- qmode -->\n",
@@ -957,7 +957,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p12201c4d34\">\n",
+       "  <clipPath id=\"p9d6919ffad\">\n",
        "   <rect x=\"7.2\" y=\"7.2\" width=\"144\" height=\"216\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -1000,7 +1000,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 43,
    "id": "f1478f68",
    "metadata": {},
    "outputs": [
@@ -1010,7 +1010,7 @@
        "array(-0.+0.j)"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 43,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1024,7 +1024,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 44,
    "id": "801f0884",
    "metadata": {},
    "outputs": [
@@ -1034,7 +1034,7 @@
        "{(0, 2): 0.5, (1, 1): 4.9303806576313227e-32, (2, 0): 0.5}"
       ]
      },
-     "execution_count": 4,
+     "execution_count": 44,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1053,7 +1053,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 45,
    "id": "47e64a7d",
    "metadata": {},
    "outputs": [],
@@ -1076,7 +1076,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 47,
    "id": "8fa3a149",
    "metadata": {},
    "outputs": [],
@@ -1100,7 +1100,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 51,
    "id": "8c0301af",
    "metadata": {},
    "outputs": [],
@@ -1121,7 +1121,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 52,
    "id": "174c4713",
    "metadata": {},
    "outputs": [],
@@ -1146,7 +1146,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 53,
    "id": "bb29783a",
    "metadata": {},
    "outputs": [
@@ -1156,7 +1156,7 @@
        "True"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 53,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1174,7 +1174,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 55,
    "id": "25af2db6",
    "metadata": {},
    "outputs": [
@@ -1184,7 +1184,7 @@
        "True"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 55,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1257,7 +1257,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 56,
    "id": "c557c4b8",
    "metadata": {},
    "outputs": [],
@@ -1272,7 +1272,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 57,
    "id": "a1764edb",
    "metadata": {},
    "outputs": [],
@@ -1294,7 +1294,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 58,
    "id": "7bb5e46f",
    "metadata": {},
    "outputs": [],
@@ -1315,7 +1315,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 59,
    "id": "4b5ee771",
    "metadata": {},
    "outputs": [
@@ -1330,7 +1330,7 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-22T16:09:07.230615</dc:date>\n",
+       "    <dc:date>2025-09-22T17:06:57.972030</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -1359,217 +1359,217 @@
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-       "\" clip-path=\"url(#p343a897278)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
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@@ -3038,7 +3038,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 60,
    "id": "c19354d7",
    "metadata": {},
    "outputs": [
@@ -3048,7 +3048,7 @@
        "True"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 60,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3073,7 +3073,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 62,
    "id": "51acb733",
    "metadata": {},
    "outputs": [],
@@ -3088,48 +3088,22 @@
     "    den = np.linalg.norm(a) * np.linalg.norm(b)\n",
     "    if den == 0:\n",
     "        return 0.0\n",
-    "    return float(num / den)\n",
-    "\n",
-    "def average_fidelity(SU, SV, d):\n",
-    "    Fp = process_fidelity(SU, SV)\n",
-    "    return float((d * Fp + 1) / (d + 1))"
+    "    return float(num / den)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 63,
    "id": "fb497580",
    "metadata": {},
    "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
-      "  warnings.warn(\n"
-     ]
-    },
     {
      "data": {
       "text/plain": [
-       "Text(0.5, 1.0, 'Fusion-based Teleportation Fidelity vs Contraction Chi')"
+       "Text(0.5, 1.0, 'Fusion-based Teleportation similarity vs Contraction Chi')"
       ]
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-     "execution_count": 17,
+     "execution_count": 63,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -3144,7 +3118,7 @@
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-       "    <dc:date>2025-09-22T16:11:08.655997</dc:date>\n",
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        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
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@@ -3296,11 +3270,11 @@
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@@ -3342,11 +3316,11 @@
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@@ -3362,11 +3336,11 @@
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@@ -3416,11 +3390,11 @@
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@@ -3477,11 +3451,11 @@
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@@ -4756,18 +4734,18 @@
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        "     </g>\n",
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@@ -5188,19 +5166,19 @@
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        "     </g>\n",
-       "     <g id=\"text_8\">\n",
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@@ -5208,19 +5186,19 @@
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-       "     <g id=\"text_9\">\n",
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@@ -5228,19 +5206,19 @@
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        "     </g>\n",
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        "     </g>\n",
-       "     <g id=\"text_10\">\n",
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@@ -5248,19 +5226,19 @@
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        "     </g>\n",
-       "     <g id=\"text_11\">\n",
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@@ -5268,17 +5246,17 @@
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        "    <g id=\"ytick_6\">\n",
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        "     </g>\n",
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        " <defs>\n",
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@@ -5615,7 +5580,7 @@
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
     "\n",
-    "ps = np.linspace(0.05, 1.0, 20)\n",
+    "ps = np.linspace(0.0, 1.0, 20)\n",
     "\n",
     "F_avg_vals = []\n",
     "succ_probs = []\n",
@@ -5631,7 +5596,7 @@
     "plt.grid(True)\n",
     "plt.xlabel('Photon Survival Probability (p)')\n",
     "plt.ylabel('Fidelity')\n",
-    "plt.title('Fusion-based Teleportation: Success Probability vs Fidelity')\n"
+    "plt.title('Fusion-based Teleportation: Photon Survival Probability vs Fidelity')\n"
    ]
   },
   {
@@ -5671,28 +5636,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 67,
    "id": "fcbe90b6",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[1, 0] [0, 1]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "internal_state_1 = [1, 0]\n",
-    "internal_state_2 = [0, 1]\n",
-    "\n",
-    "print(internal_state_1, internal_state_2)"
+    "internal_state_2 = [0, 1]"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 68,
    "id": "bdb9611d",
    "metadata": {},
    "outputs": [
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-       "    <dc:date>2025-09-22T16:11:48.160380</dc:date>\n",
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@@ -7194,7 +7149,7 @@
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        "   <g id=\"text_34\">\n",
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@@ -7217,7 +7172,7 @@
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        "   <g id=\"text_35\">\n",
-       "    <g clip-path=\"url(#pced80a7f19)\">\n",
+       "    <g clip-path=\"url(#p56b857efbe)\">\n",
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@@ -7243,7 +7198,7 @@
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        "   <g id=\"text_36\">\n",
-       "    <g clip-path=\"url(#pced80a7f19)\">\n",
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        "     <g transform=\"translate(465.863352 250.51125) scale(0.12 -0.12)\">\n",
        "      <use xlink:href=\"#DejaVuSans-5a\"/>\n",
@@ -7254,7 +7209,7 @@
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        "   </g>\n",
        "   <g id=\"text_37\">\n",
-       "    <g clip-path=\"url(#pced80a7f19)\">\n",
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@@ -7267,7 +7222,7 @@
        "  </g>\n",
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        " <defs>\n",
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@@ -7312,7 +7267,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 69,
    "id": "9e5c4078",
    "metadata": {},
    "outputs": [],
@@ -7337,7 +7292,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 70,
    "id": "30b96ad0",
    "metadata": {},
    "outputs": [],
@@ -7364,7 +7319,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 72,
    "id": "1c50f388",
    "metadata": {},
    "outputs": [
@@ -7379,7 +7334,7 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-22T16:12:41.489701</dc:date>\n",
+       "    <dc:date>2025-09-22T17:14:51.666648</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
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        "      <defs>\n",
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@@ -7516,11 +7471,11 @@
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@@ -7557,11 +7512,11 @@
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@@ -7609,11 +7564,11 @@
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-       "\" clip-path=\"url(#p28e97f9b12)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
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        "     </g>\n",
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        "      <g>\n",
-       "       <use xlink:href=\"#m75bc3b44c0\" x=\"302.812216\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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@@ -7670,11 +7625,11 @@
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-       "\" clip-path=\"url(#p28e97f9b12)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
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        "     <g id=\"line2d_12\">\n",
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-       "       <use xlink:href=\"#m75bc3b44c0\" x=\"363.684943\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#m05ca9b6030\" x=\"363.684943\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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@@ -7940,16 +7895,16 @@
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-       "\" clip-path=\"url(#p28e97f9b12)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
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        "     <g id=\"line2d_14\">\n",
        "      <defs>\n",
-       "       <path id=\"ma4e8e93a7e\" d=\"M 0 0 \n",
+       "       <path id=\"m9bdbad5369\" d=\"M 0 0 \n",
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        "     </g>\n",
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@@ -7992,11 +7947,11 @@
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-       "\" clip-path=\"url(#p28e97f9b12)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#pfc4c6b495d)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
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@@ -8012,11 +7967,11 @@
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@@ -8044,11 +7999,11 @@
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@@ -8064,11 +8019,11 @@
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-       "\" clip-path=\"url(#p28e97f9b12)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#pfc4c6b495d)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
        "     </g>\n",
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-       "       <use xlink:href=\"#ma4e8e93a7e\" x=\"44.103125\" y=\"72.718125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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@@ -8116,11 +8071,11 @@
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-       "\" clip-path=\"url(#p28e97f9b12)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
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@@ -8404,9 +8359,9 @@
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-       "\" clip-path=\"url(#p28e97f9b12)\" style=\"fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#pfc4c6b495d)\" style=\"fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square\"/>\n",
        "    <defs>\n",
-       "     <path id=\"mc48bf99ecc\" d=\"M 0 3 \n",
+       "     <path id=\"m00281a2979\" d=\"M 0 3 \n",
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@@ -8418,22 +8373,22 @@
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+       "     <use xlink:href=\"#m00281a2979\" x=\"221.252524\" y=\"176.933606\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "     <use xlink:href=\"#m00281a2979\" x=\"191.379739\" y=\"196.045897\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
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        "   <g id=\"patch_3\">\n",
@@ -8675,7 +8630,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p28e97f9b12\">\n",
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@@ -8721,7 +8676,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 73,
    "id": "79f358ae",
    "metadata": {},
    "outputs": [
@@ -8743,7 +8698,7 @@
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-       "    <dc:date>2025-09-22T16:12:41.572896</dc:date>\n",
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+       "\" clip-path=\"url(#pc54d94e5e6)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
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        "L 166.400086 92.36 \n",
-       "\" clip-path=\"url(#pfb4929274f)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
+       "\" clip-path=\"url(#pc54d94e5e6)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 40.024391 87.326433 \n",
        "Q 106.045262 62.640169 171.018913 38.345478 \n",
-       "\" clip-path=\"url(#pfb4929274f)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
+       "\" clip-path=\"url(#pc54d94e5e6)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
        "    <path d=\"M 166.571796 37.873085 \n",
        "L 171.018913 38.345478 \n",
        "L 167.972729 41.619735 \n",
-       "\" clip-path=\"url(#pfb4929274f)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
+       "\" clip-path=\"url(#pc54d94e5e6)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
        "   </g>\n",
        "   <g id=\"matplotlib.axis_1\">\n",
        "    <g id=\"xtick_1\"/>\n",
@@ -8924,11 +8879,11 @@
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        "L 169.081412 33.262286 \n",
        "L 170.382137 33.454569 \n",
-       "\" clip-path=\"url(#pfb4929274f)\" style=\"fill: none; stroke: #d62728; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#pc54d94e5e6)\" style=\"fill: none; stroke: #d62728; stroke-linecap: square\"/>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_1\">\n",
        "    <defs>\n",
-       "     <path id=\"m9b8ffc2ff8\" d=\"M 0 9.354143 \n",
+       "     <path id=\"mb50a492a97\" d=\"M 0 9.354143 \n",
        "C 2.480748 9.354143 4.860225 8.368532 6.614378 6.614378 \n",
        "C 8.368532 4.860225 9.354143 2.480748 9.354143 0 \n",
        "C 9.354143 -2.480748 8.368532 -4.860225 6.614378 -6.614378 \n",
@@ -8940,13 +8895,13 @@
        "z\n",
        "\" style=\"stroke: #ff0000\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#pfb4929274f)\">\n",
-       "     <use xlink:href=\"#m9b8ffc2ff8\" x=\"180.18\" y=\"90.36\" style=\"fill: #d3d3d3; stroke: #ff0000\"/>\n",
+       "    <g clip-path=\"url(#pc54d94e5e6)\">\n",
+       "     <use xlink:href=\"#mb50a492a97\" x=\"180.18\" y=\"90.36\" style=\"fill: #d3d3d3; stroke: #ff0000\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_2\">\n",
        "    <defs>\n",
-       "     <path id=\"m309266ec36\" d=\"M 0 9.354143 \n",
+       "     <path id=\"mde32974aea\" d=\"M 0 9.354143 \n",
        "C 2.480748 9.354143 4.860225 8.368532 6.614378 6.614378 \n",
        "C 8.368532 4.860225 9.354143 2.480748 9.354143 0 \n",
        "C 9.354143 -2.480748 8.368532 -4.860225 6.614378 -6.614378 \n",
@@ -8958,13 +8913,13 @@
        "z\n",
        "\" style=\"stroke: #ff0000\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#pfb4929274f)\">\n",
-       "     <use xlink:href=\"#m309266ec36\" x=\"31.911429\" y=\"90.36\" style=\"fill: #add8e6; stroke: #ff0000\"/>\n",
+       "    <g clip-path=\"url(#pc54d94e5e6)\">\n",
+       "     <use xlink:href=\"#mde32974aea\" x=\"31.911429\" y=\"90.36\" style=\"fill: #add8e6; stroke: #ff0000\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_3\">\n",
        "    <defs>\n",
-       "     <path id=\"m144a483857\" d=\"M 0 9.354143 \n",
+       "     <path id=\"m07d0988678\" d=\"M 0 9.354143 \n",
        "C 2.480748 9.354143 4.860225 8.368532 6.614378 6.614378 \n",
        "C 8.368532 4.860225 9.354143 2.480748 9.354143 0 \n",
        "C 9.354143 -2.480748 8.368532 -4.860225 6.614378 -6.614378 \n",
@@ -8976,13 +8931,13 @@
        "z\n",
        "\" style=\"stroke: #000000\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#pfb4929274f)\">\n",
-       "     <use xlink:href=\"#m144a483857\" x=\"31.911429\" y=\"34.92\" style=\"fill: #add8e6; stroke: #000000\"/>\n",
+       "    <g clip-path=\"url(#pc54d94e5e6)\">\n",
+       "     <use xlink:href=\"#m07d0988678\" x=\"31.911429\" y=\"34.92\" style=\"fill: #add8e6; stroke: #000000\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_4\">\n",
        "    <defs>\n",
-       "     <path id=\"m11ceddbdb0\" d=\"M 0 9.354143 \n",
+       "     <path id=\"m20a1087d5c\" d=\"M 0 9.354143 \n",
        "C 2.480748 9.354143 4.860225 8.368532 6.614378 6.614378 \n",
        "C 8.368532 4.860225 9.354143 2.480748 9.354143 0 \n",
        "C 9.354143 -2.480748 8.368532 -4.860225 6.614378 -6.614378 \n",
@@ -8994,8 +8949,8 @@
        "z\n",
        "\" style=\"stroke: #000000\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#pfb4929274f)\">\n",
-       "     <use xlink:href=\"#m11ceddbdb0\" x=\"180.18\" y=\"34.92\" style=\"fill: #d3d3d3; stroke: #000000\"/>\n",
+       "    <g clip-path=\"url(#pc54d94e5e6)\">\n",
+       "     <use xlink:href=\"#m20a1087d5c\" x=\"180.18\" y=\"34.92\" style=\"fill: #d3d3d3; stroke: #000000\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"line2d_2\"/>\n",
@@ -9032,7 +8987,7 @@
        "\" style=\"fill: none; stroke: #d62728; stroke-linecap: round\"/>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
-       "    <g clip-path=\"url(#pfb4929274f)\">\n",
+       "    <g clip-path=\"url(#pc54d94e5e6)\">\n",
        "     <!-- 0 -->\n",
        "     <g transform=\"translate(176.3625 93.67125) scale(0.12 -0.12)\">\n",
        "      <defs>\n",
@@ -9063,7 +9018,7 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_2\">\n",
-       "    <g clip-path=\"url(#pfb4929274f)\">\n",
+       "    <g clip-path=\"url(#pc54d94e5e6)\">\n",
        "     <!-- 1 -->\n",
        "     <g transform=\"translate(28.093929 93.67125) scale(0.12 -0.12)\">\n",
        "      <defs>\n",
@@ -9087,7 +9042,7 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_3\">\n",
-       "    <g clip-path=\"url(#pfb4929274f)\">\n",
+       "    <g clip-path=\"url(#pc54d94e5e6)\">\n",
        "     <!-- 2 -->\n",
        "     <g transform=\"translate(28.093929 38.23125) scale(0.12 -0.12)\">\n",
        "      <defs>\n",
@@ -9121,7 +9076,7 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_4\">\n",
-       "    <g clip-path=\"url(#pfb4929274f)\">\n",
+       "    <g clip-path=\"url(#pc54d94e5e6)\">\n",
        "     <!-- 3 -->\n",
        "     <g transform=\"translate(176.3625 38.23125) scale(0.12 -0.12)\">\n",
        "      <defs>\n",
@@ -9560,7 +9515,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"pfb4929274f\">\n",
+       "  <clipPath id=\"pc54d94e5e6\">\n",
        "   <rect x=\"7.2\" y=\"7.2\" width=\"345.96\" height=\"110.88\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -9587,7 +9542,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 74,
    "id": "bff50dee",
    "metadata": {},
    "outputs": [],
@@ -9598,7 +9553,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 75,
    "id": "bf2d9106",
    "metadata": {},
    "outputs": [],
@@ -9614,7 +9569,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 76,
    "id": "908e477d",
    "metadata": {},
    "outputs": [],
@@ -9641,7 +9596,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 77,
    "id": "988c9618",
    "metadata": {},
    "outputs": [
@@ -9850,10 +9805,10 @@
        "</svg>"
       ],
       "text/plain": [
-       "<drawsvg.drawing.Drawing at 0x796261dbd850>"
+       "<drawsvg.drawing.Drawing at 0x796261bd98e0>"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 77,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -9894,7 +9849,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 78,
    "id": "96d5bf6b",
    "metadata": {},
    "outputs": [],
@@ -9916,7 +9871,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 79,
    "id": "bce649df",
    "metadata": {},
    "outputs": [],
@@ -9937,7 +9892,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 80,
    "id": "f0c1fbf3",
    "metadata": {},
    "outputs": [],
@@ -9955,7 +9910,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 81,
    "id": "463bcb6f",
    "metadata": {},
    "outputs": [],
@@ -9967,7 +9922,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 82,
    "id": "3f3fca2d",
    "metadata": {},
    "outputs": [],
@@ -9989,7 +9944,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 83,
    "id": "54633b7a",
    "metadata": {},
    "outputs": [],
@@ -9999,7 +9954,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 84,
    "id": "e019251e",
    "metadata": {},
    "outputs": [],
@@ -10015,7 +9970,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 85,
    "id": "ca6102c5",
    "metadata": {},
    "outputs": [],

From 573693033fb65b5f7f541c11d51461a30267d3dc Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Mon, 22 Sep 2025 17:31:33 +0100
Subject: [PATCH 20/59] fix rounding issue with backends

---
 optyx/core/backends.py | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/optyx/core/backends.py b/optyx/core/backends.py
index ab9e1565..1d01c668 100644
--- a/optyx/core/backends.py
+++ b/optyx/core/backends.py
@@ -205,15 +205,17 @@ def _convert_array_to_dict(
         entries of an array.
         """
 
-        if round_digits is not None:
-            array = np.round(array, round_digits)
-
         nz_flat = np.flatnonzero(array)
         if nz_flat.size == 0:
             return {}
 
         nz_vals = array.flat[nz_flat]
         nz_multi = np.vstack(np.unravel_index(nz_flat, array.shape)).T
+
+        if round_digits is not None:
+            return {tuple(idx): np.round(val, round_digits) for
+                    idx, val in zip(nz_multi, nz_vals)}
+
         return {tuple(idx): val for idx, val in zip(nz_multi, nz_vals)}
 
     def _prob_dist_pure(self, round_digits: int = None) -> dict:

From dceb26600033728614f36d94e73e990180b52414 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Mon, 22 Sep 2025 17:53:55 +0100
Subject: [PATCH 21/59] add comments to readme

---
 docs/notebooks/graphix_workshop.ipynb | 9182 +------------------------
 1 file changed, 79 insertions(+), 9103 deletions(-)

diff --git a/docs/notebooks/graphix_workshop.ipynb b/docs/notebooks/graphix_workshop.ipynb
index 3ffad86a..d14950c8 100644
--- a/docs/notebooks/graphix_workshop.ipynb
+++ b/docs/notebooks/graphix_workshop.ipynb
@@ -26,954 +26,29 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": null,
    "id": "13dbbb3a",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/svg+xml": [
-       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
-       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
-       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
-       "<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"161.609375pt\" height=\"86.4pt\" viewBox=\"0 0 161.609375 86.4\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
-       " <metadata>\n",
-       "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
-       "   <cc:Work>\n",
-       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-22T17:00:56.423581</dc:date>\n",
-       "    <dc:format>image/svg+xml</dc:format>\n",
-       "    <dc:creator>\n",
-       "     <cc:Agent>\n",
-       "      <dc:title>Matplotlib v3.10.5, https://matplotlib.org/</dc:title>\n",
-       "     </cc:Agent>\n",
-       "    </dc:creator>\n",
-       "   </cc:Work>\n",
-       "  </rdf:RDF>\n",
-       " </metadata>\n",
-       " <defs>\n",
-       "  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n",
-       " </defs>\n",
-       " <g id=\"figure_1\">\n",
-       "  <g id=\"patch_1\">\n",
-       "   <path d=\"M 0 86.4 \n",
-       "L 161.609375 86.4 \n",
-       "L 161.609375 0 \n",
-       "L 0 0 \n",
-       "z\n",
-       "\" style=\"fill: #ffffff\"/>\n",
-       "  </g>\n",
-       "  <g id=\"axes_1\">\n",
-       "   <g id=\"patch_2\">\n",
-       "    <path d=\"M 7.2 79.2 \n",
-       "L 151.2 79.2 \n",
-       "L 151.2 7.2 \n",
-       "L 7.2 7.2 \n",
-       "z\n",
-       "\" clip-path=\"url(#p82ef8c5618)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
-       "   </g>\n",
-       "   <g id=\"patch_3\">\n",
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+   "outputs": [],
    "source": [
     "from optyx.photonic import BBS\n",
     "\n",
+    "# diagram generators:\n",
+    "# beam-splitter\n",
     "beam_splitter = BBS(0)\n",
-    "\n",
     "beam_splitter.draw()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": null,
    "id": "79ab4b08",
    "metadata": {},
-   "outputs": [
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-      "text/plain": [
-       "<Figure size 200x300 with 1 Axes>"
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-     },
-     "metadata": {},
-     "output_type": "display_data"
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-   ],
+   "outputs": [],
    "source": [
     "from optyx.photonic import Create\n",
     "\n",
+    "# diagram composition with function syntax\n",
     "hong_ou_mandel = (\n",
     "    Create(1) @ Create(1) >>\n",
     "    beam_splitter\n",
@@ -1000,22 +75,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": null,
    "id": "f1478f68",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array(-0.+0.j)"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
+    "# an amplitude (raw result of tensor contraction)\n",
     "from optyx.classical import Select\n",
     "(\n",
     "    hong_ou_mandel >> Select(1, 1)\n",
@@ -1024,21 +89,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": null,
    "id": "801f0884",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "{(0, 2): 0.5, (1, 1): 4.9303806576313227e-32, (2, 0): 0.5}"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "hong_ou_mandel.eval().prob_dist()"
    ]
@@ -1053,7 +107,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": null,
    "id": "47e64a7d",
    "metadata": {},
    "outputs": [],
@@ -1076,11 +130,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": null,
    "id": "8fa3a149",
    "metadata": {},
    "outputs": [],
    "source": [
+    "# function syntax\n",
+    "# CNOT from ZX generators\n",
+    "\n",
     "@Channel.from_callable(\n",
     "  dom=qubit @ qubit, cod=qubit @ qubit\n",
     ")\n",
@@ -1100,7 +157,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
+   "execution_count": null,
    "id": "8c0301af",
    "metadata": {},
    "outputs": [],
@@ -1121,11 +178,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
+   "execution_count": null,
    "id": "174c4713",
    "metadata": {},
    "outputs": [],
    "source": [
+    "# function syntax avoids explicit swaps and identity wires\n",
+    "\n",
     "teleportation_monoidal_syntax = (\n",
     "    qubit @ bell >>\n",
     "    cnot @ qubit >>\n",
@@ -1146,50 +205,31 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
+   "execution_count": null,
    "id": "bb29783a",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "from optyx.qubits import Id\n",
     "\n",
+    "# both implementations are equivalent\n",
     "np.allclose(\n",
     "    teleportation.eval().tensor.array,\n",
-    "    Id(1).double().to_tensor().eval().array,\n",
-    "    teleportation_monoidal_syntax.eval().tensor.array\n",
+    "    teleportation_monoidal_syntax.eval().tensor.array,\n",
+    "    Id(1).double().to_tensor().eval().array\n",
     ")"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": null,
    "id": "25af2db6",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 55,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
+    "# backends (Perceval, Discopy, Quimb)\n",
+    "\n",
     "from optyx.core.backends import (\n",
     "    DiscopyBackend,\n",
     "    QuimbBackend\n",
@@ -1257,7 +297,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
+   "execution_count": null,
    "id": "c557c4b8",
    "metadata": {},
    "outputs": [],
@@ -1272,7 +312,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
+   "execution_count": null,
    "id": "a1764edb",
    "metadata": {},
    "outputs": [],
@@ -1294,7 +334,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": null,
    "id": "7bb5e46f",
    "metadata": {},
    "outputs": [],
@@ -1315,1707 +355,10 @@
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   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": null,
    "id": "4b5ee771",
    "metadata": {},
-   "outputs": [
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-       "<Figure size 800x800 with 1 Axes>"
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-     },
-     "metadata": {},
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-   ],
+   "outputs": [],
    "source": [
     "from optyx.photonic import FusionTypeII\n",
     "\n",
@@ -3038,21 +381,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": null,
    "id": "c19354d7",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "from optyx.photonic import Id\n",
@@ -3073,7 +405,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 62,
+   "execution_count": null,
    "id": "51acb733",
    "metadata": {},
    "outputs": [],
@@ -3081,8 +413,7 @@
     "def _flat(x):\n",
     "    return np.asarray(x, dtype=complex).ravel()\n",
     "\n",
-    "# cosine similarity of pure unitary channels as superoperators\n",
-    "def process_fidelity(SU, SV):\n",
+    "def cosine_similarity(SU, SV):\n",
     "    a, b = _flat(SU), _flat(SV)\n",
     "    num = abs(np.vdot(a, b))\n",
     "    den = np.linalg.norm(a) * np.linalg.norm(b)\n",
@@ -3093,1241 +424,14 @@
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   {
    "cell_type": "code",
-   "execution_count": 63,
+   "execution_count": null,
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-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from cotengra import HyperCompressedOptimizer\n",
     "\n",
+    "# cosine similarity between the result of exact contaction and approximate contraction for different chis\n",
     "errors = []\n",
     "for chi in range(1, 6):\n",
     "    optimiser = HyperCompressedOptimizer(\n",
@@ -4336,7 +440,7 @@
     "    error_for_chi = []\n",
     "    for _ in range(10):\n",
     "         error_for_chi.append(\n",
-    "             process_fidelity(\n",
+    "             cosine_similarity(\n",
     "                 fusion_teleportation.eval(QuimbBackend(optimiser)).tensor.array,\n",
     "                 array_teleportation\n",
     "             )\n",
@@ -4361,13 +465,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 64,
+   "execution_count": null,
    "id": "ac439493",
    "metadata": {},
    "outputs": [],
    "source": [
     "from optyx.photonic import FusionTypeII, PhotonLoss\n",
     "\n",
+    "# photo loss is one of the main error sources in photonic quantum computing\n",
     "def fusion_teleportation_with_photon_loss(p):\n",
     "    @Channel.from_callable(\n",
     "        dom=qubit, cod=qmode**2\n",
@@ -4375,9 +480,12 @@
     "    def fusion_teleportation(a):\n",
     "        dr_input_1, dr_input_2 = DualRail(1)(a)\n",
     "        b, c, d, e = dual_rail_encoded_bell()\n",
+    "        # apply photon loss to all modes here:\n",
+    "        #-----------------------------------\n",
     "        dr_input_1_loss, dr_input_2_loss, b_loss, c_loss, d_loss, e_loss = (\n",
     "            PhotonLoss(p)(dr_input_1), PhotonLoss(p)(dr_input_2), PhotonLoss(p)(b), PhotonLoss(p)(c), PhotonLoss(p)(d), PhotonLoss(p)(e)\n",
     "        )\n",
+    "        #-----------------------------------\n",
     "        s, k = FusionTypeII()(dr_input_1_loss, dr_input_2_loss, b_loss, c_loss)\n",
     "        fusion_failure_processing(s)\n",
     "        output_rail_1, output_rail = correction(k, d_loss, e_loss)\n",
@@ -4387,7 +495,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 65,
+   "execution_count": null,
    "id": "ccefb368",
    "metadata": {},
    "outputs": [],
@@ -4412,1176 +520,17 @@
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   {
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+   "execution_count": null,
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-   "outputs": [
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-     "output_type": "stream",
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-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part\n",
-      "  return math.isfinite(val)\n",
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part\n",
-      "  return np.asarray(x, float)\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "Text(0.5, 1.0, 'Fusion-based Teleportation: Photon Survival Probability vs Fidelity')"
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+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
     "\n",
     "ps = np.linspace(0.0, 1.0, 20)\n",
     "\n",
+    "# compute fidelity for different photon loss probabilities\n",
     "F_avg_vals = []\n",
     "succ_probs = []\n",
     "for p in ps:\n",
@@ -5636,1606 +585,10 @@
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+   "outputs": [],
    "source": [
     "from optyx.qubits import Z, Scalar, Id, Measure\n",
     "from optyx.photonic import DualRail\n",
@@ -7243,9 +596,14 @@
     "from discopy.drawing import Equation\n",
     "\n",
     "bell_state = Z(0, 2) @ Scalar(0.5 ** 0.5)\n",
+    "\n",
+    "# generators introducing new qubits accepting internal states\n",
+    "internal_state_1 = [1, 0]\n",
+    "internal_state_2 = [0, 1]\n",
     "dual_rail_encoding = lambda state: DualRail(1, internal_states=[state])\n",
     "encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(internal_state_2)\n",
     "\n",
+    "# postselect on fusion success and no errors\n",
     "post_select = PostselectBit(1) @ PostselectBit(0)\n",
     "\n",
     "protocol = (\n",
@@ -7267,13 +625,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 69,
+   "execution_count": null,
    "id": "9e5c4078",
    "metadata": {},
    "outputs": [],
    "source": [
     "import math\n",
     "\n",
+    "# internal states - 2 dimensional - move further and further apart\n",
     "def rotated_unit_vectors(n: int = 10):\n",
     "    for i in range(n):\n",
     "        theta = i * (math.pi / 2) / (n - 1)\n",
@@ -7292,7 +651,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 70,
+   "execution_count": null,
    "id": "30b96ad0",
    "metadata": {},
    "outputs": [],
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-      "text/plain": [
-       "<Figure size 600x400 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "\n",
@@ -8676,859 +714,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 73,
+   "execution_count": null,
    "id": "79f358ae",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The pattern is not consistent with flow or gflow structure.\n"
-     ]
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+   "outputs": [],
    "source": [
     "import graphix\n",
     "\n",
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-       "<path d=\"M28,275 L72,375\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M25,275 L28,275 L72,375 L75,375\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M77,2 L473,2 L473,298 L77,298 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"79\" y=\"305\" font-size=\"8\" text-anchor=\"start\">POSTPROCESSED CNOT</text>\n",
-       "<path d=\"M25,125 L53,125 L72,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M78,144 L97,125 L125,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M25,175 L53,175 L72,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M78,156 L97,175 L125,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M50,143 L100,143 L100,157 L50,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"75\" y=\"185\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<text x=\"75\" y=\"126\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<path d=\"M50,143 L100,143 L100,147 L50,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M93,150 L103,150 L103,160 L93,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"98\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
-       "<path d=\"M25,75.0 L125,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M128,75 L172,175\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M125,75 L128,75 L172,175 L175,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M128,125 L172,125\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M125,125 L128,125 L172,125 L175,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M128,175 L172,225\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M125,175 L128,175 L172,225 L175,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M25,25.0 L175,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M175,25 L203,25 L222,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M228,44 L247,25 L275,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M175,75 L203,75 L222,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M228,56 L247,75 L275,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M200,43 L250,43 L250,57 L200,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"225\" y=\"80\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<text x=\"225\" y=\"26\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
-       "<path d=\"M200,43 L250,43 L250,47 L200,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M243,50 L253,50 L253,60 L243,60 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"248\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
-       "<path d=\"M175,125 L203,125 L222,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M228,144 L247,125 L275,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M175,175 L203,175 L222,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M228,156 L247,175 L275,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M200,143 L250,143 L250,157 L200,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"225\" y=\"180\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<text x=\"225\" y=\"126\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
-       "<path d=\"M200,143 L250,143 L250,147 L200,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M243,150 L253,150 L253,160 L243,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"248\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
-       "<path d=\"M175,225 L203,225 L222,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M228,244 L247,225 L275,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M175,275 L203,275 L222,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M228,256 L247,275 L275,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M200,243 L250,243 L250,257 L200,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"225\" y=\"280\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<text x=\"225\" y=\"226\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
-       "<path d=\"M200,243 L250,243 L250,247 L200,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M243,250 L253,250 L253,260 L243,260 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"248\" y=\"257\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
-       "<path d=\"M278,125 L322,125\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M275,125 L278,125 L322,125 L325,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M278,175 L322,75\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M275,175 L278,175 L322,75 L325,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M278,225 L322,175\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M275,225 L278,225 L322,175 L325,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M325,125 L353,125 L372,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M378,144 L397,125 L425,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M325,175 L353,175 L372,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M378,156 L397,175 L425,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M350,143 L400,143 L400,157 L350,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"375\" y=\"185\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<text x=\"375\" y=\"126\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<path d=\"M350,143 L400,143 L400,147 L350,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M393,150 L403,150 L403,160 L393,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"398\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
-       "<path d=\"M275,25.0 L425,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M325,75.0 L425,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M75,325.0 L425,325.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M75,375.0 L425,375.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M428,325 L472,225\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M425,325 L428,325 L472,225 L475,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M428,375 L472,275\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
-       "<path d=\"M425,375 L428,375 L472,275 L475,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M425,25 L453,25 L472,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M478,44 L497,25 L525,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M425,75 L453,75 L472,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M478,56 L497,75 L525,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M450,43 L500,43 L500,57 L450,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"475\" y=\"85\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<text x=\"475\" y=\"26\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
-       "<path d=\"M450,43 L500,43 L500,47 L450,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M493,50 L503,50 L503,60 L493,60 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"498\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
-       "<path d=\"M425,125.0 L525,125.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M425,175.0 L525,175.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M475,225.0 L525,225.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M475,275.0 L525,275.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M525,25 L575,25\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M525,75 L575,75\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M549,10 L551,10 L551,90 L549,90 Z\" stroke=\"dimgrey\" fill=\"dimgrey\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M525,225 L575,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M525,275 L575,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M549,210 L551,210 L551,290 L549,290 Z\" stroke=\"dimgrey\" fill=\"dimgrey\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M525,125 L550,125\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M550,125 L575,125\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M545,135 L537,135 L537,115 L545,115 C545,115,555,115,555,125 C555,135,545,135,545,135 L545,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
-       "<text x=\"537\" y=\"112\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
-       "<path d=\"M525,175 L550,175\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M550,175 L575,175\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M545,185 L537,185 L537,165 L545,165 C545,165,555,165,555,175 C555,185,545,185,545,185 L545,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
-       "<text x=\"537\" y=\"162\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
-       "<path d=\"M575,125 L675,125\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M575,175 L675,175\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M625,190.0 L625,205.0\" stroke=\"white\" stroke-width=\"5\" fill=\"none\" />\n",
-       "<path d=\"M625,190.0 L625,205.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" stroke-dasharray=\"4,4\" />\n",
-       "<path d=\"M625,198.0 L622,195.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M625,198.0 L628,195.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M580,110 L670,110 L670,190 L580,190 Z\" stroke=\"black\" fill=\"lightgreen\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"625\" y=\"155.0\" font-size=\"10\" text-anchor=\"middle\">FFC</text>\n",
-       "<path d=\"M575,225 L675,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M575,275 L675,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M580,205 L670,205 L670,295 L580,295 Z\" stroke=\"black\" fill=\"lightyellow\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"625\" y=\"250\" font-size=\"10\" text-anchor=\"middle\">U(FFC)</text>\n",
-       "<path d=\"M575,25.0 L675,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M575,75.0 L675,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M675,125 L725,125\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M675,175 L725,175\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M675,225 L725,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M675,275 L725,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M699,110 L701,110 L701,290 L699,290 Z\" stroke=\"dimgrey\" fill=\"dimgrey\" stroke-linejoin=\"miter\" />\n",
-       "<path d=\"M675,25.0 L725,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M675,75.0 L725,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M725,25 L750,25\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M750,25 L775,25\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M745,35 L737,35 L737,15 L745,15 C745,15,755,15,755,25 C755,35,745,35,745,35 L745,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
-       "<text x=\"737\" y=\"12\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
-       "<path d=\"M725,75 L750,75\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M750,75 L775,75\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M745,85 L737,85 L737,65 L745,65 C745,65,755,65,755,75 C755,85,745,85,745,85 L745,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
-       "<text x=\"737\" y=\"62\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
-       "<path d=\"M775,25 L825,25\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M775,75 L825,75\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M800,90.0 L800,255.0\" stroke=\"white\" stroke-width=\"5\" fill=\"none\" />\n",
-       "<path d=\"M800,90.0 L800,255.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" stroke-dasharray=\"4,4\" />\n",
-       "<path d=\"M800,98.0 L797,95.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M800,98.0 L803,95.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M780,10 L820,10 L820,90 L780,90 Z\" stroke=\"black\" fill=\"lightgreen\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"800\" y=\"55.0\" font-size=\"10\" text-anchor=\"middle\">FFC</text>\n",
-       "<path d=\"M725,275 L775,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M730,290 L739,290 L753,260 L744,260 L730,290 L739,290 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"747\" y=\"288\" font-size=\"7\" text-anchor=\"start\">Φ=phi</text>\n",
-       "<path d=\"M725,125.0 L825,125.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M725,175.0 L825,175.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M725,225.0 L825,225.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M775,275.0 L825,275.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
-       "<path d=\"M825,25.0 L840,25.0\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M825,75.0 L840,75.0\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M825,125.0 L840,125.0\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M825,175.0 L840,175.0\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M825,225.0 L840,225.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M825,275.0 L840,275.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
-       "<path d=\"M157,75 C157,75,157,65,167,65 L175,65 L175,85 L167,85 C157,85,157,75,157,75 L157,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n",
-       "<text x=\"163\" y=\"91\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\">[herald0]</text>\n",
-       "<text x=\"167\" y=\"78\" font-size=\"7\" text-anchor=\"middle\">0</text>\n",
-       "<path d=\"M157,275 C157,275,157,265,167,265 L175,265 L175,285 L167,285 C157,285,157,275,157,275 L157,275\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n",
-       "<text x=\"163\" y=\"291\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\">[herald1]</text>\n",
-       "<text x=\"167\" y=\"278\" font-size=\"7\" text-anchor=\"middle\">0</text>\n",
-       "<path d=\"M-2,15 L10,15 L10,85 L-2,85 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"-2\" y=\"91\" font-size=\"6\" text-anchor=\"start\" font-style=\"italic\">[ctrl]</text>\n",
-       "<path d=\"M-2,115 L10,115 L10,185 L-2,185 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"-2\" y=\"191\" font-size=\"6\" text-anchor=\"start\" font-style=\"italic\">[data]</text>\n",
-       "<path d=\"M840,15 L852,15 L852,85 L840,85 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"852\" y=\"91\" font-size=\"6\" text-anchor=\"end\" font-style=\"italic\">[ctrl]</text>\n",
-       "<path d=\"M840,115 L852,115 L852,185 L840,185 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
-       "<text x=\"852\" y=\"191\" font-size=\"6\" text-anchor=\"end\" font-style=\"italic\">[data]</text>\n",
-       "<path d=\"M283,85 L275,85 L275,65 L283,65 C283,65,293,65,293,75 C293,85,283,85,283,85 L283,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n",
-       "<text x=\"288\" y=\"61\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\">[herald0]</text>\n",
-       "<text x=\"283\" y=\"78\" font-size=\"7\" text-anchor=\"middle\">0</text>\n",
-       "<path d=\"M283,285 L275,285 L275,265 L283,265 C283,265,293,265,293,275 C293,285,283,285,283,285 L283,285\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n",
-       "<text x=\"288\" y=\"261\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\">[herald1]</text>\n",
-       "<text x=\"283\" y=\"278\" font-size=\"7\" text-anchor=\"middle\">0</text>\n",
-       "<text x=\"850\" y=\"28.0\" font-size=\"9\" text-anchor=\"end\">0</text>\n",
-       "<text x=\"850\" y=\"78.0\" font-size=\"9\" text-anchor=\"end\">1</text>\n",
-       "<text x=\"850\" y=\"128.0\" font-size=\"9\" text-anchor=\"end\">2</text>\n",
-       "<text x=\"850\" y=\"178.0\" font-size=\"9\" text-anchor=\"end\">3</text>\n",
-       "<text x=\"850\" y=\"228.0\" font-size=\"9\" text-anchor=\"end\">4</text>\n",
-       "<text x=\"850\" y=\"278.0\" font-size=\"9\" text-anchor=\"end\">5</text>\n",
-       "<text x=\"0\" y=\"28.0\" font-size=\"9\" text-anchor=\"start\">0</text>\n",
-       "<text x=\"0\" y=\"78.0\" font-size=\"9\" text-anchor=\"start\">1</text>\n",
-       "<text x=\"0\" y=\"128.0\" font-size=\"9\" text-anchor=\"start\">2</text>\n",
-       "<text x=\"0\" y=\"178.0\" font-size=\"9\" text-anchor=\"start\">3</text>\n",
-       "<text x=\"0\" y=\"228.0\" font-size=\"9\" text-anchor=\"start\">4</text>\n",
-       "<text x=\"0\" y=\"278.0\" font-size=\"9\" text-anchor=\"start\">5</text>\n",
-       "</svg>"
-      ],
-      "text/plain": [
-       "<drawsvg.drawing.Drawing at 0x796261bd98e0>"
-      ]
-     },
-     "execution_count": 77,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import perceval as pcvl\n",
     "\n",
@@ -9849,7 +825,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 78,
+   "execution_count": null,
    "id": "96d5bf6b",
    "metadata": {},
    "outputs": [],
@@ -9871,7 +847,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 79,
+   "execution_count": null,
    "id": "bce649df",
    "metadata": {},
    "outputs": [],
@@ -9892,7 +868,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 80,
+   "execution_count": null,
    "id": "f0c1fbf3",
    "metadata": {},
    "outputs": [],
@@ -9910,7 +886,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 81,
+   "execution_count": null,
    "id": "463bcb6f",
    "metadata": {},
    "outputs": [],
@@ -9922,7 +898,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 82,
+   "execution_count": null,
    "id": "3f3fca2d",
    "metadata": {},
    "outputs": [],
@@ -9944,7 +920,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 83,
+   "execution_count": null,
    "id": "54633b7a",
    "metadata": {},
    "outputs": [],
@@ -9954,7 +930,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 84,
+   "execution_count": null,
    "id": "e019251e",
    "metadata": {},
    "outputs": [],
@@ -9970,7 +946,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 85,
+   "execution_count": null,
    "id": "ca6102c5",
    "metadata": {},
    "outputs": [],

From a1c8375775e6a5d950488f4b24da25a191ed739a Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Tue, 23 Sep 2025 13:10:25 +0100
Subject: [PATCH 22/59] rename readme notebook

---
 docs/notebooks/readme_example.ipynb | 10075 ++++++++++++++++++++++++++
 1 file changed, 10075 insertions(+)
 create mode 100644 docs/notebooks/readme_example.ipynb

diff --git a/docs/notebooks/readme_example.ipynb b/docs/notebooks/readme_example.ipynb
new file mode 100644
index 00000000..c05af05a
--- /dev/null
+++ b/docs/notebooks/readme_example.ipynb
@@ -0,0 +1,10075 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "0d360e60",
+   "metadata": {},
+   "source": [
+    "# Optyx: A ZX-based Python library for networked quantum architectures"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b1adf8d9",
+   "metadata": {},
+   "source": [
+    "## Hong-Ou-Mandel effect"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6f3dab5d",
+   "metadata": {},
+   "source": [
+    "### Experiment definition"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "13dbbb3a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/svg+xml": [
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+       " <metadata>\n",
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+       "   <cc:Work>\n",
+       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
+       "    <dc:date>2025-09-23T09:38:17.988554</dc:date>\n",
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+       "    <dc:creator>\n",
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+       " </metadata>\n",
+       " <defs>\n",
+       "  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n",
+       " </defs>\n",
+       " <g id=\"figure_1\">\n",
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+       " </g>\n",
+       " <defs>\n",
+       "  <clipPath id=\"pcb02312399\">\n",
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+       "  </clipPath>\n",
+       " </defs>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 200x100 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from optyx.photonic import BBS\n",
+    "\n",
+    "# diagram generators:\n",
+    "# beam-splitter\n",
+    "beam_splitter = BBS(0)\n",
+    "beam_splitter.draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "79ab4b08",
+   "metadata": {},
+   "outputs": [
+    {
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+       " </g>\n",
+       " <defs>\n",
+       "  <clipPath id=\"pb5ed9dbb53\">\n",
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+       "  </clipPath>\n",
+       " </defs>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 200x300 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from optyx.photonic import Create\n",
+    "\n",
+    "# diagram composition with monoidal syntax\n",
+    "hong_ou_mandel = (\n",
+    "    Create(1) @ Create(1) >>\n",
+    "    beam_splitter\n",
+    ")\n",
+    "\n",
+    "hong_ou_mandel.draw()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a869643c",
+   "metadata": {},
+   "source": [
+    " ![HOM](./hom.png \"Hong-Ou-Mandel Effect\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "94bfc225",
+   "metadata": {},
+   "source": [
+    "### Diagram evaluation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "f1478f68",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array(-0.+0.j)"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# an amplitude (raw result of tensor contraction)\n",
+    "from optyx.classical import Select\n",
+    "(\n",
+    "    hong_ou_mandel >> Select(1, 1)\n",
+    ").eval().tensor.array"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "801f0884",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{(0, 2): 0.5, (1, 1): 4.9303806576313227e-32, (2, 0): 0.5}"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "hong_ou_mandel.eval().prob_dist()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b1f34bd2",
+   "metadata": {},
+   "source": [
+    "## Qubit teleportation - function syntax and backends"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "47e64a7d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx import qubit, bit\n",
+    "from optyx.qubits import Scalar\n",
+    "\n",
+    "from optyx import Channel\n",
+    "from optyx.qubits import Z, X, H, Measure, Scalar, qubit, bit\n",
+    "from optyx.classical import BitControlledGate"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "748d7e3d",
+   "metadata": {},
+   "source": [
+    "### Define the protocol"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "8fa3a149",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# function syntax\n",
+    "# CNOT from ZX generators\n",
+    "\n",
+    "@Channel.from_callable(\n",
+    "  dom=qubit @ qubit, cod=qubit @ qubit\n",
+    ")\n",
+    "def cnot(a, b):\n",
+    "  c, d = Z(1, 2)(a)\n",
+    "  Scalar(2 ** 0.5)()\n",
+    "  return c, X(2, 1)(d, b)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "668cadf7",
+   "metadata": {},
+   "source": [
+    "<img src=\"teleport.svg\" alt=\"Teleportation Protocol\" width=\"800\" style=\"max-width:100%;\">\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "8c0301af",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "bell = Scalar(0.5 ** 0.5) @ Z(0, 2)\n",
+    "\n",
+    "@Channel.from_callable(\n",
+    "  dom=qubit, cod=qubit\n",
+    ")\n",
+    "def teleportation(c):\n",
+    "  a, b = bell()\n",
+    "  cc, aa = cnot(c, a)\n",
+    "  c_ = Measure(1)(H()(cc))\n",
+    "  a_ = Measure(1)(aa)\n",
+    "  bb = BitControlledGate(X(1, 1, 0.5))(a_, b)\n",
+    "  return BitControlledGate(Z(1, 1, 0.5))(c_, bb)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "174c4713",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# function syntax avoids explicit swaps and identity wires\n",
+    "\n",
+    "teleportation_monoidal_syntax = (\n",
+    "    qubit @ bell >>\n",
+    "    cnot @ qubit >>\n",
+    "    H() @ qubit ** 2 >>\n",
+    "    Measure(1) @ Measure(1) @ qubit >>\n",
+    "    bit @ BitControlledGate(X(1, 1, 0.5)) >>\n",
+    "    BitControlledGate(Z(1, 1, 0.5))\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7fcce92a",
+   "metadata": {},
+   "source": [
+    "### Verify the protocol"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "bb29783a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "from optyx.qubits import Id\n",
+    "\n",
+    "# both implementations are equivalent\n",
+    "np.allclose(\n",
+    "    teleportation.eval().tensor.array,\n",
+    "    teleportation_monoidal_syntax.eval().tensor.array,\n",
+    "    Id(1).double().to_tensor().eval().array\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "25af2db6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# backends (Perceval, Discopy, Quimb)\n",
+    "\n",
+    "from optyx.core.backends import (\n",
+    "    DiscopyBackend,\n",
+    "    QuimbBackend\n",
+    ")\n",
+    "\n",
+    "np.allclose(\n",
+    "    teleportation.eval(DiscopyBackend()).tensor.array,\n",
+    "    teleportation.eval(QuimbBackend()).tensor.array\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "36241fe2",
+   "metadata": {},
+   "source": [
+    "## Fusion teleportation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7043700a",
+   "metadata": {},
+   "source": [
+    "Ursin, R., Jennewein, T., Aspelmeyer, M. et al. Quantum teleportation across the Danube. Nature 430, 849 (2004). https://doi.org/10.1038/430849a\n",
+    "\n",
+    "<img src=\"./teleportation_danube.png\" alt=\"Fusion teleportation across the Danube\" width=\"1150px\">"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5721aeab",
+   "metadata": {},
+   "source": [
+    "Graphically, the fusion measurement we would like to use, takes the following form:\n",
+    "\n",
+    "<img src=\"./fusion_ii.png\" alt=\"Fusion measurement\" width=\"1200px\">\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1ab1655b",
+   "metadata": {},
+   "source": [
+    "where $\\underline{a}, \\underline{b}, \\underline{c}, \\underline{d}$ are the measurement outcomes as the measured photon numbers. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ea1f931a",
+   "metadata": {},
+   "source": [
+    "$\\underline{s} = \\underline{a} \\oplus \\underline{b}$\n",
+    "\n",
+    "$\\underline{k} = \\underline{s} (\\underline{b} + \\underline{d}) + \\neg \\underline s (1 - \\frac{\\underline{a} + \\underline{b}}{2})$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "515133cf",
+   "metadata": {},
+   "source": [
+    "### Define the protocol"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "c557c4b8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.photonic import DualRail\n",
+    "\n",
+    "dual_rail_encoded_bell = (\n",
+    "    bell >>\n",
+    "    DualRail(1) @ DualRail(1)\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "a1764edb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.classical import PostselectBit, BitControlledGate\n",
+    "from optyx.photonic import Phase\n",
+    "from optyx.photonic import HadamardBS, qmode\n",
+    "\n",
+    "# postselect on fusion success\n",
+    "fusion_failure_processing = PostselectBit(1)\n",
+    "\n",
+    "# apply the box if the control bit is 1, otherwise apply an identity channel\n",
+    "correction = BitControlledGate(\n",
+    "    HadamardBS() >>\n",
+    "    (Phase(0.5) @ qmode) >>\n",
+    "    HadamardBS()\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e83e3857",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "7bb5e46f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.photonic import FusionTypeII\n",
+    "\n",
+    "@Channel.from_callable(\n",
+    "    dom=qubit, cod=qmode @ qmode\n",
+    ")\n",
+    "def fusion_teleportation(a):\n",
+    "    dual_rail_encoded_input = DualRail(1)(a)\n",
+    "    b, c, d, e = dual_rail_encoded_bell()\n",
+    "    s, k = FusionTypeII()(*dual_rail_encoded_input, b, c)\n",
+    "    fusion_failure_processing(s)\n",
+    "    dr_output_1, dr_output_2 = correction(k, d, e)\n",
+    "    return dr_output_1, dr_output_2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "4b5ee771",
+   "metadata": {},
+   "outputs": [
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+       " </defs>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 800x800 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from optyx.photonic import FusionTypeII\n",
+    "\n",
+    "fusion_teleportation_monoidal_syntax = (\n",
+    "    DualRail(1) @ dual_rail_encoded_bell >>\n",
+    "    FusionTypeII() @ qmode**2 >>\n",
+    "    fusion_failure_processing @ correction\n",
+    ")\n",
+    "\n",
+    "fusion_teleportation_monoidal_syntax.foliation().draw(figsize=(8, 8))\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5017fe5a",
+   "metadata": {},
+   "source": [
+    "### Verify the protocol"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "c19354d7",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "from optyx.photonic import Id\n",
+    "\n",
+    "array_teleportation = fusion_teleportation_monoidal_syntax.eval().tensor.array\n",
+    "array_dr = (DualRail(1) @ Scalar(0.5**0.5)).double().to_tensor().eval().array\n",
+    "\n",
+    "np.allclose(array_teleportation[:, :, :2, :2, :2, :2], array_dr)\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6e6b4039",
+   "metadata": {},
+   "source": [
+    "### Approximate contraction with Quimb and Cotengra"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "51acb733",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def _flat(x):\n",
+    "    return np.asarray(x, dtype=complex).ravel()\n",
+    "\n",
+    "def cosine_similarity(SU, SV):\n",
+    "    a, b = _flat(SU), _flat(SV)\n",
+    "    num = abs(np.vdot(a, b))\n",
+    "    den = np.linalg.norm(a) * np.linalg.norm(b)\n",
+    "    if den == 0:\n",
+    "        return 0.0\n",
+    "    return float(num / den)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "fb497580",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "Text(0.5, 1.0, 'Fusion-based Teleportation similarity vs Contraction Chi')"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
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+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from cotengra import HyperCompressedOptimizer\n",
+    "\n",
+    "# cosine similarity between the result of exact contaction and approximate contraction for different chis\n",
+    "errors = []\n",
+    "for chi in range(1, 6):\n",
+    "    optimiser = HyperCompressedOptimizer(\n",
+    "        chi=chi\n",
+    "    )\n",
+    "    error_for_chi = []\n",
+    "    for _ in range(10):\n",
+    "         error_for_chi.append(\n",
+    "             cosine_similarity(\n",
+    "                 fusion_teleportation.eval(QuimbBackend(optimiser)).tensor.array,\n",
+    "                 array_teleportation\n",
+    "             )\n",
+    "         )\n",
+    "    errors.append(np.median(error_for_chi))\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "plt.plot(range(1, 6), errors, marker='o')\n",
+    "plt.grid()\n",
+    "plt.xlabel('Chi')\n",
+    "plt.ylabel('Average cosine similarity')\n",
+    "plt.title('Fusion-based Teleportation similarity vs Contraction Chi')\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "351608f0",
+   "metadata": {},
+   "source": [
+    "### Photon loss and channel fidelity"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "ac439493",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.photonic import FusionTypeII, PhotonLoss\n",
+    "\n",
+    "# photo loss is one of the main error sources in photonic quantum computing\n",
+    "def fusion_teleportation_with_photon_loss(p):\n",
+    "    @Channel.from_callable(\n",
+    "        dom=qubit, cod=qmode**2\n",
+    "    )\n",
+    "    def fusion_teleportation(a):\n",
+    "        dr_input_1, dr_input_2 = DualRail(1)(a)\n",
+    "        b, c, d, e = dual_rail_encoded_bell()\n",
+    "        # apply photon loss to all modes here:\n",
+    "        #-----------------------------------\n",
+    "        dr_input_1_loss, dr_input_2_loss, b_loss, c_loss, d_loss, e_loss = (\n",
+    "            PhotonLoss(p)(dr_input_1), PhotonLoss(p)(dr_input_2), PhotonLoss(p)(b), PhotonLoss(p)(c), PhotonLoss(p)(d), PhotonLoss(p)(e)\n",
+    "        )\n",
+    "        #-----------------------------------\n",
+    "        s, k = FusionTypeII()(dr_input_1_loss, dr_input_2_loss, b_loss, c_loss)\n",
+    "        fusion_failure_processing(s)\n",
+    "        output_rail_1, output_rail = correction(k, d_loss, e_loss)\n",
+    "        return output_rail_1, output_rail\n",
+    "    return fusion_teleportation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "ccefb368",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.core.channel import Spider, Diagram\n",
+    "\n",
+    "def get_perm(n):\n",
+    "    return sorted(sorted(list(range(n))), key=lambda i: i % 2)\n",
+    "\n",
+    "def channel_fidelity(diagram_1, diagram_2):\n",
+    "    bell_1 = Channel.tensor(*[Spider(0, 2, ty) for ty in diagram_1.dom])\n",
+    "    permutation_1 = Diagram.permutation(get_perm(len(bell_1.cod)), bell_1.cod)\n",
+    "\n",
+    "    bell_2 = Channel.tensor(*[Spider(0, 2, ty) for ty in diagram_2.dom])\n",
+    "    permutation_2 = Diagram.permutation(get_perm(len(bell_2.cod)), bell_2.cod)\n",
+    "\n",
+    "    choi_1 = bell_1 >> permutation_1 >> (diagram_1 @ diagram_1.dom)\n",
+    "    choi_2 = bell_2 >> permutation_2 >> (diagram_2 @ diagram_2.dom)\n",
+    "\n",
+    "    return (choi_1 >> choi_2.dagger()).eval().tensor.array\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "7e1a2957",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part\n",
+      "  return math.isfinite(val)\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part\n",
+      "  return np.asarray(x, float)\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "Text(0.5, 1.0, 'Fusion-based Teleportation: Photon Survival Probability vs Fidelity')"
+      ]
+     },
+     "execution_count": 25,
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+       " </g>\n",
+       " <defs>\n",
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+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "ps = np.linspace(0.0, 1.0, 20)\n",
+    "\n",
+    "# compute fidelity for different photon loss probabilities\n",
+    "F_avg_vals = []\n",
+    "succ_probs = []\n",
+    "for p in ps:\n",
+    "    S_impl = fusion_teleportation_with_photon_loss(p)\n",
+    "    S_tgt  = fusion_teleportation_monoidal_syntax\n",
+    "    s = channel_fidelity(S_impl, S_tgt)\n",
+    "\n",
+    "    succ_probs.append(s)\n",
+    "\n",
+    "plt.figure()\n",
+    "plt.plot(ps, succ_probs, marker='o')\n",
+    "plt.grid(True)\n",
+    "plt.xlabel('Photon Survival Probability (p)')\n",
+    "plt.ylabel('Fidelity')\n",
+    "plt.title('Fusion-based Teleportation: Photon Survival Probability vs Fidelity')\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "07c143a0",
+   "metadata": {},
+   "source": [
+    "## Distributed entanglement generation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9fa0ec11",
+   "metadata": {},
+   "source": [
+    "![Distributed entanglement](./distributed_entanglement.png \"An example of distributed entanglement generation\")\n",
+    "\n",
+    "Main, D., Drmota, P., Nadlinger, D.P. et al. Distributed quantum computing across an optical network link. Nature 638, 383–388 (2025). https://doi.org/10.1038/s41586-024-08404-x~\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e20c30a8",
+   "metadata": {},
+   "source": [
+    "### Fusion and photon distinguishability"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "18ab5a86",
+   "metadata": {},
+   "source": [
+    "#### Define the protocol"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "id": "bdb9611d",
+   "metadata": {},
+   "outputs": [
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+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from optyx.qubits import Z, Scalar, Id, Measure\n",
+    "from optyx.photonic import DualRail\n",
+    "from optyx.classical import PostselectBit\n",
+    "from discopy.drawing import Equation\n",
+    "\n",
+    "bell_state = Z(0, 2) @ Scalar(0.5 ** 0.5)\n",
+    "\n",
+    "# generators introducing new qubits accepting internal states\n",
+    "internal_state_1 = [1, 0]\n",
+    "internal_state_2 = [0, 1]\n",
+    "dual_rail_encoding = lambda state: DualRail(1, internal_states=[state])\n",
+    "encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(internal_state_2)\n",
+    "\n",
+    "# postselect on fusion success and no errors\n",
+    "post_select = PostselectBit(1) @ PostselectBit(0)\n",
+    "\n",
+    "protocol = (\n",
+    "    bell_state @ bell_state >>\n",
+    "    Id(1) @ (encoding_layer >> FusionTypeII() >> post_select) @ Id(1)\n",
+    ")\n",
+    "measure = Measure(2)\n",
+    "\n",
+    "Equation(protocol >> measure, bell_state >> measure).draw(figsize=(8, 8))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eb9f34b3",
+   "metadata": {},
+   "source": [
+    "#### Define a set of internal states with varying degrees of distinguishability"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "9e5c4078",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import math\n",
+    "\n",
+    "# internal states - 2 dimensional - move further and further apart\n",
+    "def rotated_unit_vectors(n: int = 10):\n",
+    "    for i in range(n):\n",
+    "        theta = i * (math.pi / 2) / (n - 1)\n",
+    "        yield (math.cos(theta), math.sin(theta))\n",
+    "\n",
+    "unit_vectors = list(rotated_unit_vectors(15))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "945ace07",
+   "metadata": {},
+   "source": [
+    "#### Run the experiments"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "30b96ad0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.qubits import Discard\n",
+    "\n",
+    "inner_product_states = []\n",
+    "inner_product_bell_states = []\n",
+    "\n",
+    "result_bell = bell_state.eval().tensor.array.flatten()\n",
+    "result_bell = result_bell / np.linalg.norm(result_bell)\n",
+    "\n",
+    "for vector in unit_vectors:\n",
+    "    encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(vector)\n",
+    "    experiment = bell_state @ bell_state >> Id(1) @ (encoding_layer >> FusionTypeII()\n",
+    "                                                                                >> post_select) @ Id(1)\n",
+    "\n",
+    "    f = (experiment >> bell_state.dagger()).inflate(2).eval().tensor.array\n",
+    "    normalisation = (experiment >> Discard(2)).inflate(2).eval().tensor.array\n",
+    "\n",
+    "    inner_product_states.append(np.inner(vector, internal_state_1))\n",
+    "    inner_product_bell_states.append(f/normalisation)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "id": "1c50f388",
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+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 600x400 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "plt.figure(figsize=(6, 4))\n",
+    "plt.plot(inner_product_states, inner_product_bell_states, marker='o')\n",
+    "plt.xlabel('<Internal state 1 | Internal state 2>')\n",
+    "plt.ylabel('<Result | Bell State> (fidelity)')\n",
+    "plt.title('Fidelity of the resulting state with the perfect Bell state')\n",
+    "plt.grid(True)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7aa6a1d2",
+   "metadata": {},
+   "source": [
+    "## Interfacing with external libraries"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e4b64d36",
+   "metadata": {},
+   "source": [
+    "### Graphix\n",
+    "\n",
+    "Open graphs only for now (graph + measurements; desire to implement deterministically - no corrections)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "id": "79f358ae",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The pattern is not consistent with flow or gflow structure.\n"
+     ]
+    },
+    {
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+      ],
+      "text/plain": [
+       "<Figure size 620x200 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import graphix\n",
+    "\n",
+    "circuit = graphix.Circuit(2)\n",
+    "circuit.cnot(0, 1)\n",
+    "\n",
+    "pattern = circuit.transpile().pattern\n",
+    "\n",
+    "pattern.draw_graph()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "bff50dee",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "simulator = graphix.simulator.PatternSimulator(pattern, backend=\"statevector\")\n",
+    "graphix_result = simulator.run().psi.conj()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "id": "bf2d9106",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx import qubits\n",
+    "\n",
+    "optyx_zx = qubits.Circuit(pattern)\n",
+    "\n",
+    "optyx_res = (\n",
+    "    qubits.Ket(\"+\")**2 >> optyx_zx\n",
+    ").eval().amplitudes()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "id": "908e477d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "for keys in optyx_res.keys():\n",
+    "    assert np.isclose(optyx_res[keys], graphix_result[keys], atol=1e-6)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "598ab8dc",
+   "metadata": {},
+   "source": [
+    "### Perceval circuits and processors"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7d106d80",
+   "metadata": {},
+   "source": [
+    "#### Define the protocol in Perceval"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "id": "988c9618",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
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+       "<path d=\"M25,225 L28,225 L72,325 L75,325\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
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+       "<text x=\"79\" y=\"305\" font-size=\"8\" text-anchor=\"start\">POSTPROCESSED CNOT</text>\n",
+       "<path d=\"M25,125 L53,125 L72,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M78,144 L97,125 L125,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M25,175 L53,175 L72,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M78,156 L97,175 L125,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M50,143 L100,143 L100,157 L50,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
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+       "<text x=\"75\" y=\"126\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<path d=\"M50,143 L100,143 L100,147 L50,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M93,150 L103,150 L103,160 L93,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"98\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M25,75.0 L125,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M128,75 L172,175\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M125,75 L128,75 L172,175 L175,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M128,125 L172,125\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M125,125 L128,125 L172,125 L175,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M128,175 L172,225\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M125,175 L128,175 L172,225 L175,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
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+       "<path d=\"M228,44 L247,25 L275,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M175,75 L203,75 L222,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,56 L247,75 L275,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M200,43 L250,43 L250,57 L200,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"225\" y=\"80\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"225\" y=\"26\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
+       "<path d=\"M200,43 L250,43 L250,47 L200,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M243,50 L253,50 L253,60 L243,60 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"248\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M175,125 L203,125 L222,144\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,144 L247,125 L275,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M175,175 L203,175 L222,156\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,156 L247,175 L275,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M200,143 L250,143 L250,157 L200,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"225\" y=\"180\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"225\" y=\"126\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
+       "<path d=\"M200,143 L250,143 L250,147 L200,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M243,150 L253,150 L253,160 L243,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"248\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M175,225 L203,225 L222,244\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,244 L247,225 L275,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M175,275 L203,275 L222,256\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M228,256 L247,275 L275,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M200,243 L250,243 L250,257 L200,257 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"225\" y=\"280\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"225\" y=\"226\" font-size=\"7\" text-anchor=\"middle\">Θ=1.910633</text>\n",
+       "<path d=\"M200,243 L250,243 L250,247 L200,247 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M243,250 L253,250 L253,260 L243,260 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"248\" y=\"257\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M278,125 L322,125\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M275,125 L278,125 L322,125 L325,125\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
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+       "<path d=\"M378,156 L397,175 L425,175\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M350,143 L400,143 L400,157 L350,157 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"375\" y=\"185\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"375\" y=\"126\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<path d=\"M350,143 L400,143 L400,147 L350,147 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M393,150 L403,150 L403,160 L393,160 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"398\" y=\"157\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M275,25.0 L425,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M325,75.0 L425,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M75,325.0 L425,325.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M75,375.0 L425,375.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M428,325 L472,225\" stroke=\"white\" stroke-width=\"6\" fill=\"none\" />\n",
+       "<path d=\"M425,325 L428,325 L472,225 L475,225\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
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+       "<path d=\"M425,375 L428,375 L472,275 L475,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M425,25 L453,25 L472,44\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M478,44 L497,25 L525,25\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M425,75 L453,75 L472,56\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M478,56 L497,75 L525,75\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M450,43 L500,43 L500,57 L450,57 Z\" stroke=\"black\" fill=\"black\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"475\" y=\"85\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<text x=\"475\" y=\"26\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
+       "<path d=\"M450,43 L500,43 L500,47 L450,47 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M493,50 L503,50 L503,60 L493,60 Z\" stroke=\"black\" fill=\"aquamarine\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"498\" y=\"57\" font-size=\"6\" text-anchor=\"middle\">H</text>\n",
+       "<path d=\"M425,125.0 L525,125.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M425,175.0 L525,175.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M475,225.0 L525,225.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M475,275.0 L525,275.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M525,25 L575,25\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M525,75 L575,75\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M549,10 L551,10 L551,90 L549,90 Z\" stroke=\"dimgrey\" fill=\"dimgrey\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M525,225 L575,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M525,275 L575,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M549,210 L551,210 L551,290 L549,290 Z\" stroke=\"dimgrey\" fill=\"dimgrey\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M525,125 L550,125\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M550,125 L575,125\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M545,135 L537,135 L537,115 L545,115 C545,115,555,115,555,125 C555,135,545,135,545,135 L545,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
+       "<text x=\"537\" y=\"112\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
+       "<path d=\"M525,175 L550,175\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M550,175 L575,175\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M545,185 L537,185 L537,165 L545,165 C545,165,555,165,555,175 C555,185,545,185,545,185 L545,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
+       "<text x=\"537\" y=\"162\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
+       "<path d=\"M575,125 L675,125\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M575,175 L675,175\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M625,190.0 L625,205.0\" stroke=\"white\" stroke-width=\"5\" fill=\"none\" />\n",
+       "<path d=\"M625,190.0 L625,205.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" stroke-dasharray=\"4,4\" />\n",
+       "<path d=\"M625,198.0 L622,195.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M625,198.0 L628,195.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M580,110 L670,110 L670,190 L580,190 Z\" stroke=\"black\" fill=\"lightgreen\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"625\" y=\"155.0\" font-size=\"10\" text-anchor=\"middle\">FFC</text>\n",
+       "<path d=\"M575,225 L675,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M575,275 L675,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M580,205 L670,205 L670,295 L580,295 Z\" stroke=\"black\" fill=\"lightyellow\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"625\" y=\"250\" font-size=\"10\" text-anchor=\"middle\">U(FFC)</text>\n",
+       "<path d=\"M575,25.0 L675,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M575,75.0 L675,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M675,125 L725,125\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M675,175 L725,175\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M675,225 L725,225\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M675,275 L725,275\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M699,110 L701,110 L701,290 L699,290 Z\" stroke=\"dimgrey\" fill=\"dimgrey\" stroke-linejoin=\"miter\" />\n",
+       "<path d=\"M675,25.0 L725,25.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M675,75.0 L725,75.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M725,25 L750,25\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M750,25 L775,25\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M745,35 L737,35 L737,15 L745,15 C745,15,755,15,755,25 C755,35,745,35,745,35 L745,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
+       "<text x=\"737\" y=\"12\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
+       "<path d=\"M725,75 L750,75\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M750,75 L775,75\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M745,85 L737,85 L737,65 L745,65 C745,65,755,65,755,75 C755,85,745,85,745,85 L745,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
+       "<text x=\"737\" y=\"62\" font-size=\"5\" text-anchor=\"start\" font-style=\"italic\">PNR</text>\n",
+       "<path d=\"M775,25 L825,25\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M775,75 L825,75\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M800,90.0 L800,255.0\" stroke=\"white\" stroke-width=\"5\" fill=\"none\" />\n",
+       "<path d=\"M800,90.0 L800,255.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" stroke-dasharray=\"4,4\" />\n",
+       "<path d=\"M800,98.0 L797,95.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M800,98.0 L803,95.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M780,10 L820,10 L820,90 L780,90 Z\" stroke=\"black\" fill=\"lightgreen\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"800\" y=\"55.0\" font-size=\"10\" text-anchor=\"middle\">FFC</text>\n",
+       "<path d=\"M725,275 L775,275\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M730,290 L739,290 L753,260 L744,260 L730,290 L739,290 Z\" stroke=\"black\" fill=\"gray\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"747\" y=\"288\" font-size=\"7\" text-anchor=\"start\">Φ=phi</text>\n",
+       "<path d=\"M725,125.0 L825,125.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M725,175.0 L825,175.0\" stroke=\"orange\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M725,225.0 L825,225.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M775,275.0 L825,275.0\" stroke=\"darkred\" stroke-width=\"3\" fill=\"none\" />\n",
+       "<path d=\"M825,25.0 L840,25.0\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M825,75.0 L840,75.0\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M825,125.0 L840,125.0\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M825,175.0 L840,175.0\" stroke-width=\"3\" stroke=\"orange\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M825,225.0 L840,225.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M825,275.0 L840,275.0\" stroke-width=\"3\" stroke=\"darkred\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
+       "<path d=\"M157,75 C157,75,157,65,167,65 L175,65 L175,85 L167,85 C157,85,157,75,157,75 L157,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"white\" />\n",
+       "<text x=\"163\" y=\"91\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\">[herald0]</text>\n",
+       "<text x=\"167\" y=\"78\" font-size=\"7\" text-anchor=\"middle\">0</text>\n",
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+       "<text x=\"163\" y=\"291\" font-size=\"6\" text-anchor=\"middle\" font-style=\"italic\">[herald1]</text>\n",
+       "<text x=\"167\" y=\"278\" font-size=\"7\" text-anchor=\"middle\">0</text>\n",
+       "<path d=\"M-2,15 L10,15 L10,85 L-2,85 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"-2\" y=\"91\" font-size=\"6\" text-anchor=\"start\" font-style=\"italic\">[ctrl]</text>\n",
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+       "<text x=\"-2\" y=\"191\" font-size=\"6\" text-anchor=\"start\" font-style=\"italic\">[data]</text>\n",
+       "<path d=\"M840,15 L852,15 L852,85 L840,85 Z\" stroke=\"black\" fill=\"lightgray\" stroke-linejoin=\"miter\" />\n",
+       "<text x=\"852\" y=\"91\" font-size=\"6\" text-anchor=\"end\" font-style=\"italic\">[ctrl]</text>\n",
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+       "</svg>"
+      ],
+      "text/plain": [
+       "<drawsvg.drawing.Drawing at 0x77ef9ee5ac00>"
+      ]
+     },
+     "execution_count": 35,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import perceval as pcvl\n",
+    "\n",
+    "p = pcvl.Processor(\"SLOS\", 6)\n",
+    "p.add(0, pcvl.catalog[\"postprocessed cnot\"].build_processor())\n",
+    "\n",
+    "p.add(0, pcvl.BS.H())\n",
+    "p.add(0, pcvl.Detector.pnr())\n",
+    "p.add(1, pcvl.Detector.pnr())\n",
+    "p.add(2, pcvl.Detector.pnr())\n",
+    "p.add(3, pcvl.Detector.pnr())\n",
+    "\n",
+    "ff_X = pcvl.FFCircuitProvider(\n",
+    "  2, 0, pcvl.Circuit(2)\n",
+    ")\n",
+    "ff_X.add_configuration(\n",
+    "  [0, 1], pcvl.PERM([1, 0])\n",
+    ")\n",
+    "p.add(2, ff_X)\n",
+    "\n",
+    "phi = pcvl.P(\"phi\")\n",
+    "ff_Z = pcvl.FFConfigurator(\n",
+    "  2, 3,\n",
+    "  pcvl.PS(phi),\n",
+    "  {\"phi\": 0}\n",
+    ").add_configuration(\n",
+    "  [0, 1],\n",
+    "  {\"phi\": np.pi}\n",
+    ")\n",
+    "p.add(0, ff_Z)\n",
+    "\n",
+    "pcvl.pdisplay(p, recursive=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "id": "96d5bf6b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.qubits import Ket\n",
+    "\n",
+    "state = Ket(\"+\") >> Z(1, 1, 0.3)\n",
+    "state_array = state.eval().tensor.array\n",
+    "state_array = state_array / np.linalg.norm(state_array)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f64e6adb",
+   "metadata": {},
+   "source": [
+    "#### Evaluate the protocol in Perceval"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "id": "bce649df",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "to_transmit = (complex(state_array[0])*pcvl.BasicState([1, 0]) +\n",
+    "               complex(state_array[1])*pcvl.BasicState([0, 1]))\n",
+    "\n",
+    "sg = pcvl.StateGenerator(pcvl.Encoding.DUAL_RAIL)\n",
+    "bell_state = sg.bell_state(\"phi+\")\n",
+    "\n",
+    "input_state = to_transmit * bell_state\n",
+    "p.min_detected_photons_filter(2)\n",
+    "\n",
+    "input_state *= pcvl.BasicState([0, 0])\n",
+    "\n",
+    "p.with_input(input_state)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "id": "f0c1fbf3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "result_perceval = p.probs()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ab098b6e",
+   "metadata": {},
+   "source": [
+    "#### Convert to Optyx and simulate"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "id": "463bcb6f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx import Channel\n",
+    "\n",
+    "optyx_diagram = Channel.from_perceval(p)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "id": "3f3fca2d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.qubits import Scalar, Ket\n",
+    "from optyx.photonic import DualRail\n",
+    "\n",
+    "bell_state = Z(0, 2) @ Scalar(0.5**0.5)\n",
+    "transmit = Ket(\"+\") >> Z(1, 1, 0.3)\n",
+    "\n",
+    "input_state = transmit @ bell_state\n",
+    "\n",
+    "protocol = (\n",
+    "    input_state >>\n",
+    "    DualRail(3) >>\n",
+    "    Channel.from_perceval(p)\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "id": "54633b7a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "result_optyx = protocol.eval().prob_dist()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "id": "e019251e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def check_dict_agreement(d1, d2, rtol=1e-5, atol=1e-8):\n",
+    "    for key in d1.keys() - d2.keys():\n",
+    "        assert np.isclose(d1[key], 0, rtol=rtol, atol=atol)\n",
+    "    for key in d2.keys() - d1.keys():\n",
+    "        assert np.isclose(d2[key], 0, rtol=rtol, atol=atol)\n",
+    "    for key in d1.keys() & d2.keys():\n",
+    "        assert np.isclose(d1[key], d2[key], rtol=rtol, atol=atol)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "id": "ca6102c5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "check_dict_agreement(\n",
+    "    {tuple(k): v for k, v in dict(result_perceval[\"results\"]).items()},\n",
+    "    result_optyx\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a7c85548",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": ".venv",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

From 36789b382501a14884b823118375b0d764d76c12 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Tue, 23 Sep 2025 13:10:54 +0100
Subject: [PATCH 23/59] remove an unused example notebook

---
 docs/notebooks/graphix_workshop.ipynb | 990 --------------------------
 1 file changed, 990 deletions(-)
 delete mode 100644 docs/notebooks/graphix_workshop.ipynb

diff --git a/docs/notebooks/graphix_workshop.ipynb b/docs/notebooks/graphix_workshop.ipynb
deleted file mode 100644
index d14950c8..00000000
--- a/docs/notebooks/graphix_workshop.ipynb
+++ /dev/null
@@ -1,990 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "0d360e60",
-   "metadata": {},
-   "source": [
-    "# Optyx: A ZX-based Python library for networked quantum architectures"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b1adf8d9",
-   "metadata": {},
-   "source": [
-    "## Hong-Ou-Mandel effect"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "6f3dab5d",
-   "metadata": {},
-   "source": [
-    "### Experiment definition"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "13dbbb3a",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.photonic import BBS\n",
-    "\n",
-    "# diagram generators:\n",
-    "# beam-splitter\n",
-    "beam_splitter = BBS(0)\n",
-    "beam_splitter.draw()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "79ab4b08",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.photonic import Create\n",
-    "\n",
-    "# diagram composition with function syntax\n",
-    "hong_ou_mandel = (\n",
-    "    Create(1) @ Create(1) >>\n",
-    "    beam_splitter\n",
-    ")\n",
-    "\n",
-    "hong_ou_mandel.draw()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "a869643c",
-   "metadata": {},
-   "source": [
-    " ![HOM](./hom.png \"Hong-Ou-Mandel Effect\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "94bfc225",
-   "metadata": {},
-   "source": [
-    "### Diagram evaluation"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "f1478f68",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# an amplitude (raw result of tensor contraction)\n",
-    "from optyx.classical import Select\n",
-    "(\n",
-    "    hong_ou_mandel >> Select(1, 1)\n",
-    ").eval().tensor.array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "801f0884",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "hong_ou_mandel.eval().prob_dist()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b1f34bd2",
-   "metadata": {},
-   "source": [
-    "## Qubit teleportation - function syntax and backends"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "47e64a7d",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx import qubit, bit\n",
-    "from optyx.qubits import Scalar\n",
-    "\n",
-    "from optyx import Channel\n",
-    "from optyx.qubits import Z, X, H, Measure, Scalar, qubit, bit\n",
-    "from optyx.classical import BitControlledGate"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "748d7e3d",
-   "metadata": {},
-   "source": [
-    "### Define the protocol"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "8fa3a149",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# function syntax\n",
-    "# CNOT from ZX generators\n",
-    "\n",
-    "@Channel.from_callable(\n",
-    "  dom=qubit @ qubit, cod=qubit @ qubit\n",
-    ")\n",
-    "def cnot(a, b):\n",
-    "  c, d = Z(1, 2)(a)\n",
-    "  Scalar(2 ** 0.5)()\n",
-    "  return X(2, 1)(c, b), d"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "668cadf7",
-   "metadata": {},
-   "source": [
-    "<img src=\"teleport.svg\" alt=\"Teleportation Protocol\" width=\"800\" style=\"max-width:100%;\">\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "8c0301af",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "bell = Scalar(0.5 ** 0.5) @ Z(0, 2)\n",
-    "\n",
-    "@Channel.from_callable(\n",
-    "  dom=qubit, cod=qubit\n",
-    ")\n",
-    "def teleportation(c):\n",
-    "  a, b = bell()\n",
-    "  aa, cc = cnot(a, c)\n",
-    "  c_ = Measure(1)(H()(cc))\n",
-    "  a_ = Measure(1)(aa)\n",
-    "  bb = BitControlledGate(X(1, 1, 0.5))(a_, b)\n",
-    "  return BitControlledGate(Z(1, 1, 0.5))(c_, bb)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "174c4713",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# function syntax avoids explicit swaps and identity wires\n",
-    "\n",
-    "teleportation_monoidal_syntax = (\n",
-    "    qubit @ bell >>\n",
-    "    cnot @ qubit >>\n",
-    "    H() @ qubit ** 2 >>\n",
-    "    Measure(1) @ Measure(1) @ qubit >>\n",
-    "    bit @ BitControlledGate(X(1, 1, 0.5)) >>\n",
-    "    BitControlledGate(Z(1, 1, 0.5))\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7fcce92a",
-   "metadata": {},
-   "source": [
-    "### Verify the protocol"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "bb29783a",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "from optyx.qubits import Id\n",
-    "\n",
-    "# both implementations are equivalent\n",
-    "np.allclose(\n",
-    "    teleportation.eval().tensor.array,\n",
-    "    teleportation_monoidal_syntax.eval().tensor.array,\n",
-    "    Id(1).double().to_tensor().eval().array\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "25af2db6",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# backends (Perceval, Discopy, Quimb)\n",
-    "\n",
-    "from optyx.core.backends import (\n",
-    "    DiscopyBackend,\n",
-    "    QuimbBackend\n",
-    ")\n",
-    "\n",
-    "np.allclose(\n",
-    "    teleportation.eval(DiscopyBackend()).tensor.array,\n",
-    "    teleportation.eval(QuimbBackend()).tensor.array\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "36241fe2",
-   "metadata": {},
-   "source": [
-    "## Fusion teleportation"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7043700a",
-   "metadata": {},
-   "source": [
-    "Ursin, R., Jennewein, T., Aspelmeyer, M. et al. Quantum teleportation across the Danube. Nature 430, 849 (2004). https://doi.org/10.1038/430849a\n",
-    "\n",
-    "<img src=\"./teleportation_danube.png\" alt=\"Fusion teleportation across the Danube\" width=\"1150px\">"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "5721aeab",
-   "metadata": {},
-   "source": [
-    "Graphically, the fusion measurement we would like to use, takes the following form:\n",
-    "\n",
-    "<img src=\"./fusion_ii.png\" alt=\"Fusion measurement\" width=\"1200px\">\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1ab1655b",
-   "metadata": {},
-   "source": [
-    "where $\\underline{a}, \\underline{b}, \\underline{c}, \\underline{d}$ are the measurement outcomes as the measured photon numbers. "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "ea1f931a",
-   "metadata": {},
-   "source": [
-    "$\\underline{s} = \\underline{a} \\oplus \\underline{b}$\n",
-    "\n",
-    "$\\underline{k} = \\underline{s} (\\underline{b} + \\underline{d}) + \\neg \\underline s (1 - \\frac{\\underline{a} + \\underline{b}}{2})$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "515133cf",
-   "metadata": {},
-   "source": [
-    "### Define the protocol"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "c557c4b8",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.photonic import DualRail\n",
-    "\n",
-    "dual_rail_encoded_bell = (\n",
-    "    bell >>\n",
-    "    DualRail(1) @ DualRail(1)\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "a1764edb",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.classical import PostselectBit, BitControlledGate\n",
-    "from optyx.photonic import Phase\n",
-    "from optyx.photonic import HadamardBS, qmode\n",
-    "\n",
-    "# postselect on fusion success\n",
-    "fusion_failure_processing = PostselectBit(1)\n",
-    "\n",
-    "# apply the box if the control bit is 1, otherwise apply an identity channel\n",
-    "correction = BitControlledGate(\n",
-    "    HadamardBS() >>\n",
-    "    (Phase(0.5) @ qmode) >>\n",
-    "    HadamardBS()\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "7bb5e46f",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.photonic import FusionTypeII\n",
-    "\n",
-    "@Channel.from_callable(\n",
-    "    dom=qubit, cod=qmode @ qmode\n",
-    ")\n",
-    "def fusion_teleportation(a):\n",
-    "    dual_rail_encoded_input = DualRail(1)(a)\n",
-    "    b, c, d, e = dual_rail_encoded_bell()\n",
-    "    s, k = FusionTypeII()(*dual_rail_encoded_input, b, c)\n",
-    "    fusion_failure_processing(s)\n",
-    "    dr_output_1, dr_output_2 = correction(k, d, e)\n",
-    "    return dr_output_1, dr_output_2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "4b5ee771",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.photonic import FusionTypeII\n",
-    "\n",
-    "fusion_teleportation_monoidal_syntax = (\n",
-    "    DualRail(1) @ dual_rail_encoded_bell >>\n",
-    "    FusionTypeII() @ qmode**2 >>\n",
-    "    fusion_failure_processing @ correction\n",
-    ")\n",
-    "\n",
-    "fusion_teleportation_monoidal_syntax.foliation().draw(figsize=(8, 8))\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "5017fe5a",
-   "metadata": {},
-   "source": [
-    "### Verify the protocol"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "c19354d7",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "from optyx.photonic import Id\n",
-    "\n",
-    "array_teleportation = fusion_teleportation_monoidal_syntax.eval().tensor.array\n",
-    "array_dr = (DualRail(1) @ Scalar(0.5**0.5)).double().to_tensor().eval().array\n",
-    "\n",
-    "np.allclose(array_teleportation[:, :, :2, :2, :2, :2], array_dr)\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "6e6b4039",
-   "metadata": {},
-   "source": [
-    "### Approximate contraction with Quimb and Cotengra"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "51acb733",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def _flat(x):\n",
-    "    return np.asarray(x, dtype=complex).ravel()\n",
-    "\n",
-    "def cosine_similarity(SU, SV):\n",
-    "    a, b = _flat(SU), _flat(SV)\n",
-    "    num = abs(np.vdot(a, b))\n",
-    "    den = np.linalg.norm(a) * np.linalg.norm(b)\n",
-    "    if den == 0:\n",
-    "        return 0.0\n",
-    "    return float(num / den)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "fb497580",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from cotengra import HyperCompressedOptimizer\n",
-    "\n",
-    "# cosine similarity between the result of exact contaction and approximate contraction for different chis\n",
-    "errors = []\n",
-    "for chi in range(1, 6):\n",
-    "    optimiser = HyperCompressedOptimizer(\n",
-    "        chi=chi\n",
-    "    )\n",
-    "    error_for_chi = []\n",
-    "    for _ in range(10):\n",
-    "         error_for_chi.append(\n",
-    "             cosine_similarity(\n",
-    "                 fusion_teleportation.eval(QuimbBackend(optimiser)).tensor.array,\n",
-    "                 array_teleportation\n",
-    "             )\n",
-    "         )\n",
-    "    errors.append(np.median(error_for_chi))\n",
-    "\n",
-    "import matplotlib.pyplot as plt\n",
-    "plt.plot(range(1, 6), errors, marker='o')\n",
-    "plt.grid()\n",
-    "plt.xlabel('Chi')\n",
-    "plt.ylabel('Average cosine similarity')\n",
-    "plt.title('Fusion-based Teleportation similarity vs Contraction Chi')\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "351608f0",
-   "metadata": {},
-   "source": [
-    "### Photon loss and channel fidelity"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "ac439493",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.photonic import FusionTypeII, PhotonLoss\n",
-    "\n",
-    "# photo loss is one of the main error sources in photonic quantum computing\n",
-    "def fusion_teleportation_with_photon_loss(p):\n",
-    "    @Channel.from_callable(\n",
-    "        dom=qubit, cod=qmode**2\n",
-    "    )\n",
-    "    def fusion_teleportation(a):\n",
-    "        dr_input_1, dr_input_2 = DualRail(1)(a)\n",
-    "        b, c, d, e = dual_rail_encoded_bell()\n",
-    "        # apply photon loss to all modes here:\n",
-    "        #-----------------------------------\n",
-    "        dr_input_1_loss, dr_input_2_loss, b_loss, c_loss, d_loss, e_loss = (\n",
-    "            PhotonLoss(p)(dr_input_1), PhotonLoss(p)(dr_input_2), PhotonLoss(p)(b), PhotonLoss(p)(c), PhotonLoss(p)(d), PhotonLoss(p)(e)\n",
-    "        )\n",
-    "        #-----------------------------------\n",
-    "        s, k = FusionTypeII()(dr_input_1_loss, dr_input_2_loss, b_loss, c_loss)\n",
-    "        fusion_failure_processing(s)\n",
-    "        output_rail_1, output_rail = correction(k, d_loss, e_loss)\n",
-    "        return output_rail_1, output_rail\n",
-    "    return fusion_teleportation"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "ccefb368",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.core.channel import Spider, Diagram\n",
-    "\n",
-    "def get_perm(n):\n",
-    "    return sorted(sorted(list(range(n))), key=lambda i: i % 2)\n",
-    "\n",
-    "def channel_fidelity(diagram_1, diagram_2):\n",
-    "    bell_1 = Channel.tensor(*[Spider(0, 2, ty) for ty in diagram_1.dom])\n",
-    "    permutation_1 = Diagram.permutation(get_perm(len(bell_1.cod)), bell_1.cod)\n",
-    "\n",
-    "    bell_2 = Channel.tensor(*[Spider(0, 2, ty) for ty in diagram_2.dom])\n",
-    "    permutation_2 = Diagram.permutation(get_perm(len(bell_2.cod)), bell_2.cod)\n",
-    "\n",
-    "    choi_1 = bell_1 >> permutation_1 >> (diagram_1 @ diagram_1.dom)\n",
-    "    choi_2 = bell_2 >> permutation_2 >> (diagram_2 @ diagram_2.dom)\n",
-    "\n",
-    "    return (choi_1 >> choi_2.dagger()).eval().tensor.array\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "7e1a2957",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "import matplotlib.pyplot as plt\n",
-    "\n",
-    "ps = np.linspace(0.0, 1.0, 20)\n",
-    "\n",
-    "# compute fidelity for different photon loss probabilities\n",
-    "F_avg_vals = []\n",
-    "succ_probs = []\n",
-    "for p in ps:\n",
-    "    S_impl = fusion_teleportation_with_photon_loss(p)\n",
-    "    S_tgt  = fusion_teleportation_monoidal_syntax\n",
-    "    s = channel_fidelity(S_impl, S_tgt)\n",
-    "\n",
-    "    succ_probs.append(s)\n",
-    "\n",
-    "plt.figure()\n",
-    "plt.plot(ps, succ_probs, marker='o')\n",
-    "plt.grid(True)\n",
-    "plt.xlabel('Photon Survival Probability (p)')\n",
-    "plt.ylabel('Fidelity')\n",
-    "plt.title('Fusion-based Teleportation: Photon Survival Probability vs Fidelity')\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "07c143a0",
-   "metadata": {},
-   "source": [
-    "## Distributed entanglement generation"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9fa0ec11",
-   "metadata": {},
-   "source": [
-    "![Distributed entanglement](./distributed_entanglement.png \"An example of distributed entanglement generation\")\n",
-    "\n",
-    "Main, D., Drmota, P., Nadlinger, D.P. et al. Distributed quantum computing across an optical network link. Nature 638, 383–388 (2025). https://doi.org/10.1038/s41586-024-08404-x~\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e20c30a8",
-   "metadata": {},
-   "source": [
-    "### Fusion and photon distinguishability"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "18ab5a86",
-   "metadata": {},
-   "source": [
-    "#### Define the protocol"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "bdb9611d",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.qubits import Z, Scalar, Id, Measure\n",
-    "from optyx.photonic import DualRail\n",
-    "from optyx.classical import PostselectBit\n",
-    "from discopy.drawing import Equation\n",
-    "\n",
-    "bell_state = Z(0, 2) @ Scalar(0.5 ** 0.5)\n",
-    "\n",
-    "# generators introducing new qubits accepting internal states\n",
-    "internal_state_1 = [1, 0]\n",
-    "internal_state_2 = [0, 1]\n",
-    "dual_rail_encoding = lambda state: DualRail(1, internal_states=[state])\n",
-    "encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(internal_state_2)\n",
-    "\n",
-    "# postselect on fusion success and no errors\n",
-    "post_select = PostselectBit(1) @ PostselectBit(0)\n",
-    "\n",
-    "protocol = (\n",
-    "    bell_state @ bell_state >>\n",
-    "    Id(1) @ (encoding_layer >> FusionTypeII() >> post_select) @ Id(1)\n",
-    ")\n",
-    "measure = Measure(2)\n",
-    "\n",
-    "Equation(protocol >> measure, bell_state >> measure).draw(figsize=(8, 8))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "eb9f34b3",
-   "metadata": {},
-   "source": [
-    "#### Define a set of internal states with varying degrees of distinguishability"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "9e5c4078",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import math\n",
-    "\n",
-    "# internal states - 2 dimensional - move further and further apart\n",
-    "def rotated_unit_vectors(n: int = 10):\n",
-    "    for i in range(n):\n",
-    "        theta = i * (math.pi / 2) / (n - 1)\n",
-    "        yield (math.cos(theta), math.sin(theta))\n",
-    "\n",
-    "unit_vectors = list(rotated_unit_vectors(15))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "945ace07",
-   "metadata": {},
-   "source": [
-    "#### Run the experiments"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "30b96ad0",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.qubits import Discard\n",
-    "\n",
-    "inner_product_states = []\n",
-    "inner_product_bell_states = []\n",
-    "\n",
-    "result_bell = bell_state.eval().tensor.array.flatten()\n",
-    "result_bell = result_bell / np.linalg.norm(result_bell)\n",
-    "\n",
-    "for vector in unit_vectors:\n",
-    "    encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(vector)\n",
-    "    experiment = bell_state @ bell_state >> Id(1) @ (encoding_layer >> FusionTypeII()\n",
-    "                                                                                >> post_select) @ Id(1)\n",
-    "\n",
-    "    f = (experiment >> bell_state.dagger()).inflate(2).eval().tensor.array\n",
-    "    normalisation = (experiment >> Discard(2)).inflate(2).eval().tensor.array\n",
-    "\n",
-    "    inner_product_states.append(np.inner(vector, internal_state_1))\n",
-    "    inner_product_bell_states.append(f/normalisation)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "1c50f388",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import matplotlib.pyplot as plt\n",
-    "\n",
-    "plt.figure(figsize=(6, 4))\n",
-    "plt.plot(inner_product_states, inner_product_bell_states, marker='o')\n",
-    "plt.xlabel('<Internal state 1 | Internal state 2>')\n",
-    "plt.ylabel('<Result | Bell State> (fidelity)')\n",
-    "plt.title('Fidelity of the resulting state with the perfect Bell state')\n",
-    "plt.grid(True)\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7aa6a1d2",
-   "metadata": {},
-   "source": [
-    "## Interfacing with external libraries"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e4b64d36",
-   "metadata": {},
-   "source": [
-    "### Graphix\n",
-    "\n",
-    "Open graphs only for now (graph + measurements; desire to implement deterministically - no corrections)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "79f358ae",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import graphix\n",
-    "\n",
-    "circuit = graphix.Circuit(2)\n",
-    "circuit.cnot(0, 1)\n",
-    "\n",
-    "pattern = circuit.transpile().pattern\n",
-    "\n",
-    "pattern.draw_graph()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "bff50dee",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "simulator = graphix.simulator.PatternSimulator(pattern, backend=\"statevector\")\n",
-    "graphix_result = simulator.run().psi.conj()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "bf2d9106",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx import qubits\n",
-    "\n",
-    "optyx_zx = qubits.Circuit(pattern)\n",
-    "\n",
-    "optyx_res = (\n",
-    "    qubits.Ket(\"+\")**2 >> optyx_zx\n",
-    ").eval().amplitudes()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "908e477d",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "for keys in optyx_res.keys():\n",
-    "    assert np.isclose(optyx_res[keys], graphix_result[keys], atol=1e-6)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "598ab8dc",
-   "metadata": {},
-   "source": [
-    "### Perceval circuits and processors"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7d106d80",
-   "metadata": {},
-   "source": [
-    "#### Define the protocol in Perceval"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "988c9618",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import perceval as pcvl\n",
-    "\n",
-    "p = pcvl.Processor(\"SLOS\", 6)\n",
-    "p.add(0, pcvl.catalog[\"postprocessed cnot\"].build_processor())\n",
-    "\n",
-    "p.add(0, pcvl.BS.H())\n",
-    "p.add(0, pcvl.Detector.pnr())\n",
-    "p.add(1, pcvl.Detector.pnr())\n",
-    "p.add(2, pcvl.Detector.pnr())\n",
-    "p.add(3, pcvl.Detector.pnr())\n",
-    "\n",
-    "ff_X = pcvl.FFCircuitProvider(\n",
-    "  2, 0, pcvl.Circuit(2)\n",
-    ")\n",
-    "ff_X.add_configuration(\n",
-    "  [0, 1], pcvl.PERM([1, 0])\n",
-    ")\n",
-    "p.add(2, ff_X)\n",
-    "\n",
-    "phi = pcvl.P(\"phi\")\n",
-    "ff_Z = pcvl.FFConfigurator(\n",
-    "  2, 3,\n",
-    "  pcvl.PS(phi),\n",
-    "  {\"phi\": 0}\n",
-    ").add_configuration(\n",
-    "  [0, 1],\n",
-    "  {\"phi\": np.pi}\n",
-    ")\n",
-    "p.add(0, ff_Z)\n",
-    "\n",
-    "pcvl.pdisplay(p, recursive=True)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "96d5bf6b",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.qubits import Ket\n",
-    "\n",
-    "state = Ket(\"+\") >> Z(1, 1, 0.3)\n",
-    "state_array = state.eval().tensor.array\n",
-    "state_array = state_array / np.linalg.norm(state_array)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "f64e6adb",
-   "metadata": {},
-   "source": [
-    "#### Evaluate the protocol in Perceval"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "bce649df",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "to_transmit = (complex(state_array[0])*pcvl.BasicState([1, 0]) +\n",
-    "               complex(state_array[1])*pcvl.BasicState([0, 1]))\n",
-    "\n",
-    "sg = pcvl.StateGenerator(pcvl.Encoding.DUAL_RAIL)\n",
-    "bell_state = sg.bell_state(\"phi+\")\n",
-    "\n",
-    "input_state = to_transmit * bell_state\n",
-    "p.min_detected_photons_filter(2)\n",
-    "\n",
-    "input_state *= pcvl.BasicState([0, 0])\n",
-    "\n",
-    "p.with_input(input_state)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "f0c1fbf3",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "result_perceval = p.probs()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "ab098b6e",
-   "metadata": {},
-   "source": [
-    "#### Convert to Optyx and simulate"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "463bcb6f",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx import Channel\n",
-    "\n",
-    "optyx_diagram = Channel.from_perceval(p)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "3f3fca2d",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.qubits import Scalar, Ket\n",
-    "from optyx.photonic import DualRail\n",
-    "\n",
-    "bell_state = Z(0, 2) @ Scalar(0.5**0.5)\n",
-    "transmit = Ket(\"+\") >> Z(1, 1, 0.3)\n",
-    "\n",
-    "input_state = transmit @ bell_state\n",
-    "\n",
-    "protocol = (\n",
-    "    input_state >>\n",
-    "    DualRail(3) >>\n",
-    "    Channel.from_perceval(p)\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "54633b7a",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "result_optyx = protocol.eval().prob_dist()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "e019251e",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def check_dict_agreement(d1, d2, rtol=1e-5, atol=1e-8):\n",
-    "    for key in d1.keys() - d2.keys():\n",
-    "        assert np.isclose(d1[key], 0, rtol=rtol, atol=atol)\n",
-    "    for key in d2.keys() - d1.keys():\n",
-    "        assert np.isclose(d2[key], 0, rtol=rtol, atol=atol)\n",
-    "    for key in d1.keys() & d2.keys():\n",
-    "        assert np.isclose(d1[key], d2[key], rtol=rtol, atol=atol)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "ca6102c5",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "check_dict_agreement(\n",
-    "    {tuple(k): v for k, v in dict(result_perceval[\"results\"]).items()},\n",
-    "    result_optyx\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "a7c85548",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": ".venv",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.12.3"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}

From 43d2bdc73055562f3f6b0908cc35f5d07fe39184 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Wed, 24 Sep 2025 11:22:51 +0100
Subject: [PATCH 24/59] Fixed a bug in daggers for Multiply and Divide

---
 optyx/core/diagram.py | 11 +++++++++--
 optyx/core/zw.py      | 37 +++++++++++++++++--------------------
 optyx/utils/utils.py  | 34 ++++++++++++++++++++++++++++------
 3 files changed, 54 insertions(+), 28 deletions(-)

diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index ce40e78e..35cc9b50 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -303,6 +303,7 @@ def to_tensor(
     ) -> tensor.Diagram:
         """Returns a :class:`tensor.Diagram` for evaluation"""
         from optyx.core import zw
+        from optyx.utils.utils import is_diagram_LO, is_identity
 
         prev_layers: List[Tuple[int, Box]] = []
 
@@ -321,7 +322,7 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
             )
         layer_dims = input_dims
 
-        if len(self.boxes) == 0 and len(self.offsets) == 0:
+        if is_identity(self):
             return tensor.Diagram.id(list_to_dim(layer_dims))
 
         for i, (box, left_offset) in enumerate(zip(self.boxes, self.offsets)):
@@ -336,13 +337,19 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
                 input_dims,
                 prev_layers
             )
+
             dims_in = layer_dims[left_offset:left_offset + len(box.dom)]
+
             dims_out, _ = modify_io_dims_against_max_dim(
                 box.determine_output_dimensions(dims_in),
                 None,
                 max_dim
             )
-            if isinstance(box, zw.LO_ELEMENTS):
+
+            if (
+                isinstance(box, zw.LO_ELEMENTS) or
+                is_identity(box)
+            ):
                 prev_layers.append((left_offset, box))
             elif isinstance(box, DualRail):
                 prev_layers.append((left_offset, zw.Select(1)))
diff --git a/optyx/core/zw.py b/optyx/core/zw.py
index d23b95d8..65cf0ce5 100644
--- a/optyx/core/zw.py
+++ b/optyx/core/zw.py
@@ -291,7 +291,6 @@ def __init__(
         super().__init__(legs_in, legs_out, diagram.Mode(1))
         self.legs_in = legs_in
         self.legs_out = legs_out
-        self.photon_sum_preserving = False
 
     def conjugate(self):
         return ZBox(self.legs_in, self.legs_out, self.amplitudes.conjugate())
@@ -430,7 +429,6 @@ def __init__(self,
 
         name = "Create(1)" if self.photons == (1,) else f"Create({photons})"
         super().__init__(name, 0, len(self.photons))
-        self.photon_sum_preserving = False
 
     def conjugate(self):
         return self
@@ -534,7 +532,6 @@ def __init__(self,
         self.photons = photons or (1,)
         name = "Select(1)" if self.photons == (1,) else f"Select({photons})"
         super().__init__(name, len(self.photons), 0)
-        self.photon_sum_preserving = False
 
     def inflate(self, d):
 
@@ -690,20 +687,20 @@ class Multiply(ZWBox):
 
     Example
     -------
-    >>> mbox = Multiply()
-    >>> result = mbox.to_tensor(input_dims=[3, 3]).eval().array
-    >>> import numpy as np
-    >>> assert result.shape == (3, 3, 9)
-    >>> nonzero = np.nonzero(result)
-    >>> assert len(nonzero[0]) > 0
+    >>> mbox = Create(3, 2) >> Multiply() >> Select(6)
+    >>> mbox_dagger = mbox.dagger()
+    >>> tensor = mbox.to_tensor().eval().array
+    >>> assert np.allclose(tensor, 1.0)
+    >>> tensor_dagger = mbox_dagger.to_tensor().eval().array
+    >>> assert np.allclose(tensor_dagger, 1.0)
+
     """
 
     def __init__(self, is_dagger: bool = False):
         dom = diagram.Mode(1) if is_dagger else diagram.Mode(2)
         cod = diagram.Mode(2) if is_dagger else diagram.Mode(1)
-
         super().__init__("Multiply", dom, cod)
-        self.photon_sum_preserving = False
+        self.is_dagger = is_dagger
 
     def truncation_specification(
         self,
@@ -716,7 +713,7 @@ def truncation_specification(
 
     def determine_output_dimensions(self, input_dims: List[int]) -> List[int]:
         if self.is_dagger:
-            return [int(input_dims[0])]
+            return [int(input_dims[0]), int(input_dims[0])]
         return [int(np.prod(input_dims))]
 
     def conjugate(self):
@@ -732,11 +729,12 @@ class Divide(ZWBox):
 
     Example
     -------
-    >>> dbox = Divide()
-    >>> result = dbox.to_tensor(input_dims=[3, 3]).eval().array
-    >>> import numpy as np
-    >>> assert result.shape == (3, 3, 9)
-    >>> assert np.all(result >= 0)
+    >>> dbox = Create(9, 3) >> Divide() >> Select(3)
+    >>> dbox_dagger = dbox.dagger()
+    >>> result = dbox.to_tensor().eval().array
+    >>> assert np.allclose(result, 1.0)
+    >>> result_dagger = dbox_dagger.to_tensor().eval().array
+    >>> assert np.allclose(result_dagger, 1.0)
     """
 
     def __init__(self, is_dagger: bool = False):
@@ -744,7 +742,6 @@ def __init__(self, is_dagger: bool = False):
         cod = diagram.Mode(2) if is_dagger else diagram.Mode(1)
         super().__init__("Divide", dom, cod)
         self.is_dagger = is_dagger
-        self.photon_sum_preserving = False
 
     def truncation_specification(
         self,
@@ -759,8 +756,8 @@ def truncation_specification(
 
     def determine_output_dimensions(self, input_dims: List[int]) -> List[int]:
         if self.is_dagger:
-            return [int(input_dims[0])]
-        return [int(np.prod(input_dims))]
+            return [diagram.MAX_DIM, diagram.MAX_DIM]
+        return [int(input_dims[0])]
 
     def conjugate(self):
         return self
diff --git a/optyx/utils/utils.py b/optyx/utils/utils.py
index df0e6502..e485f4aa 100644
--- a/optyx/utils/utils.py
+++ b/optyx/utils/utils.py
@@ -453,12 +453,19 @@ def update_connections(
     end = len(wires_in_light_cone) - previous_right_offset
 
     # replace cod slice with a dom-length slice of the same boolean
+    from optyx.core.control import BitControlledBox
+    if isinstance(previous_box, BitControlledBox):
+        return (
+            wires_in_light_cone[:start]
+            + [False]  # control wire always out of light-cone
+            + [connected] * (len(previous_box.dom) - 1)
+            + wires_in_light_cone[end:]
+        )
     return (
         wires_in_light_cone[:start]
         + [connected] * len(previous_box.dom)
         + wires_in_light_cone[end:]
     )
-
 def calculate_right_offset(total_wires: int, left_offset: int, span_len: int) -> int:
     """Right offset = number of wires to the right of a span."""
     return total_wires - span_len - left_offset
@@ -517,10 +524,11 @@ def get_max_dim_for_box(
     prev_layers,
 ):
     from optyx.core.diagram import Swap, DualRail
-    from optyx.core.zw import Create, Endo
+    from optyx.core.zw import Create, Endo, Divide, Multiply
     from optyx.core.control import BitControlledBox
 
-    if len(box.dom) == 0 or isinstance(box, (Swap, Endo)):
+    if (len(box.dom) == 0 or
+        isinstance(box, (Swap, Endo, Divide, Multiply))):
         return 1e20
 
     dim_for_box = 0
@@ -567,10 +575,8 @@ def get_max_dim_for_box(
                 )
                 if idxs:
                     dim_for_box += sum(previous_box.photons[i] for i in idxs)
-
             if isinstance(previous_box, DualRail):
                 dim_for_box += 1
-
         if isinstance(previous_box, Swap):
             wires_in_light_cone = (
                 wires_in_light_cone[:adj_left]
@@ -586,4 +592,20 @@ def get_max_dim_for_box(
                 previous_right_offset,
             )
     dim_for_box += sum(2 * dim for wire, dim in zip(wires_in_light_cone, input_dims) if wire) + 1
-    return max(dim_for_box, 3)
+    return max(dim_for_box, 2)
+
+
+def is_diagram_LO(diagram):
+    from optyx.core.zw import LO_ELEMENTS
+    if is_identity(diagram):
+        return True
+
+    for box in diagram.boxes:
+        if is_identity(box):
+            continue
+        if not isinstance(box, LO_ELEMENTS):
+            return False
+
+    return True
+
+is_identity = lambda box: len(box.boxes) == 0 and len(box.offsets) == 0
\ No newline at end of file

From c5e9df413493c71531f23d18b97ec17566f498f2 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Wed, 24 Sep 2025 11:57:15 +0100
Subject: [PATCH 25/59] Fixed a bug in zw.Mod2

---
 optyx/core/zw.py | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/optyx/core/zw.py b/optyx/core/zw.py
index 65cf0ce5..afec0796 100644
--- a/optyx/core/zw.py
+++ b/optyx/core/zw.py
@@ -780,7 +780,9 @@ class Mod2(ZWBox):
     """
 
     def __init__(self, is_dagger: bool = False):
-        super().__init__("Mod2", diagram.Mode(1), diagram.Bit(1))
+        dom = diagram.Bit(1) if is_dagger else diagram.Mode(1)
+        cod = diagram.Mode(1) if is_dagger else diagram.Bit(1)
+        super().__init__("Mod2", dom, cod)
         self.is_dagger = is_dagger
 
     def truncation_specification(
@@ -794,7 +796,7 @@ def truncation_specification(
 
     def determine_output_dimensions(self, input_dims: List[int]) -> List[int]:
         if self.is_dagger:
-            return [input_dims[0]]
+            return [diagram.MAX_DIM]
         return [2]
 
     def conjugate(self):

From b399ccbd47b8cda1d97c50f94e53262fe350227e Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Wed, 24 Sep 2025 18:40:26 +0100
Subject: [PATCH 26/59] refactored the max dimension finding algorithm

---
 optyx/classical.py    |   2 +-
 optyx/core/channel.py |   4 +-
 optyx/core/control.py |  15 +++-
 optyx/core/diagram.py | 154 ++++++++++++++++++++++++++++--------------
 optyx/core/zw.py      |  37 +++++++++-
 optyx/core/zx.py      |   4 ++
 optyx/utils/utils.py  |  77 ++++++++++-----------
 7 files changed, 195 insertions(+), 98 deletions(-)

diff --git a/optyx/classical.py b/optyx/classical.py
index 382ab4c7..b6e0c5eb 100644
--- a/optyx/classical.py
+++ b/optyx/classical.py
@@ -192,7 +192,7 @@ def __init__(
             )
 
             super().__init__(
-                f"BitControlledGate",
+                "BitControlledGate",
                 kraus,
                 bit @ tp**len(control_gate_single.dom),
                 tp**len(control_gate_single.cod)
diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index cabf31f3..5fd5a838 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -240,7 +240,8 @@ def is_pure(self):
         for layer in self:
             generator = layer.inside[0][1]
 
-            # if we have a discard/measure acting on quantum types, it's not pure
+            # if we have a discard/measure
+            # acting on quantum types, it's not pure
             if (
                 isinstance(generator, (Discard, Measure)) and
                 any(not ty.is_classical for ty in generator.dom.inside)
@@ -878,6 +879,7 @@ class Cap(frobenius.Cap, Channel):
 class Hypergraph(hypergraph.Hypergraph):  # pragma: no cover
     category, functor = Category, Functor
 
+
 Hypergraph.ty_factory = Ty
 Diagram.spider_factory = Spider
 Diagram.cup_factory = Cup
diff --git a/optyx/core/control.py b/optyx/core/control.py
index f691b6c8..b210431d 100644
--- a/optyx/core/control.py
+++ b/optyx/core/control.py
@@ -40,7 +40,7 @@
 from discopy import tensor
 from discopy.frobenius import Dim
 import numpy as np
-from optyx.utils.utils import BasisTransition
+from optyx.utils.utils import BasisTransition, is_diagram_LO
 
 from optyx.core import diagram, zw
 
@@ -119,7 +119,18 @@ def __init__(
         self.action_box = action_box
         self.default_box = default_box
         self.is_dagger = is_dagger
-        self.photon_sum_preserving = False
+        self.photon_preservation_behaviour = \
+            diagram.PhotonNumberPreservation.CUSTOM
+
+    def photon_number_transform(self, dims_in, dims_out):
+        if is_diagram_LO(self.action_box) and is_diagram_LO(self.default_box):
+            from optyx.core.zx import Z
+            return Z(1, 0) @ self.default_box if not self.is_dagger else \
+                Z(0, 1) @ self.default_box
+        else:
+            self.photon_preservation_behaviour = \
+                diagram.PhotonNumberPreservation.NON_LO
+            return super().photon_number_transform(dims_in, dims_out)
 
     def determine_output_dimensions(self, input_dims: List[int]) -> List[int]:
 
diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index 35cc9b50..d4adee98 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -226,8 +226,8 @@
 from discopy.cat import factory, rsubs
 from discopy.frobenius import Dim
 from discopy.quantum.gates import format_number
+from enum import Enum
 from optyx.utils.utils import (
-    modify_io_dims_against_max_dim,
     BasisTransition,
     calculate_right_offset,
     get_max_dim_for_box
@@ -237,6 +237,24 @@
 MAX_DIM = 10
 
 
+class PhotonNumberPreservation(Enum):
+    """This is used as a flag to indicate how a box acts
+    on the incoming photons. Used by the tensor network building
+    algorithm to determine the bond dimensions / truncations.
+
+    LO: Linear Optical - preserves photon number between input and output
+    NON_LO: Does not preserve photon number between input and output
+    CUSTOM: Custom behaviour defined by the user
+                (a box need to implement a method)
+    QUBIT: Qubit - does not act on photons
+    """
+
+    LO = "lo"
+    NON_LO = "non_lo"
+    CUSTOM = "custom"
+    QUBIT = "qubit"
+
+
 class Ob(frobenius.Ob):
     """Basic object in an optyx Diagram: bit or mode"""
 
@@ -303,28 +321,21 @@ def to_tensor(
     ) -> tensor.Diagram:
         """Returns a :class:`tensor.Diagram` for evaluation"""
         from optyx.core import zw
-        from optyx.utils.utils import is_diagram_LO, is_identity
-
-        prev_layers: List[Tuple[int, Box]] = []
-
-        # pylint: disable=import-outside-toplevel
-        def list_to_dim(dims: np.ndarray | list) -> Dim:
-            """Converts a list of dimensions to a Dim object"""
-            return Dim(*[int(i) for i in dims])
-
-        number_of_input_layer_wires = len(self.dom)
+        from optyx.utils.utils import is_identity
 
         if input_dims is None:
             input_dims = [2 for _ in range(len(self.dom))]
         else:
             assert len(self.dom) == len(input_dims), (
-                f"Input dims length {len(input_dims)} does not match number of input wires {len(self.dom)}"
+                "Input dims length does not match number of input wires"
             )
         layer_dims = input_dims
 
         if is_identity(self):
-            return tensor.Diagram.id(list_to_dim(layer_dims))
+            return tensor.Diagram.id(Dim(*[int(i) for i in layer_dims]))
 
+        number_of_input_layer_wires = len(self.dom)
+        prev_layers: List[Tuple[int, Box]] = []
         for i, (box, left_offset) in enumerate(zip(self.boxes, self.offsets)):
             right_offset = calculate_right_offset(
                 number_of_input_layer_wires, left_offset, len(box.dom)
@@ -337,47 +348,23 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
                 input_dims,
                 prev_layers
             )
-
             dims_in = layer_dims[left_offset:left_offset + len(box.dom)]
+            dims_out = [max_dim if i > max_dim else i
+                        for i in box.determine_output_dimensions(dims_in)]
 
-            dims_out, _ = modify_io_dims_against_max_dim(
-                box.determine_output_dimensions(dims_in),
-                None,
-                max_dim
-            )
-
-            if (
-                isinstance(box, zw.LO_ELEMENTS) or
-                is_identity(box)
-            ):
-                prev_layers.append((left_offset, box))
-            elif isinstance(box, DualRail):
-                prev_layers.append((left_offset, zw.Select(1)))
-                prev_layers.append((left_offset, zw.Create(0)))
-                prev_layers.append((left_offset, box))
-            else:
-                if len(dims_in) > 0:
-                    prev_layers.append(
-                        (
-                            left_offset,
-                            zw.Select(*[int(i) for i in np.array(dims_in)-1])
-                        )
-                    )
-                if len(dims_out) > 0:
-                    prev_layers.append(
-                        (
-                            left_offset,
-                            zw.Create(*[int(i) for i in np.array(dims_out)-1])
-                        )
-                    )
+            prev_layers += [
+                (left_offset, replacement_box) for replacement_box in
+                box.photon_number_transform(dims_in, dims_out)
+            ]
 
             left = Dim()
             if left_offset > 0:
-                left = list_to_dim(layer_dims[0:left_offset])
+                left = Dim(*[int(i) for i in layer_dims[0:left_offset]])
             right = Dim()
             if left_offset + len(box.dom) < number_of_input_layer_wires:
-                right = list_to_dim(
-                    layer_dims[left_offset + len(box.dom): number_of_input_layer_wires]
+                right = Dim(
+                    *[int(i) for i in layer_dims[left_offset + len(box.dom):
+                                                 number_of_input_layer_wires]]
                 )
 
             number_of_input_layer_wires += -len(box.dom) + len(box.cod)
@@ -405,7 +392,6 @@ def list_to_dim(dims: np.ndarray | list) -> Dim:
         diagram >>= zboxes
         return diagram
 
-
     @classmethod
     def from_bosonic_operator(cls, n_modes, operators, scalar=1):
         """Create a :class:`zw` diagram from a bosonic operator."""
@@ -474,8 +460,42 @@ class Box(frobenius.Box, Diagram):
 
     def __init__(self, name, dom, cod, array=None, **params):
         self._array = array
-        self.photon_sum_preserving = True
         super().__init__(name, dom, cod, **params)
+        self.photon_preservation_behaviour = PhotonNumberPreservation.NON_LO
+
+    def photon_number_transform(
+        self, dims_in: list[int], dims_out: list[int]
+    ) -> Box:
+        if (
+            self.photon_preservation_behaviour ==
+            PhotonNumberPreservation.LO or
+            self.photon_preservation_behaviour ==
+            PhotonNumberPreservation.QUBIT
+        ):
+            return [self]
+        elif self.photon_preservation_behaviour == \
+                PhotonNumberPreservation.NON_LO:
+            from optyx.core.zw import Create, Select
+
+            return_list = []
+            if len(dims_in) > 0:
+                return_list.append(
+                    (
+                        Select(*[int(i) for i in np.array(dims_in)-1])
+                    )
+                )
+            if len(dims_out) > 0:
+                return_list.append(
+                    (
+                        Create(*[int(i) for i in np.array(dims_out)-1])
+                    )
+                )
+            return return_list
+        else:
+            raise NotImplementedError(
+                f"{self.__class__.__name__} does not implement "
+                "photon_number_transform method"
+            )
 
     @classmethod
     def get_perm(self, n, d):
@@ -654,6 +674,7 @@ class Spider(frobenius.Spider, Box):
 
     draw_as_spider = True
     color = "green"
+    photon_preservation_behaviour = PhotonNumberPreservation.NON_LO
 
     def conjugate(self):
         return self
@@ -766,6 +787,8 @@ def grad(self, var, **params):
 class Swap(frobenius.Swap, Box):
     """Swap in optyx diagram"""
 
+    photon_preservation_behaviour = PhotonNumberPreservation.LO
+
     def conjugate(self):
         return self
 
@@ -811,6 +834,7 @@ def __init__(self, scalar: complex | Symbol):
         super().__init__(
             name="scalar", dom=Mode(0), cod=Mode(0), data=self.scalar
         )
+        self.photon_preservation_behaviour = PhotonNumberPreservation.LO
 
     def conjugate(self):
         return Scalar(self.scalar.conjugate())
@@ -870,7 +894,22 @@ def __init__(self,
         super().__init__("2R", dom, cod)
         self.internal_state = internal_state
         self.is_dagger = is_dagger
-        self.photon_sum_preserving = False
+        self.photon_preservation_behaviour = \
+            PhotonNumberPreservation.CUSTOM
+
+    def photon_number_transform(self, dims_in, dims_out):
+        from optyx.core.zw import Create
+        from optyx.core.zx import Z
+        from copy import deepcopy
+
+        prev_layers = []
+        prev_layers.append(Z(1, 0) if not self.is_dagger else Z(0, 1))
+        prev_layers.append(Create(1) if not self.is_dagger else Z(1, 0))
+        box = deepcopy(self)
+        if not self.is_dagger:
+            box.dom = Mode(1)
+        prev_layers.append(box)
+        return prev_layers if not self.is_dagger else prev_layers[::-1]
 
     def conjugate(self):
         return self
@@ -930,6 +969,21 @@ def __init__(self, is_dagger=False):
         else:
             super().__init__("PTD", Mode(1), Bit(1))
         self.is_dagger = is_dagger
+        self.photon_preservation_behaviour = \
+            PhotonNumberPreservation.CUSTOM
+
+    def photon_number_transform(self, dims_in, dims_out):
+        from optyx.core.zw import Create, Select
+        from optyx.core.zx import Z
+
+        prev_layers = []
+        if self.is_dagger:
+            prev_layers.append(Z(1, 0))
+            prev_layers.append(Create(dims_out[0]-1))
+        else:
+            prev_layers.append(Select(0))
+            prev_layers.append(Z(0, 1))
+        return prev_layers
 
     def truncation_specification(
         self,
diff --git a/optyx/core/zw.py b/optyx/core/zw.py
index afec0796..1306fa6f 100644
--- a/optyx/core/zw.py
+++ b/optyx/core/zw.py
@@ -171,6 +171,8 @@ def __init__(self, name, dom, cod, **params):
         if isinstance(cod, int):
             cod = diagram.Mode(cod)
         super().__init__(name=name, dom=dom, cod=cod, **params)
+        self.photon_preservation_behaviour = \
+            diagram.PhotonNumberPreservation.LO
 
 
 class IndexableAmplitudes:
@@ -291,6 +293,8 @@ def __init__(
         super().__init__(legs_in, legs_out, diagram.Mode(1))
         self.legs_in = legs_in
         self.legs_out = legs_out
+        self.photon_preservation_behaviour = \
+            diagram.PhotonNumberPreservation.NON_LO
 
     def conjugate(self):
         return ZBox(self.legs_in, self.legs_out, self.amplitudes.conjugate())
@@ -426,10 +430,14 @@ def __init__(self,
                 "All internal states must be of the same length"
 
         self.internal_states = internal_states
-
+        self.photon_preservation_behaviour = \
+            diagram.PhotonNumberPreservation.CUSTOM
         name = "Create(1)" if self.photons == (1,) else f"Create({photons})"
         super().__init__(name, 0, len(self.photons))
 
+    def photon_number_transform(self, dims_in, dims_out):
+        return super().photon_number_transform(dims_in, dims_out)
+
     def conjugate(self):
         return self
 
@@ -530,9 +538,14 @@ def __init__(self,
 
         self.internal_states = internal_states
         self.photons = photons or (1,)
+        self.photon_preservation_behaviour = \
+            diagram.PhotonNumberPreservation.CUSTOM
         name = "Select(1)" if self.photons == (1,) else f"Select({photons})"
         super().__init__(name, len(self.photons), 0)
 
+    def photon_number_transform(self, dims_in, dims_out):
+        return super().photon_number_transform(dims_in, dims_out)
+
     def inflate(self, d):
 
         dgrm = Create(
@@ -701,6 +714,8 @@ def __init__(self, is_dagger: bool = False):
         cod = diagram.Mode(2) if is_dagger else diagram.Mode(1)
         super().__init__("Multiply", dom, cod)
         self.is_dagger = is_dagger
+        self.photon_preservation_behaviour = \
+            diagram.PhotonNumberPreservation.NON_LO
 
     def truncation_specification(
         self,
@@ -742,6 +757,8 @@ def __init__(self, is_dagger: bool = False):
         cod = diagram.Mode(2) if is_dagger else diagram.Mode(1)
         super().__init__("Divide", dom, cod)
         self.is_dagger = is_dagger
+        self.photon_preservation_behaviour = \
+            diagram.PhotonNumberPreservation.NON_LO
 
     def truncation_specification(
         self,
@@ -784,6 +801,19 @@ def __init__(self, is_dagger: bool = False):
         cod = diagram.Mode(1) if is_dagger else diagram.Bit(1)
         super().__init__("Mod2", dom, cod)
         self.is_dagger = is_dagger
+        self.photon_preservation_behaviour = \
+            diagram.PhotonNumberPreservation.CUSTOM
+
+    def photon_number_transform(self, dims_in, dims_out):
+        from optyx.core.zx import Z
+        prev_layers = []
+        if self.is_dagger:
+            prev_layers.append(Z(1, 0))
+            prev_layers.append(Create(dims_out[0] - 1))
+        else:
+            prev_layers.append(Select(0))
+            prev_layers.append(Z(0, 1))
+        return prev_layers
 
     def truncation_specification(
         self,
@@ -828,5 +858,6 @@ def Id(n):
     Select,
     Add,
     Endo,
-    diagram.Swap
-)
\ No newline at end of file
+    diagram.Swap,
+    Add
+)
diff --git a/optyx/core/zx.py b/optyx/core/zx.py
index 8a441dc1..c52c20c3 100644
--- a/optyx/core/zx.py
+++ b/optyx/core/zx.py
@@ -375,6 +375,8 @@ def __init__(self, name, dom, cod, **params):
         if isinstance(cod, int):
             cod = diagram.Bit(cod)
         super().__init__(name=name, dom=dom, cod=cod, **params)
+        self.photon_preservation_behaviour = \
+            diagram.PhotonNumberPreservation.QUBIT
 
     def conjugate(self):
         raise NotImplementedError
@@ -413,6 +415,8 @@ def __init__(self, n_legs_in, n_legs_out, phase=0):
         phase_str = f", {self.phase}" if self.phase else ""
         self.name = f"{factory_str}({n_legs_in}, {n_legs_out}{phase_str})"
         self.n_legs_in, self.n_legs_out = n_legs_in, n_legs_out
+        self.photon_preservation_behaviour = \
+            diagram.PhotonNumberPreservation.QUBIT
 
     def conjugate(self):
         return type(self)(self.n_legs_in, self.n_legs_out, -self.phase)
diff --git a/optyx/utils/utils.py b/optyx/utils/utils.py
index e485f4aa..8e3d2a14 100644
--- a/optyx/utils/utils.py
+++ b/optyx/utils/utils.py
@@ -158,15 +158,6 @@ def basis_vector_from_kets(
     return j
 
 
-def modify_io_dims_against_max_dim(input_dims, output_dims, max_dim):
-    """Modify the input and output dimensions against the maximum dimension"""
-    if input_dims is not None:
-        input_dims = [max_dim if i > max_dim else i for i in input_dims]
-    if output_dims is not None:
-        output_dims = [max_dim if i > max_dim else i for i in output_dims]
-    return input_dims, output_dims
-
-
 def amplitudes_2_tensor(perceval_result, input_occ, output_occ):
     # pylint: disable=import-outside-toplevel
     from discopy.tensor import Tensor
@@ -437,8 +428,9 @@ def update_connections(
     previous_box,
     previous_right_offset: int,
 ) -> List[bool]:
+    from optyx.core.diagram import mode
     """
-    Replace the previous box's COD segment in the light-cone by a DOM-length
+    Replace the previous box's cod segment in the light-cone by a dom-length
     segment that is either all True (if connected) or all False.
     This pulls the cone one layer backward.
     """
@@ -452,24 +444,22 @@ def update_connections(
     start = previous_left_offset
     end = len(wires_in_light_cone) - previous_right_offset
 
-    # replace cod slice with a dom-length slice of the same boolean
-    from optyx.core.control import BitControlledBox
-    if isinstance(previous_box, BitControlledBox):
-        return (
-            wires_in_light_cone[:start]
-            + [False]  # control wire always out of light-cone
-            + [connected] * (len(previous_box.dom) - 1)
-            + wires_in_light_cone[end:]
-        )
     return (
         wires_in_light_cone[:start]
-        + [connected] * len(previous_box.dom)
+        + [connected if t == mode else False for t in previous_box.dom]
         + wires_in_light_cone[end:]
     )
-def calculate_right_offset(total_wires: int, left_offset: int, span_len: int) -> int:
+
+
+def calculate_right_offset(
+        total_wires: int,
+        left_offset: int,
+        span_len: int
+) -> int:
     """Right offset = number of wires to the right of a span."""
     return total_wires - span_len - left_offset
 
+
 def is_previous_box_connected_to_current_box(
     wires_in_light_cone: List[bool],
     previous_left_offset: int,
@@ -486,11 +476,13 @@ def is_previous_box_connected_to_current_box(
     )
     # lengths should match by construction
     assert len(mask) == len(wires_in_light_cone), (
-        f"Mask/wires length mismatch: {len(mask)} != {len(wires_in_light_cone)}"
+        (f"Mask/wires length mismatch: {len(mask)}"
+         + f" != {len(wires_in_light_cone)}")
     )
 
     return any(w and m for w, m in zip(wires_in_light_cone, mask))
 
+
 def get_previous_box_cod_index_in_light_cone(
     wires_in_light_cone: List[bool],
     previous_left_offset: int,
@@ -498,7 +490,8 @@ def get_previous_box_cod_index_in_light_cone(
     previous_right_offset: int,
 ) -> List[int]:
     """
-    Get the indices of the COD of the previous box that are in the current light-cone.
+    Get the indices of the cod of the previous box
+    that are in the current light-cone.
     """
     mask = (
         [False] * previous_left_offset
@@ -507,11 +500,13 @@ def get_previous_box_cod_index_in_light_cone(
     )
     # lengths should match by construction
     assert len(mask) == len(wires_in_light_cone), (
-        f"Mask/wires length mismatch: {len(mask)} != {len(wires_in_light_cone)}"
+        (f"Mask/wires length mismatch: {len(mask)}"
+         + f" != {len(wires_in_light_cone)}")
     )
 
     return [
-        i - previous_left_offset for i, (w, m) in enumerate(zip(wires_in_light_cone, mask))
+        i - previous_left_offset for i, (w, m) in
+        enumerate(zip(wires_in_light_cone, mask))
         if w and m
     ]
 
@@ -523,27 +518,24 @@ def get_max_dim_for_box(
     input_dims: List[int],
     prev_layers,
 ):
-    from optyx.core.diagram import Swap, DualRail
+    from optyx.core.diagram import Swap, mode
     from optyx.core.zw import Create, Endo, Divide, Multiply
-    from optyx.core.control import BitControlledBox
 
-    if (len(box.dom) == 0 or
-        isinstance(box, (Swap, Endo, Divide, Multiply))):
+    if (
+        len(box.dom) == 0 or
+        isinstance(box, (Swap, Endo, Divide, Multiply))
+    ):
         return 1e20
 
     dim_for_box = 0
 
-    # light-cone at the current layer inputs
+    # light-cone at the current layer [connected] * len(previous_box.dom)inputs
     wires_in_light_cone: List[bool] = (
         [False] * left_offset
-        + [True] * len(box.dom)
-        + [False] * right_offset
-    ) if not isinstance(box, BitControlledBox) else (
-        [False] * (left_offset + 1)
-        + [True] * (len(box.dom) - 1)
+        + [True if t == mode else False for t in box.dom]
         + [False] * right_offset
-
     )
+
     # walk previous layers from nearest to farthest
     for previous_left_offset, previous_box in prev_layers[::-1]:
         total = len(wires_in_light_cone)
@@ -558,7 +550,8 @@ def get_max_dim_for_box(
         elif adj_left > max_left:
             adj_left = max_left
 
-        previous_right_offset = calculate_right_offset(total, adj_left, cod_len)
+        previous_right_offset = \
+            calculate_right_offset(total, adj_left, cod_len)
 
         if is_previous_box_connected_to_current_box(
             wires_in_light_cone,
@@ -575,8 +568,7 @@ def get_max_dim_for_box(
                 )
                 if idxs:
                     dim_for_box += sum(previous_box.photons[i] for i in idxs)
-            if isinstance(previous_box, DualRail):
-                dim_for_box += 1
+
         if isinstance(previous_box, Swap):
             wires_in_light_cone = (
                 wires_in_light_cone[:adj_left]
@@ -591,7 +583,8 @@ def get_max_dim_for_box(
                 previous_box,
                 previous_right_offset,
             )
-    dim_for_box += sum(2 * dim for wire, dim in zip(wires_in_light_cone, input_dims) if wire) + 1
+    dim_for_box += sum(2 * dim for wire, dim in
+                       zip(wires_in_light_cone, input_dims) if wire) + 1
     return max(dim_for_box, 2)
 
 
@@ -608,4 +601,6 @@ def is_diagram_LO(diagram):
 
     return True
 
-is_identity = lambda box: len(box.boxes) == 0 and len(box.offsets) == 0
\ No newline at end of file
+
+is_identity = lambda box: (len(box.boxes) == 0 and  # noqa: E731
+                           len(box.offsets) == 0)

From cd12a774a751387f21ad63c5f04a3c3a0a73102a Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Thu, 25 Sep 2025 09:52:27 +0100
Subject: [PATCH 27/59] linting qubits

---
 optyx/qubits.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/optyx/qubits.py b/optyx/qubits.py
index c2212c82..d2958768 100644
--- a/optyx/qubits.py
+++ b/optyx/qubits.py
@@ -412,7 +412,9 @@ def _to_optyx_from_graphix(cls, underlying_circuit):
 
         og = opengraph.OpenGraph.from_pattern(underlying_circuit)
         pyzx_diagram = pyzx.to_pyzx_graph(og)
+        # pylint: disable=protected-access
         pyzx_diagram._inputs = tuple(pyzx_diagram._inputs)
+        # pylint: disable=protected-access
         pyzx_diagram._outputs = tuple(pyzx_diagram._outputs)
         return cls._to_optyx_from_pyzx(pyzx_diagram)
 

From 142b50771f6b5cc492efbd9e0f8a85f710639bc1 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Thu, 25 Sep 2025 10:03:53 +0100
Subject: [PATCH 28/59] linting photonic

---
 optyx/photonic.py | 58 +++++++++++++++++++++++++++++++++++------------
 1 file changed, 44 insertions(+), 14 deletions(-)

diff --git a/optyx/photonic.py b/optyx/photonic.py
index 2b6de50c..6641fd55 100644
--- a/optyx/photonic.py
+++ b/optyx/photonic.py
@@ -245,13 +245,13 @@
 """
 
 
+from functools import cached_property
+from abc import abstractmethod, ABC
+from collections.abc import Iterable
 import numpy as np
 import sympy as sp
 from sympy import Expr, lambdify, Symbol, Mul
 from discopy.cat import rsubs
-from functools import cached_property
-from abc import abstractmethod, ABC
-from collections.abc import Iterable
 
 from optyx.core import (
     channel,
@@ -384,6 +384,9 @@ def _normal_form(self, dom, cod):
 
     @cached_property
     def array(self):
+        """
+        Array to be used for building zw diagrams.
+        """
         return np.asarray(self._compute_array())
 
     @abstractmethod
@@ -417,9 +420,7 @@ class Gate(AbstractGate):
     ...                 diagram.Id(diagram.Mode(2)).to_path().eval(2).array)
     """
 
-    # need to make it a Circuit?
-    # this should also take a perceval matrix
-    # as an input
+    # pylint: disable=too-many-positional-arguments
     def __init__(
         self,
         matrix,
@@ -443,6 +444,9 @@ def dagger(self):
         )
 
     def conjugate(self):
+        """
+        Conjugate defined on the underlying matrix.
+        """
         return Gate(
             np.conjugate(self.array),
             len(self.dom),
@@ -497,10 +501,16 @@ def dagger(self):
         return Phase(-self.angle)
 
     def conjugate(self):
+        """
+        Conjugate defined on the underlying matrix.
+        """
         return Phase(-self.angle)
 
 
 class NumOp(Channel):
+    """
+    Number operator.
+    """
     def __init__(self):
         super().__init__(
             "NumOp",
@@ -589,6 +599,9 @@ def dagger(self):
         return BBS(0.5 - self.bias)
 
     def conjugate(self):
+        """
+        Conjugate defined on the underlying matrix.
+        """
         return BBS(self.bias, not self.is_conj)
 
 
@@ -641,6 +654,9 @@ def __init__(self,
 
     @cached_property
     def global_phase(self):
+        """
+        Global phase of the TBS.
+        """
         backend = sp if self.dtype is Expr else np
         return (
             -1j * backend.exp(-1j * self.theta * backend.pi)
@@ -677,6 +693,9 @@ def grad(self, var):
         return self._decomp().grad(var)
 
     def conjugate(self):
+        """
+        Conjugate defined on the underlying matrix.
+        """
         return TBS(self.theta, self.is_gate_dagger, not self.is_conj)
 
     def dagger(self):
@@ -740,6 +759,9 @@ def __init__(self,
 
     @cached_property
     def global_phase(self):
+        """
+        Global phase of the MZI.
+        """
         backend = sp if self.dtype is Expr else np
         return (
             -1j * backend.exp(-1j * self.theta * backend.pi)
@@ -783,6 +805,9 @@ def dagger(self):
                    is_conj=self.is_conj)
 
     def conjugate(self):
+        """
+        Conjugate defined on the underlying matrix.
+        """
         return MZI(self.theta, self.phi, self.is_gate_dagger, not self.is_conj)
 
 
@@ -864,11 +889,11 @@ def __init__(self, phase):
 
 
 class ZMeasurementDR(Diagram):
+    """
+    ZMeasurement circuit that performs a measurement in the Z basis
+    after applying a phase shift of alpha.
+    """
     def __new__(cls, alpha):
-        """
-        ZMeasurement circuit that performs a measurement in the Z basis
-        after applying a phase shift of alpha.
-        """
         return (
             qmode @ Phase(alpha) >>
             HadamardBS() >>
@@ -878,11 +903,11 @@ def __new__(cls, alpha):
 
 
 class XMeasurementDR(Diagram):
+    """
+    XMeasurement circuit that performs a measurement in the X basis
+    after applying a Hadamard beam splitter.
+    """
     def __new__(cls, alpha):
-        """
-        XMeasurement circuit that performs a measurement in the X basis
-        after applying a Hadamard beam splitter.
-        """
         return (
             HadamardBS() >>
             ZMeasurementDR(alpha)
@@ -926,6 +951,7 @@ class FusionTypeI(Diagram):
         :align: center
     """
     def __new__(cls):
+        # pylint: disable=invalid-name
         kraus_map_fusion_I = (
             diagram.Mode(1) @ diagram.Swap(
                 diagram.Mode(1),
@@ -971,6 +997,9 @@ def fusion_I_function(x):
 
 
 class Swap(channel.Swap):
+    """
+    Swap channel for qmodes.
+    """
     def __init__(self, left, right):
         super().__init__(qmode**left, qmode**right)
 
@@ -1061,6 +1090,7 @@ class FusionTypeII(Diagram):
         :align: center
     """
     def __new__(cls):
+        # pylint: disable=invalid-name
         fusion_II = Channel(
             "Fusion II",
             (

From f4e54a44fcef94dd26df4b117472f4129ce7f1d1 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Thu, 25 Sep 2025 10:27:41 +0100
Subject: [PATCH 29/59] linting classical

---
 optyx/core/channel.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index 5fd5a838..7b243b63 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -493,7 +493,7 @@ def eval(self, backend=None, **kwargs):
         return backend.eval(self, **kwargs)
 
 
-class Channel(frobenius.Box, Diagram):
+class Channel(Diagram, frobenius.Box):
     """
     Channel initialised by its Kraus map.
     """
@@ -647,7 +647,7 @@ def eval(self, n_photons=0, permanent=None, dtype=complex):
         )
 
 
-class CQMap(frobenius.Box, Diagram):
+class CQMap(Diagram, frobenius.Box):
     """
     Channel initialised by its Density matrix.
     """

From 43dc36a217222143fb4eb0fb4eeb6cd9712eb6e3 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Thu, 25 Sep 2025 10:30:12 +0100
Subject: [PATCH 30/59] linting backends

---
 optyx/core/backends.py | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/optyx/core/backends.py b/optyx/core/backends.py
index 1d01c668..0c46726f 100644
--- a/optyx/core/backends.py
+++ b/optyx/core/backends.py
@@ -195,7 +195,6 @@ def prob(self, occupation: tuple) -> float:
         prob_dist = self.prob_dist()
         return prob_dist.get(occupation, 0.0)
 
-    # pylint: disable=no-self-use
     def _convert_array_to_dict(
             self,
             array: np.ndarray,
@@ -290,7 +289,6 @@ class AbstractBackend(ABC):
     All backends must implement the `eval` method.
     """
 
-    # pylint: disable=no-self-use
     def _get_matrix(
         self,
         diagram: Diagram
@@ -321,7 +319,6 @@ def _get_quimb_tensor(
         """
         return self._get_discopy_tensor(diagram).to_quimb()
 
-    # pylint: disable=no-self-use
     def _umatrix_to_perceval_circuit(
             self,
             matrix: np.ndarray) -> pcvl.Circuit:
@@ -332,7 +329,6 @@ def _umatrix_to_perceval_circuit(
         perceval_matrix = pcvl.Matrix(matrix.T)
         return pcvl.components.Unitary(U=perceval_matrix)
 
-    # pylint: disable=no-self-use
     def _get_discopy_tensor(
         self,
         diagram: Diagram

From 83571878feb66e30a7c055e2ce7d6f99be5f8387 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Thu, 25 Sep 2025 10:45:04 +0100
Subject: [PATCH 31/59] linting channel

---
 optyx/core/channel.py | 34 ++++++++++++++++++++++++++++++----
 1 file changed, 30 insertions(+), 4 deletions(-)

diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index 7b243b63..4e3c0668 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -111,13 +111,13 @@
 from discopy import tensor
 from discopy import symmetric, frobenius, hypergraph
 from discopy.cat import factory
-from optyx.core import zx, diagram
 from pytket.extensions.pyzx import pyzx_to_tk
 from pyzx import extract_circuit
-
+from optyx.core import zx, diagram
 from optyx.utils.utils import explode_channel
 
 
+
 class Ob(frobenius.Ob):
     """Basic object: bit, mode, qubit or qmode"""
 
@@ -175,15 +175,24 @@ def double(self):
     @staticmethod
     # pylint: disable=invalid-name
     def from_optyx(ty):
+        """
+        Get quantum types from core/diagram.Ty.
+        """
         assert isinstance(ty, diagram.Ty)
         # pylint: disable=protected-access
         return Ty(*[Ob._quantum[ob.name] for ob in ty.inside])
 
     def needs_inflation(self) -> bool:
+        """
+        Diagrams with at least one :code:`qmode` need inflation.
+        """
         return "qmode" in self.name
 
     # pylint: disable=invalid-name
     def inflate(self, d) -> Ty:
+        """
+        Inflate the type.
+        """
         return (mode**0).tensor(
                 *(o**d if o.needs_inflation() else o for o in self)
         )
@@ -203,6 +212,10 @@ class Diagram(frobenius.Diagram):
     grad = tensor.Diagram.grad
 
     def needs_inflation(self) -> bool:
+        """
+        If the domain or codomain need inflation,
+        the diagram needs inflation.
+        """
         return self.dom.needs_inflation() or self.cod.needs_inflation()
 
     # pylint: disable=invalid-name
@@ -235,6 +248,11 @@ def double(self):
 
     @property
     def is_pure(self):
+        """
+        Check if the diagram is pure, i.e. it does not
+        contain any discards or measures acting on quantum types,
+        and does not prepare quantum types from classical types.
+        """
         are_layers_pure = []
         are_layers_classical = []
         for layer in self:
@@ -273,6 +291,9 @@ def is_pure(self):
         return not any(are_layers_pure) or all(are_layers_classical)
 
     def get_kraus(self):
+        """
+        Obtain the Kraus map of a pure circuit.
+        """
         assert self.is_pure, "Cannot get a Kraus map of non-pure circuit"
         kraus_maps = [diagram.Id(self.dom.single())]
         for layer in self:
@@ -363,7 +384,7 @@ def to_tket(self):
         )
 
     def to_pyzx(self):
-
+        """Convert to PyZX circuit. The circuit must be a pure circuit."""
         assert self.is_pure, "Diagram must be pure for conversion."
 
         return self.get_kraus().to_pyzx()
@@ -391,6 +412,8 @@ def from_discopy(cls, discopy_circuit):
 
     @classmethod
     def from_bosonic_operator(cls, n_modes, operators, scalar=1):
+        """Convert from a list of bosonic operators. Based on
+        diagram.Diagram.from_bosonic_operator."""
         return Channel(
             "Bosonic operator",
             diagram.Diagram.from_bosonic_operator(
@@ -415,6 +438,7 @@ def from_perceval(cls, p):
         acting on polarisation modes, time delays,
         and with symbols.
         """
+        # pylint: disable=import-outside-toplevel
         from optyx import photonic
         from optyx.utils import perceval_conversion
         import perceval as pcvl
@@ -605,6 +629,9 @@ def inflate(self, d):
 
 
 class Spider(frobenius.Spider, Channel):  # pragma: no cover
+    """
+    Spider as a channel.
+    """
     def __init__(self, n_legs_in: int, n_legs_out: int, typ: Ty, data=None,
                  **params):
         super().__init__(
@@ -726,7 +753,6 @@ def inflate(self, d):
         return diagram.Diagram.tensor(*diagrams)
 
     # pylint: disable=invalid-name
-    # pylint: disable=no-self-use
     def _measure_wire(self, ob, d):
         """Return the diagram that measures one `ob`."""
         # pylint: disable=import-outside-toplevel

From 5bcc25757ccc17a9ce3d3f77de604571fdaa6f1d Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Thu, 25 Sep 2025 10:50:55 +0100
Subject: [PATCH 32/59] linting control

---
 optyx/core/control.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/optyx/core/control.py b/optyx/core/control.py
index b210431d..d22948d7 100644
--- a/optyx/core/control.py
+++ b/optyx/core/control.py
@@ -153,7 +153,7 @@ def determine_output_dimensions(self, input_dims: List[int]) -> List[int]:
         return dims
 
     def truncation(
-        self, input_dims: List[int], output_dims: List[int]
+        self, input_dims: list[int] = None, output_dims: list[int] = None
     ) -> tensor.Box:
 
         if self.is_dagger:
@@ -260,7 +260,7 @@ def __init__(
         self.n_control_modes = n_control_modes
 
     def truncation(
-        self, input_dims: List[int], output_dims: List[int]
+        self, input_dims: list[int] = None, output_dims: list[int] = None
     ) -> tensor.Box:
 
         if self.is_dagger:

From a0c59693f512bfaf7d5e9e0251d8227ca0dd806f Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Thu, 25 Sep 2025 10:52:55 +0100
Subject: [PATCH 33/59] pflake channel

---
 optyx/core/channel.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index 4e3c0668..2616431d 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -117,7 +117,6 @@
 from optyx.utils.utils import explode_channel
 
 
-
 class Ob(frobenius.Ob):
     """Basic object: bit, mode, qubit or qmode"""
 

From 68f6897831c6b1bf8102c7cf3f5ce70286fd842d Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Thu, 25 Sep 2025 11:01:59 +0100
Subject: [PATCH 34/59] remove unused functions in utils

---
 optyx/utils/utils.py | 77 --------------------------------------------
 1 file changed, 77 deletions(-)

diff --git a/optyx/utils/utils.py b/optyx/utils/utils.py
index 8e3d2a14..ca9ed494 100644
--- a/optyx/utils/utils.py
+++ b/optyx/utils/utils.py
@@ -345,83 +345,6 @@ def preprocess_quimb_tensors_safe(tn, epsilon=1e-12, value_limit=1e10):
     return tn
 
 
-def total_photons_created(
-        diagram,
-        input_dims: Optional[List[int]] = None
-) -> int:
-    """
-    Scan `diagram` once and return the total number of photons created.
-
-    Counts:
-      - zw.Create(*photons) -> +sum(photons)
-    Everything else is ignored for 'creation'
-    (they conserve or consume photons).
-
-    Parameters
-    ----------
-    diagram : optyx.core.diagram.Diagram
-        The diagram to scan (sequential list of
-        boxes is in `diagram.boxes`).
-    input_dims : Optional[List[int]]
-
-    Returns
-    -------
-    int
-        Total number of photons created in the diagram.
-    """
-    created = 0
-
-    from optyx.core import zw
-
-    if input_dims is None:
-        input_dims = []
-
-    for box in diagram.boxes:
-        if isinstance(box, zw.Create):
-            created += sum(int(p) for p in box.photons)
-            continue
-
-    return max(int(created) + int(sum(input_dims, 0)), 3)
-
-
-def max_postselection(
-        diagram,
-        input_dims: Optional[List[int]] = None
-) -> int:
-    """
-    Scan `diagram` once and return the
-    maximum post-selection dimension.
-
-    Counts:
-      - zw.Create(*photons) -> +sum(photons)
-    Everything else is ignored for 'selection'
-    Parameters
-    ----------
-    diagram : optyx.core.diagram.Diagram
-        The diagram to scan (sequential list
-        of boxes is in `diagram.boxes`).
-    input_dims : Optional[List[int]]
-
-    Returns
-    -------
-    int
-        Maximum post-selection dimension in the diagram.
-    """
-    max_dim = 0
-
-    from optyx.core import zw
-
-    if input_dims is None:
-        input_dims = []
-
-    for box in diagram.boxes:
-        if isinstance(box, zw.Select):
-            max_dim = max(max_dim, max(int(p) for p in box.photons))
-            continue
-
-    return max(int(max_dim) + int(sum(input_dims, 0)), 3)
-
-
 def update_connections(
     wires_in_light_cone: List[bool],
     previous_left_offset: int,

From d2dea274abffbe18cf9ecec26689054073763487 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Thu, 25 Sep 2025 11:05:52 +0100
Subject: [PATCH 35/59] pflake8 utils

---
 optyx/utils/utils.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/optyx/utils/utils.py b/optyx/utils/utils.py
index ca9ed494..40f7e716 100644
--- a/optyx/utils/utils.py
+++ b/optyx/utils/utils.py
@@ -12,7 +12,6 @@
 from typing import (
     NamedTuple,
     Tuple,
-    Optional,
     List
 )
 from numbers import Number

From 366356cd68b9f6a6e5eca4cd992a7ef2a04c8c52 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Mon, 6 Oct 2025 19:22:07 +0100
Subject: [PATCH 36/59] Remove Cup/Cap from channel and add description to
 PhotonNumberPreservation

---
 optyx/core/channel.py | 24 ------------------------
 optyx/core/diagram.py |  4 +++-
 2 files changed, 3 insertions(+), 25 deletions(-)

diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index 2616431d..d83c9914 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -879,36 +879,12 @@ def __call__(self, other):
         return frobenius.Functor.__call__(self, other)
 
 
-class Cup(frobenius.Cup, Channel):
-    """
-    A frobenius cup is a compact cup in a frobenius diagram.
-
-    Parameters:
-        left (Ty) : The atomic type.
-        right (Ty) : Its adjoint.
-    """
-    __ambiguous_inheritance__ = (frobenius.Cup, )
-
-
-class Cap(frobenius.Cap, Channel):
-    """
-    A frobenius cap is a compact cap in a frobenius diagram.
-
-    Parameters:
-        left (Ty) : The atomic type.
-        right (Ty) : Its adjoint.
-    """
-    __ambiguous_inheritance__ = (frobenius.Cap, )
-
-
 class Hypergraph(hypergraph.Hypergraph):  # pragma: no cover
     category, functor = Category, Functor
 
 
 Hypergraph.ty_factory = Ty
 Diagram.spider_factory = Spider
-Diagram.cup_factory = Cup
-Diagram.cap_factory = Cap
 Diagram.hypergraph_factory = Hypergraph
 Diagram.braid_factory = Swap
 Diagram.sum_factory = Sum
diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index d4adee98..3850a210 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -240,7 +240,9 @@
 class PhotonNumberPreservation(Enum):
     """This is used as a flag to indicate how a box acts
     on the incoming photons. Used by the tensor network building
-    algorithm to determine the bond dimensions / truncations.
+    algorithm to determine the bond dimensions / truncations
+    based on number of photons in the past light
+    cone of the Box to minimise the truncation dimensions.
 
     LO: Linear Optical - preserves photon number between input and output
     NON_LO: Does not preserve photon number between input and output

From c7dd3ef8d3adbe3ac988c7db81691cd7fd490d64 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Fri, 5 Sep 2025 17:23:16 +0100
Subject: [PATCH 37/59] making the notebooks work with the backends

---
 docs/notebooks/bosonic-vqe-2.ipynb            |  292 +-
 docs/notebooks/compile_to_semm.ipynb          |   26 +-
 docs/notebooks/distributed-412-code.ipynb     | 5010 +++++++++--------
 docs/notebooks/distributed-422-code.ipynb     | 3368 +++++------
 docs/notebooks/feed_forward_example.ipynb     | 1318 +++--
 docs/notebooks/optyx-compilation.ipynb        |  279 -
 docs/notebooks/optyx-vqe-experiment.ipynb     |  160 +-
 .../notebooks/photon_distinguishability.ipynb |  776 +--
 optyx/core/backends.py                        |   59 +-
 optyx/core/channel.py                         |   84 +-
 optyx/qubits.py                               |  197 +-
 11 files changed, 6041 insertions(+), 5528 deletions(-)
 delete mode 100644 docs/notebooks/optyx-compilation.ipynb

diff --git a/docs/notebooks/bosonic-vqe-2.ipynb b/docs/notebooks/bosonic-vqe-2.ipynb
index c558f36d..2d28c183 100644
--- a/docs/notebooks/bosonic-vqe-2.ipynb
+++ b/docs/notebooks/bosonic-vqe-2.ipynb
@@ -17,11 +17,11 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-07-01T14:58:41.907047</dc:date>\n",
+       "    <dc:date>2025-09-05T11:56:11.751703</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
-       "      <dc:title>Matplotlib v3.10.0, https://matplotlib.org/</dc:title>\n",
+       "      <dc:title>Matplotlib v3.10.5, https://matplotlib.org/</dc:title>\n",
        "     </cc:Agent>\n",
        "    </dc:creator>\n",
        "   </cc:Work>\n",
@@ -46,62 +46,62 @@
        "L 223.2 7.2 \n",
        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
        "    <path d=\"M 43.2 61.2 \n",
        "Q 43.2 97.2 43.2 97.2 \n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 115.2 61.2 \n",
        "Q 115.2 97.2 115.2 97.2 \n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
        "    <path d=\"M 187.2 61.2 \n",
        "Q 187.2 169.2 187.2 169.2 \n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_6\">\n",
        "    <path d=\"M 43.2 133.2 \n",
        "Q 43.2 241.2 43.2 241.2 \n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_7\">\n",
        "    <path d=\"M 115.2 133.2 \n",
        "Q 115.2 169.2 115.2 169.2 \n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_8\">\n",
        "    <path d=\"M 115.2 205.2 \n",
        "Q 115.2 241.2 115.2 241.2 \n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_9\">\n",
        "    <path d=\"M 187.2 205.2 \n",
        "Q 187.2 313.2 187.2 313.2 \n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_10\">\n",
        "    <path d=\"M 43.2 277.2 \n",
        "Q 43.2 439.2 43.2 439.2 \n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_11\">\n",
        "    <path d=\"M 115.2 277.2 \n",
        "Q 115.2 313.2 115.2 313.2 \n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_12\">\n",
        "    <path d=\"M 115.2 349.2 \n",
        "Q 115.2 439.2 115.2 439.2 \n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_13\">\n",
        "    <path d=\"M 187.2 349.2 \n",
        "Q 187.2 385.2 187.2 385.2 \n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -109,7 +109,7 @@
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        "L 205.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -117,7 +117,7 @@
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        "z\n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -125,7 +125,7 @@
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        "z\n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -133,7 +133,7 @@
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        "z\n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -141,7 +141,7 @@
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        "z\n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -149,7 +149,7 @@
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        "z\n",
-       "\" clip-path=\"url(#pc99b687103)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   </g>\n",
        "   <g id=\"text_1\">\n",
        "    <!-- qmode -->\n",
@@ -878,7 +878,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
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+       "  <clipPath id=\"p661c0a7bc2\">\n",
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@@ -916,11 +916,11 @@
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-       "    <dc:date>2025-07-01T14:58:42.693815</dc:date>\n",
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        "    <dc:creator>\n",
        "     <cc:Agent>\n",
-       "      <dc:title>Matplotlib v3.10.0, https://matplotlib.org/</dc:title>\n",
+       "      <dc:title>Matplotlib v3.10.5, https://matplotlib.org/</dc:title>\n",
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        "   </cc:Work>\n",
@@ -945,87 +945,87 @@
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        "   </g>\n",
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-       "\" clip-path=\"url(#pdf91bd2a9d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_18\">\n",
        "    <path d=\"M 763.2 61.2 \n",
        "Q 763.2 79.2 763.2 79.2 \n",
-       "\" clip-path=\"url(#pdf91bd2a9d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -1033,7 +1033,7 @@
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        "L 133.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pdf91bd2a9d)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -1041,7 +1041,7 @@
        "L 349.2 25.2 \n",
        "L 349.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pdf91bd2a9d)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -1049,7 +1049,7 @@
        "L 565.2 25.2 \n",
        "L 565.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pdf91bd2a9d)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
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@@ -1057,11 +1057,11 @@
        "L 781.2 25.2 \n",
        "L 781.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pdf91bd2a9d)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   </g>\n",
        "   <g id=\"PathCollection_1\">\n",
        "    <defs>\n",
-       "     <path id=\"C0_0_8d207ec7c2\" d=\"M 0 4.759202 \n",
+       "     <path id=\"C0_0_f50920dcc6\" d=\"M 0 4.759202 \n",
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        "C 4.759202 -1.262155 4.257742 -2.472785 3.365264 -3.365264 \n",
@@ -1073,14 +1073,14 @@
        "z\n",
        "\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#pdf91bd2a9d)\">\n",
-       "     <use xlink:href=\"#C0_0_8d207ec7c2\" x=\"403.2\" y=\"43.2\" style=\"fill: #ffffff; stroke: #ffffff\"/>\n",
+       "    <g clip-path=\"url(#p05f3bff2b7)\">\n",
+       "     <use xlink:href=\"#C0_0_f50920dcc6\" x=\"403.2\" y=\"43.2\" style=\"fill: #ffffff; stroke: #ffffff\"/>\n",
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+       "    <g clip-path=\"url(#p05f3bff2b7)\">\n",
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-       "     <use xlink:href=\"#C0_0_8d207ec7c2\" x=\"619.2\" y=\"43.2\" style=\"fill: #ffffff; stroke: #ffffff\"/>\n",
+       "    <g clip-path=\"url(#p05f3bff2b7)\">\n",
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@@ -1674,7 +1674,7 @@
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        "   </g>\n",
        "   <g id=\"text_21\">\n",
-       "    <g clip-path=\"url(#pdf91bd2a9d)\">\n",
+       "    <g clip-path=\"url(#p05f3bff2b7)\">\n",
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        "     <g transform=\"translate(398.172188 46.51125) scale(0.12 -0.12)\">\n",
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@@ -1699,7 +1699,7 @@
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        "   </g>\n",
        "   <g id=\"text_22\">\n",
-       "    <g clip-path=\"url(#pdf91bd2a9d)\">\n",
+       "    <g clip-path=\"url(#p05f3bff2b7)\">\n",
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        "     <g transform=\"translate(182.172187 46.51125) scale(0.12 -0.12)\">\n",
        "      <use xlink:href=\"#DejaVuSans-2b\"/>\n",
@@ -1707,7 +1707,7 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_23\">\n",
-       "    <g clip-path=\"url(#pdf91bd2a9d)\">\n",
+       "    <g clip-path=\"url(#p05f3bff2b7)\">\n",
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        "     <g transform=\"translate(614.172188 46.51125) scale(0.12 -0.12)\">\n",
        "      <use xlink:href=\"#DejaVuSans-2b\"/>\n",
@@ -1717,7 +1717,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"pdf91bd2a9d\">\n",
+       "  <clipPath id=\"p05f3bff2b7\">\n",
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@@ -1761,85 +1761,44 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "05f93f4b",
+   "id": "8a02308c-aba4-4a39-9325-faee4c1f0c2d",
    "metadata": {},
    "outputs": [],
    "source": [
-    "import numpy as np\n",
-    "sum = np.sum([(term.double().to_tensor(input_dims = [3,3,3,3], max_dim=3).to_quimb()^...).data for term in terms])"
+    "expectation = circuit >> hamiltonian >> circuit.dagger()"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "4351a6e7",
+   "id": "68041095",
    "metadata": {},
    "outputs": [
     {
-     "data": {
-      "text/plain": [
-       "(67.9411254969543+0j)"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Create((1, 1, 1)) >> MZI(a_0_0, b_0_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_3_0, b_3_0) >> qmode @ qmode @ Select((1,)) >> Bosonic operator >> qmode @ qmode @ Select((1,)).dagger() >> qmode @ MZI(a_3_0, b_3_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_0_0, b_0_0) @ qmode >> Create((1, 1, 1)).dagger()\n",
+      "Create((1, 1, 1)) >> MZI(a_0_0, b_0_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_3_0, b_3_0) >> qmode @ qmode @ Select((1,)) >> Bosonic operator >> qmode @ qmode @ Select((1,)).dagger() >> qmode @ MZI(a_3_0, b_3_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_0_0, b_0_0) @ qmode >> Create((1, 1, 1)).dagger()\n",
+      "Create((1, 1, 1)) >> MZI(a_0_0, b_0_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_3_0, b_3_0) >> qmode @ qmode @ Select((1,)) >> Bosonic operator >> qmode @ qmode @ Select((1,)).dagger() >> qmode @ MZI(a_3_0, b_3_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_0_0, b_0_0) @ qmode >> Create((1, 1, 1)).dagger()\n",
+      "Create((1, 1, 1)) >> MZI(a_0_0, b_0_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_3_0, b_3_0) >> qmode @ qmode @ Select((1,)) >> Bosonic operator >> qmode @ qmode @ Select((1,)).dagger() >> qmode @ MZI(a_3_0, b_3_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_0_0, b_0_0) @ qmode >> Create((1, 1, 1)).dagger()\n"
+     ]
     }
    ],
    "source": [
-    "sum"
+    "for i in expectation.terms:\n",
+    "    print(i)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "a9759ff9",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "terms_2 = hamiltonian.double().terms\n",
-    "\n",
-    "sum = np.sum([(term_2.to_tensor(input_dims = [3,3,3,3], max_dim=3).to_quimb()^...).data for term_2 in terms_2])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "id": "c21af673",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(67.9411254969543+0j)"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "sum"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "id": "8a02308c-aba4-4a39-9325-faee4c1f0c2d",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "expectation = circuit >> hamiltonian >> circuit.dagger()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
    "id": "f4e5462d-464d-4b09-8574-6867522b61ea",
    "metadata": {},
    "outputs": [],
    "source": [
+    "from optyx.core.backends import DiscopyBackend\n",
+    "\n",
     "def to_float(x):\n",
     "    if isinstance(x, complex):\n",
     "        assert x.imag < 1e-10, x\n",
@@ -1848,18 +1807,32 @@
     "\n",
     "free_syms = list(expectation.free_symbols)\n",
     "\n",
-    "f_exp = lambda xs: to_float(expectation.lambdify(*free_syms)(*xs).eval().array[0, 0])\n",
+    "#f_exp = lambda xs: to_float(expectation.lambdify(*free_syms)(*xs).eval().array[0, 0])\n",
+    "\n",
+    "def f_exp(xs):\n",
+    "    val = 0\n",
+    "    for term in expectation.lambdify(*free_syms)(*xs).terms:\n",
+    "        val += to_float(term.eval().tensor.array)\n",
+    "    return val\n",
+    "\n",
+    "# def d_f_exp(xs):\n",
+    "#     return [\n",
+    "#         expectation.grad(s).lambdify(*free_syms)(*xs).eval().array[0, 0]\n",
+    "#         for s in free_syms\n",
+    "#     ]\n",
     "\n",
     "def d_f_exp(xs):\n",
-    "    return [\n",
-    "        expectation.grad(s).lambdify(*free_syms)(*xs).eval().array[0, 0]\n",
-    "        for s in free_syms\n",
-    "    ]"
+    "    grads = [expectation.grad(s) for s in free_syms]\n",
+    "    vals = [0] * len(grads)\n",
+    "    for i, g in enumerate(grads):\n",
+    "        for term in g.lambdify(*free_syms)(*xs).terms:\n",
+    "            vals[i] += to_float(term.eval().tensor.array)\n",
+    "    return vals"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 14,
    "id": "24355282-4c9c-40b3-b643-461981f9475f",
    "metadata": {},
    "outputs": [],
@@ -1890,7 +1863,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 15,
    "id": "e96227b0-db8e-4871-8c12-b1d034a4bc86",
    "metadata": {},
    "outputs": [
@@ -1898,7 +1871,14 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "100%|██████████| 10/10 [06:35<00:00, 39.56s/it]\n"
+      "  0%|          | 0/10 [00:00<?, ?it/s]"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 10/10 [02:35<00:00, 15.52s/it]\n"
      ]
     }
    ],
@@ -1908,7 +1888,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": null,
    "id": "088c8fa8-76b3-45bd-a5dd-b337be0d33b1",
    "metadata": {},
    "outputs": [
@@ -1923,11 +1903,11 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-07-01T15:06:04.533106</dc:date>\n",
+       "    <dc:date>2025-09-05T11:59:44.101867</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
-       "      <dc:title>Matplotlib v3.10.0, https://matplotlib.org/</dc:title>\n",
+       "      <dc:title>Matplotlib v3.10.5, https://matplotlib.org/</dc:title>\n",
        "     </cc:Agent>\n",
        "    </dc:creator>\n",
        "   </cc:Work>\n",
@@ -1958,12 +1938,12 @@
        "    <g id=\"xtick_1\">\n",
        "     <g id=\"line2d_1\">\n",
        "      <defs>\n",
-       "       <path id=\"m0e5b5a5bae\" d=\"M 0 0 \n",
+       "       <path id=\"ma382debacf\" d=\"M 0 0 \n",
        "L 0 3.5 \n",
        "\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </defs>\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m0e5b5a5bae\" x=\"54.71554\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#ma382debacf\" x=\"54.71554\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_1\">\n",
@@ -1999,7 +1979,7 @@
        "    <g id=\"xtick_2\">\n",
        "     <g id=\"line2d_2\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m0e5b5a5bae\" x=\"119.646449\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#ma382debacf\" x=\"119.646449\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_2\">\n",
@@ -2038,7 +2018,7 @@
        "    <g id=\"xtick_3\">\n",
        "     <g id=\"line2d_3\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m0e5b5a5bae\" x=\"184.577358\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#ma382debacf\" x=\"184.577358\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_3\">\n",
@@ -2072,7 +2052,7 @@
        "    <g id=\"xtick_4\">\n",
        "     <g id=\"line2d_4\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m0e5b5a5bae\" x=\"249.508267\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#ma382debacf\" x=\"249.508267\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_4\">\n",
@@ -2117,7 +2097,7 @@
        "    <g id=\"xtick_5\">\n",
        "     <g id=\"line2d_5\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m0e5b5a5bae\" x=\"314.439176\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#ma382debacf\" x=\"314.439176\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_5\">\n",
@@ -2171,7 +2151,7 @@
        "    <g id=\"xtick_6\">\n",
        "     <g id=\"line2d_6\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m0e5b5a5bae\" x=\"379.370085\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#ma382debacf\" x=\"379.370085\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_6\">\n",
@@ -2203,12 +2183,12 @@
        "    <g id=\"ytick_1\">\n",
        "     <g id=\"line2d_7\">\n",
        "      <defs>\n",
-       "       <path id=\"m99fbb71ef4\" d=\"M 0 0 \n",
+       "       <path id=\"m8a093308ac\" d=\"M 0 0 \n",
        "L -3.5 0 \n",
        "\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </defs>\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m99fbb71ef4\" x=\"38.482813\" y=\"236.616595\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#m8a093308ac\" x=\"38.482813\" y=\"236.616595\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_7\">\n",
@@ -2240,7 +2220,7 @@
        "    <g id=\"ytick_2\">\n",
        "     <g id=\"line2d_8\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m99fbb71ef4\" x=\"38.482813\" y=\"184.874401\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#m8a093308ac\" x=\"38.482813\" y=\"184.874401\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_8\">\n",
@@ -2256,7 +2236,7 @@
        "    <g id=\"ytick_3\">\n",
        "     <g id=\"line2d_9\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m99fbb71ef4\" x=\"38.482813\" y=\"133.132207\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#m8a093308ac\" x=\"38.482813\" y=\"133.132207\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_9\">\n",
@@ -2272,7 +2252,7 @@
        "    <g id=\"ytick_4\">\n",
        "     <g id=\"line2d_10\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m99fbb71ef4\" x=\"38.482813\" y=\"81.390013\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#m8a093308ac\" x=\"38.482813\" y=\"81.390013\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_10\">\n",
@@ -2287,7 +2267,7 @@
        "    <g id=\"ytick_5\">\n",
        "     <g id=\"line2d_11\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m99fbb71ef4\" x=\"38.482813\" y=\"29.647819\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#m8a093308ac\" x=\"38.482813\" y=\"29.647819\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_11\">\n",
@@ -2302,7 +2282,7 @@
        "   </g>\n",
        "   <g id=\"line2d_12\">\n",
        "    <defs>\n",
-       "     <path id=\"m4e524198b8\" d=\"M 0 1.5 \n",
+       "     <path id=\"mcd2e95b7bb\" d=\"M 0 1.5 \n",
        "C 0.397805 1.5 0.77937 1.341951 1.06066 1.06066 \n",
        "C 1.341951 0.77937 1.5 0.397805 1.5 0 \n",
        "C 1.5 -0.397805 1.341951 -0.77937 1.06066 -1.06066 \n",
@@ -2314,18 +2294,18 @@
        "z\n",
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        "    </defs>\n",
-       "    <g clip-path=\"url(#p99f766aeba)\">\n",
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-       "     <use xlink:href=\"#m4e524198b8\" x=\"346.904631\" y=\"261.06328\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
-       "     <use xlink:href=\"#m4e524198b8\" x=\"379.370085\" y=\"261.216\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "    <g clip-path=\"url(#paa5c911910)\">\n",
+       "     <use xlink:href=\"#mcd2e95b7bb\" x=\"54.71554\" y=\"19.296\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#mcd2e95b7bb\" x=\"87.180994\" y=\"128.674625\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#mcd2e95b7bb\" x=\"119.646449\" y=\"172.191339\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#mcd2e95b7bb\" x=\"152.111903\" y=\"200.84295\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#mcd2e95b7bb\" x=\"184.577358\" y=\"224.024215\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#mcd2e95b7bb\" x=\"217.042813\" y=\"240.624501\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#mcd2e95b7bb\" x=\"249.508267\" y=\"251.094574\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#mcd2e95b7bb\" x=\"281.973722\" y=\"256.858981\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#mcd2e95b7bb\" x=\"314.439176\" y=\"259.810304\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#mcd2e95b7bb\" x=\"346.904631\" y=\"261.06328\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#mcd2e95b7bb\" x=\"379.370085\" y=\"261.216\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
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        "   </g>\n",
        "   <g id=\"patch_3\">\n",
@@ -2351,7 +2331,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p99f766aeba\">\n",
+       "  <clipPath id=\"paa5c911910\">\n",
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        " </defs>\n",
@@ -2375,7 +2355,15 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ce3cd5e4-f9b5-4f29-b805-7bee285dfed7",
+   "id": "346a4294",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5e2fd068",
    "metadata": {},
    "outputs": [],
    "source": []
@@ -2383,7 +2371,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": ".venv",
    "language": "python",
    "name": "python3"
   },
@@ -2397,7 +2385,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.12"
+   "version": "3.12.3"
   }
  },
  "nbformat": 4,
diff --git a/docs/notebooks/compile_to_semm.ipynb b/docs/notebooks/compile_to_semm.ipynb
index 101cd911..05c69408 100644
--- a/docs/notebooks/compile_to_semm.ipynb
+++ b/docs/notebooks/compile_to_semm.ipynb
@@ -28,7 +28,7 @@
    "outputs": [
     {
      "data": {
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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -52,10 +52,24 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 3,
    "id": "573c939f-f521-4663-a843-7aac795fefd6",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "ename": "ValueError",
+     "evalue": "Output node cannot be measured.",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
+      "\u001b[31mValueError\u001b[39m                                Traceback (most recent call last)",
+      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[3]\u001b[39m\u001b[32m, line 7\u001b[39m\n\u001b[32m      4\u001b[39m inputs = {\u001b[32m0\u001b[39m}\n\u001b[32m      5\u001b[39m outputs = {\u001b[32m2\u001b[39m}\n\u001b[32m----> \u001b[39m\u001b[32m7\u001b[39m og = \u001b[43mOpenGraph\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmeas\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43minputs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43moutputs\u001b[49m\u001b[43m)\u001b[49m\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m<string>:7\u001b[39m, in \u001b[36m__init__\u001b[39m\u001b[34m(self, inside, measurements, inputs, outputs)\u001b[39m\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/.venv/lib/python3.12/site-packages/graphix/opengraph.py:84\u001b[39m, in \u001b[36mOpenGraph.__post_init__\u001b[39m\u001b[34m(self)\u001b[39m\n\u001b[32m     82\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[33m\"\u001b[39m\u001b[33mAll output nodes must be part of the graph\u001b[39m\u001b[33m'\u001b[39m\u001b[33ms nodes.\u001b[39m\u001b[33m\"\u001b[39m)\n\u001b[32m     83\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28many\u001b[39m(node \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m.outputs \u001b[38;5;28;01mfor\u001b[39;00m node \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m.measurements):\n\u001b[32m---> \u001b[39m\u001b[32m84\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[33m\"\u001b[39m\u001b[33mOutput node cannot be measured.\u001b[39m\u001b[33m\"\u001b[39m)\n\u001b[32m     85\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mset\u001b[39m(\u001b[38;5;28mself\u001b[39m.inputs)) != \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m.inputs):\n\u001b[32m     86\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[33m\"\u001b[39m\u001b[33mInput nodes contain duplicates.\u001b[39m\u001b[33m\"\u001b[39m)\n",
+      "\u001b[31mValueError\u001b[39m: Output node cannot be measured."
+     ]
+    }
+   ],
    "source": [
     "from optyx.compiler import OpenGraph, Measurement\n",
     "\n",
@@ -76,7 +90,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": null,
    "id": "412aa1a5-6959-447b-b1d0-fe8891060229",
    "metadata": {},
    "outputs": [
@@ -106,7 +120,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
+   "display_name": ".venv",
    "language": "python",
    "name": "python3"
   },
@@ -120,7 +134,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.9"
+   "version": "3.12.3"
   }
  },
  "nbformat": 4,
diff --git a/docs/notebooks/distributed-412-code.ipynb b/docs/notebooks/distributed-412-code.ipynb
index 2745afbb..90f19ffa 100644
--- a/docs/notebooks/distributed-412-code.ipynb
+++ b/docs/notebooks/distributed-412-code.ipynb
@@ -95,11 +95,11 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-07-01T15:29:41.334534</dc:date>\n",
+       "    <dc:date>2025-09-05T12:03:16.012191</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
-       "      <dc:title>Matplotlib v3.10.0, https://matplotlib.org/</dc:title>\n",
+       "      <dc:title>Matplotlib v3.10.5, https://matplotlib.org/</dc:title>\n",
        "     </cc:Agent>\n",
        "    </dc:creator>\n",
        "   </cc:Work>\n",
@@ -124,177 +124,177 @@
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        "L 7.2 7.2 \n",
        "z\n",
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+       "\" clip-path=\"url(#p76c1da9424)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Calculated fidelity a whole round of error detection: 0.49714692979130937\n"
+      "Calculated fidelity a whole round of error detection: 0.4971469297913094\n"
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diff --git a/docs/notebooks/distributed-422-code.ipynb b/docs/notebooks/distributed-422-code.ipynb
index 7943c846..e27600c1 100644
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        " <defs>\n",
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      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Calculated fidelity for Z error detection: 0.9864120233027301\n"
+      "Calculated fidelity for Z error detection: 0.9864120233027304\n"
      ]
     }
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      "output_type": "stream",
      "text": [
-      "Calculated fidelity a whole round of error detection: 0.9732135897032679\n"
+      "Calculated fidelity a whole round of error detection: 0.973213589703268\n"
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-       "    <dc:date>2025-07-01T15:35:13.938848</dc:date>\n",
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-       "   </g>\n",
-       "   <g id=\"text_50\">\n",
-       "    <g clip-path=\"url(#p2c1bab663b)\">\n",
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@@ -17663,10 +17635,38 @@
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        "   </g>\n",
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-       "    <g clip-path=\"url(#p2c1bab663b)\">\n",
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        "   <g id=\"text_57\">\n",
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-       "    <dc:date>2025-07-01T15:35:47.385694</dc:date>\n",
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        "    <dc:creator>\n",
        "     <cc:Agent>\n",
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        "      <defs>\n",
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@@ -18815,7 +18815,7 @@
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        " <defs>\n",
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        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-07-01T15:35:47.466024</dc:date>\n",
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        "    <dc:creator>\n",
        "     <cc:Agent>\n",
-       "      <dc:title>Matplotlib v3.10.0, https://matplotlib.org/</dc:title>\n",
+       "      <dc:title>Matplotlib v3.10.5, https://matplotlib.org/</dc:title>\n",
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@@ -18874,12 +18874,12 @@
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        "      <defs>\n",
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+       "       <path id=\"m94844d99f1\" d=\"M 0 0 \n",
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@@ -19474,7 +19474,7 @@
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@@ -19862,7 +19862,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": ".venv",
    "language": "python",
    "name": "python3"
   },
@@ -19876,7 +19876,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.12"
+   "version": "3.12.3"
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diff --git a/docs/notebooks/feed_forward_example.ipynb b/docs/notebooks/feed_forward_example.ipynb
index 1991706e..2a98f6a8 100644
--- a/docs/notebooks/feed_forward_example.ipynb
+++ b/docs/notebooks/feed_forward_example.ipynb
@@ -71,21 +71,18 @@
    "outputs": [],
    "source": [
     "from optyx import qmode\n",
-    "\n",
+    "from optyx.core.channel import Diagram, bit, qubit\n",
     "from optyx.photonic import (\n",
     "    DualRail,\n",
-    "    Swap,\n",
     "    HadamardBS\n",
     ")\n",
     "\n",
-    "fusion = (\n",
-    "    HadamardBS() @ HadamardBS() >>\n",
-    "    qmode @ Swap(1, 1) @ qmode >>\n",
-    "    qmode @ HadamardBS() @ qmode >>\n",
-    "    Swap(1, 1) @ qmode @ qmode >>\n",
-    "    qmode @ Swap(1, 1) @ qmode >>\n",
-    "    qmode @ qmode @ HadamardBS()\n",
-    ")"
+    "@Diagram.from_callable(dom=qmode**4, cod=qmode**4)\n",
+    "def fusion(*a):\n",
+    "    b = (HadamardBS() @ HadamardBS())(*a)\n",
+    "    c1, c2 = HadamardBS()(b[2], b[1])\n",
+    "    d1, d2 = HadamardBS()(b[0], b[3])\n",
+    "    return c1, c2, d1, d2"
    ]
   },
   {
@@ -234,16 +231,16 @@
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        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-07-11T08:58:10.336908</dc:date>\n",
+       "    <dc:date>2025-09-04T14:54:28.447721</dc:date>\n",
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        "    <dc:creator>\n",
        "     <cc:Agent>\n",
-       "      <dc:title>Matplotlib v3.10.0, https://matplotlib.org/</dc:title>\n",
+       "      <dc:title>Matplotlib v3.10.5, https://matplotlib.org/</dc:title>\n",
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@@ -254,393 +251,616 @@
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        "    </g>\n",
        "   </g>\n",
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        "   </g>\n",
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        "   </g>\n",
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        "   </g>\n",
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        "   </g>\n",
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       "text/plain": [
-       "<Figure size 650x1200 with 1 Axes>"
+       "<Figure size 800x1000 with 1 Axes>"
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      "metadata": {},
@@ -2152,7 +2552,7 @@
     }
    ],
    "source": [
-    "teleportation.foliation().draw()"
+    "teleportation.foliation().draw(figsize=(8, 10))"
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   {
@@ -2161,7 +2561,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "array_teleportation = teleportation.double().to_tensor().eval().array"
+    "array_teleportation = teleportation.eval().tensor.array"
    ]
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   {
@@ -2173,7 +2573,7 @@
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+   "execution_count": 14,
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@@ -2186,7 +2586,7 @@
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+   "execution_count": 15,
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@@ -2195,7 +2595,7 @@
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       ]
      },
-     "execution_count": 10,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2216,7 +2616,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": ".venv",
    "language": "python",
    "name": "python3"
   },
@@ -2230,7 +2630,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.12"
+   "version": "3.12.3"
   }
  },
  "nbformat": 4,
diff --git a/docs/notebooks/optyx-compilation.ipynb b/docs/notebooks/optyx-compilation.ipynb
deleted file mode 100644
index b22db722..00000000
--- a/docs/notebooks/optyx-compilation.ipynb
+++ /dev/null
@@ -1,279 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Transpilation to Linear Optics via ZX Dual-Rail Encoding"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Start with a simple qubit quantum circuit."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANwAAAFACAYAAADXiRINAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjAsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvlHJYcgAAAAlwSFlzAAAPYQAAD2EBqD+naQAAEGtJREFUeJzt3U9I1Pn/wPHXZ0xKDd1Bw5uBidhBCDdR8LJrEamj7UEoosMaXVsWvGgdRwjqEoXsRccVRSq8NG0oSrIXDxETZQdRSiP2kgjukDM6TDuv3+H7U2q3P6Yzr49+5vkAL+PH97zEnn5mPn4+nxxVVQFgwuf2AEA2ITjAEMEBhggOMERwgCGCAwwRHGCI4ABDBAcYyqrg2trapK2tze0x8P+y8eeRVcEBbiM4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDq5IpVKSSCRkbW1NlpaWJJVKuT2SiX1uD4DssbCwIKFQSKanpyUSici7d+9ERKS0tFQKCwulpqZGGhoa5OLFi1JeXu7ytJnBHg4ZNzMzI83NzVJRUSG9vb1SXFwsnZ2dm58fGRmRrq4uKS4ult7eXqmoqJDm5mZ58eKFi1NniGaR1tZWbW1tdXuMrJFMJjUYDGpubq5WVVVpKBTSWCymqqqrq6sqIioiurq6uvk1sVhMQ6GQVlVVaW5urgaDQU0mk259C2mXNcHNzc1pfX29Hj9+XCcmJnRubs7tkTwtHo9rS0uL5uTk6JUrV3R9ff2jz38uuA3r6+va3d2tPp9PA4GAxuNxq9EzytPBra2t6dDQkNbW1m7+cD/8qK2t1aGhIV1bW3N7VE9JJpPa0tKieXl5Oj4+/sltvhbchvHxcc3Ly9NAIOCJPZ1ngwuHw+r3+1VE1OfzfTK4jcf9fr+Gw2G3R/aMYDCoOTk5n41NdevBqaqOjY1pTk6O9vT0pHtUc54Mrq+vTx3HUcdxPhnavz82tu3r63N79D3v+fPnmpubq93d3V/c7luCU1Xt7u7W3NxcnZmZSdeornBUVQ2OzZh58OCBnDlzRrbzbTmOI/fv35fW1tYMTJYdmpubZXFxUZ49eyb79+//7HaxWEwOHjwoIiKrq6tSUFDwxXUTiYQcO3ZMysvL5eHDh2md2ZTLwafV2tqa+v3+Le/Z/v3hOI76/f7/vMHH1rx8+VIdx9FQKPTVbb91D6eq2t/fr47j6KtXr3Y6qms89Xe40dFRWVlZ2dbeTUREVWVlZUVGR0fTPFl2GBgYkKKiIjl79mxG1j937pwUFRXJwMBARta34Kngbt26JT7fzr4ln88nt2/fTtNE2WV6elpOnDgh+fn5GVk/Pz9fGhsbZXp6OiPrW/DMqV3z8/Py5MmTHa+TSqXk8ePHMj8/L5WVlWmYLDukUimJRCLS2dkpsVjsq9t/uM1Wtt9QXV0tN2/eFFUVx3G2NaubPHPQZHJyUk6dOpW29err6+XQoUNpW8/rEomETExMmD3f0tLSnvz5eOYl5erqalrXe//+fVrX8zrrs/0TiYTp86WLZ15SbhxiTpdr167JyZMn07qmly0tLUlpaamMjIxIW1vbV7ePxWJSWloqIiJv37796p8FNoTDYTl//vwX/+Swm3kmuMOHD6d1vbKysrSu53UlJSVSWFgor1+/3nI8GwoKCrb8NYuLi1JUVCQlJSXbGdN1nnlJWVlZKbW1tWk5SllXV8cBk2/k8/mkpqZGIpFIRp8nEolITU3NnjxgIuKh4EREfvnllx2/l0ilUnL58uU0TZRdGhoa5NGjRxKPxzOyfjwel6mpKWloaMjI+hY8FVx7e7v4/f5t//ZzHEf8fr+0t7enebLs0NHRIdFoVO7evZuR9e/cuSPRaFQ6Ojoysr4FTwV34MABGRwc3NEag4ODe/YNuduOHDkip0+fluvXr6f9KOL6+rrcuHFDmpqa9vbtF1w9sSxDuFrAPTMzM1wt8AWeDE6V6+HcFAwG1efzpfV6OJ/Px/Vwu936+roODw9rXV3dJ4Orq6vT4eFhrg5Is2QyqYFAQPPy8nRsbOyT22w1uLGxMa743os+vKfJ5OQk9zTJsHg8roFAQHNycrS7u3tb9zTp6uriniZ7GXftspVMJrWnp2fzrl39/f1bumtXf3//5l27enp6PLFn2+CZM02w++zbt0+uXr0qbW1t0tXVJZcuXZLOzk5pbGyU6urqze3C4bAsLi5KJBKRqakpiUaj0tTUJPfu3ftoOy/wzNUCW7Fxjl84HHZ5kuy0sLAgAwMDMj09LU+fPpVoNLr5uaKios07L3d0dOztQ/9fQHBwRSqVkqamJkmlUjIyMiLFxcU7Pi1vL+AlJVzh8/k2TzDYi9e1bZf3f6UAuwjBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYb2uT3Ah968eSPLy8sZW//vv/8WEZGnT59m7DlEREpKSqSsrCyjz4G9adcE9+bNGzl69KjE4/GMP9f333+f0fXz8/NldnaW6PAfuya45eVlicfjMjw8LEePHnV7nG2bnZ2VCxcuyPLyMsHhP3ZNcBuOHj0qNTU1bo8BZAQHTQBDBAcYIjjAEMEBhggOMERwgCGCAwwRHGCI4ABDBAcYIjjAEMEBhggOMERwgCGCAwwRHGDI88H9/PPP8tNPP/3n8T///FMcx9m8zwlgwfPBAbsJwQGGCA4wtOtuIpQJf/zxhxw8ePCjx/755x+XpkE2y4rgfvzxR/ntt98+euzx48dy4cIFlyZCtsqK4AoKCqSiouKjx/766y+XpkE24z0cYIjgAEMEBxjy/Hu433///ZOP//DDD6KqtsMg67GHAwwRHGCI4ABDBAcYIjjAEMEBhggOMERwgCGCAwwRHGCI4ABDBAcYIjjAEMEBhggOMERwgCGCAwwRHGCI4ABDu+6eJrOzs26PsCN7fX5k1q4JrqSkRPLz8z1xN+T8/HwpKSlxewzsQrsmuLKyMpmdnZXl5eWMPcevv/4qIiI3b97M2HOI/O+XR1lZWUafA3vTrglO5H/RZfIf6nfffSciIjU1NRl7DuBLOGgCGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBwRWpVEoSiYSsra3J0tKSpFIpt0cysc/tAZA9FhYWJBQKyfT0tEQiEXn37p2IiJSWlkphYaHU1NRIQ0ODXLx4UcrLy12eNjPYwyHjZmZmpLm5WSoqKqS3t1eKi4uls7Nz8/MjIyPS1dUlxcXF0tvbKxUVFdLc3CwvXrxwceoM0SzS2tqqra2tbo+RNZLJpAaDQc3NzdWqqioNhUIai8VUVXV1dVVFREVEV1dXN78mFotpKBTSqqoqzc3N1WAwqMlk0q1vIe2yJri5uTmtr6/X48eP68TEhM7Nzbk9kqfF43FtaWnRnJwcvXLliq6vr3/0+c8Ft2F9fV27u7vV5/NpIBDQeDxuNXpGeTq4tbU1HRoa0tra2s0f7ocftbW1OjQ0pGtra26P6inJZFJbWlo0Ly9Px8fHP7nN14LbMD4+rnl5eRoIBDyxp/NscOFwWP1+v4qI+ny+Twa38bjf79dwOOz2yJ4RDAY1Jyfns7Gpbj04VdWxsTHNycnRnp6edI9qzpPB9fX1qeM46jjOJ0P798fGtn19fW6Pvuc9f/5cc3Nztbu7+4vbfUtwqqrd3d2am5urMzMz6RrVFY6qqsGxGTMPHjyQM2fOyHa+Lcdx5P79+9La2pqBybJDc3OzLC4uyrNnz2T//v2f3S4Wi8nBgwdFRGR1dVUKCgq+uG4ikZBjx45JeXm5PHz4MK0zm3I5+LRaW1tTv9+/5T3bvz8cx1G/3/+fN/jYmpcvX6rjOBoKhb667bfu4VRV+/v71XEcffXq1U5HdY2n/g43OjoqKysr29q7iYioqqysrMjo6GiaJ8sOAwMDUlRUJGfPns3I+ufOnZOioiIZGBjIyPoWPBXcrVu3xOfb2bfk8/nk9u3baZoou0xPT8uJEyckPz8/I+vn5+dLY2OjTE9PZ2R9C545tWt+fl6ePHmy43VSqZQ8fvxY5ufnpbKyMg2TZYdUKiWRSEQ6OzslFot9dfsPt9nK9huqq6vl5s2boqriOM62ZnWTZw6aTE5OyqlTp9K2Xn19vRw6dCht63ldIpGQiYkJs+dbWlrakz8fz7ykXF1dTet679+/T+t6Xmd9tn8ikTB9vnTxzEvKjUPM6XLt2jU5efJkWtf0sqWlJSktLZWRkRFpa2v76vaxWExKS0tFROTt27df/bPAhnA4LOfPn//inxx2M88Ed/jw4bSuV1ZWltb1vK6kpEQKCwvl9evXW45nQ0FBwZa/ZnFxUYqKiqSkpGQ7Y7rOMy8pKysrpba2Ni1HKevq6jhg8o18Pp/U1NRIJBLJ6PNEIhGpqanZkwdMRDwUnIjIL7/8suP3EqlUSi5fvpymibJLQ0ODPHr0SOLxeEbWj8fjMjU1JQ0NDRlZ34Kngmtvbxe/37/t336O44jf75f29vY0T5YdOjo6JBqNyt27dzOy/p07dyQajUpHR0dG1rfgqeAOHDggg4ODO1pjcHBwz74hd9uRI0fk9OnTcv369bQfRVxfX5cbN25IU1PT3r79gqsnlmUIVwu4Z2ZmhqsFvsCTwalyPZybgsGg+ny+tF4P5/P5uB5ut1tfX9fh4WGtq6v7ZHB1dXU6PDzM1QFplkwmNRAIaF5eno6NjX1ym60GNzY2xhXfe9GH9zSZnJzkniYZFo/HNRAIaE5OjnZ3d2/rniZdXV3c02Qv465dtpLJpPb09Gzetau/v39Ld+3q7+/fvGtXT0+PJ/ZsGzxzpgl2n3379snVq1elra1Nurq65NKlS9LZ2SmNjY1SXV29uV04HJbFxUWJRCIyNTUl0WhUmpqa5N69ex9t5wWeuVpgKzbO8QuHwy5Pkp0WFhZkYGBApqen5enTpxKNRjc/V1RUtHnn5Y6Ojr196P8LCA6uSKVS0tTUJKlUSkZGRqS4uHjHp+XtBbykhCt8Pt/mCQZ78bq27fL+rxRgFyE4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wBDBAYYIDjBEcIAhggMMERxgiOAAQwQHGCI4wFBW/R/fgNvYwwGGCA4wRHCAIYIDDBEcYIjgAEMEBxgiOMAQwQGG/g/EooOv5o7jQQAAAABJRU5ErkJggg==",
-      "text/plain": [
-       "<Figure size 200x300 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "from discopy.quantum import CX, H, Id\n",
-    "\n",
-    "circuit = CX >> H @ Id(1) >> CX\n",
-    "circuit.draw()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Convert to ZX using `circuit2zx`"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 400x700 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "from discopy.quantum.zx import circuit2zx\n",
-    "\n",
-    "diagram = circuit2zx(circuit)\n",
-    "diagram.draw()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Convert to QPath using `zx_to_path`"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "ename": "TypeError",
-     "evalue": "can only concatenate tuple (not \"Z\") to tuple",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
-      "Cell \u001b[0;32mIn[4], line 3\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;21;01moptyx\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mzx\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mimport\u001b[39;00m zx_to_path\n\u001b[0;32m----> 3\u001b[0m circ \u001b[38;5;241m=\u001b[39m \u001b[43mzx_to_path\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdiagram\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m      4\u001b[0m circ\u001b[38;5;241m.\u001b[39mdraw(draw_box_labels\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m, draw_type_labels\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m)\n",
-      "File \u001b[0;32m~/Documents/optyx/dist_merge_gates/optyx/optyx/core/zx.py:634\u001b[0m, in \u001b[0;36mzx_to_path\u001b[0;34m(diagram)\u001b[0m\n\u001b[1;32m    630\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;21mzx_to_path\u001b[39m(diagram: diagram\u001b[38;5;241m.\u001b[39mDiagram) \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m diagram\u001b[38;5;241m.\u001b[39mDiagram:\n\u001b[1;32m    631\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    632\u001b[0m \u001b[38;5;124;03m    Dual-rail encoding of any ZX diagram as a QPath diagram.\u001b[39;00m\n\u001b[1;32m    633\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m--> 634\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m zx2path(\u001b[43mdecomp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdiagram\u001b[49m\u001b[43m)\u001b[49m)\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/symmetric.py:355\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    353\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(other, Swap):\n\u001b[1;32m    354\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar\u001b[38;5;241m.\u001b[39mswap(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom[\u001b[38;5;241m0\u001b[39m]), \u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom[\u001b[38;5;241m1\u001b[39m]))\n\u001b[0;32m--> 355\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/balanced.py:213\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    211\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(other, Trace):\n\u001b[1;32m    212\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m traced\u001b[38;5;241m.\u001b[39mFunctor\u001b[38;5;241m.\u001b[39m\u001b[38;5;21m__call__\u001b[39m(\u001b[38;5;28mself\u001b[39m, other)\n\u001b[0;32m--> 213\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mbraided\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mFunctor\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/braided.py:259\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    257\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(other, Braid) \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m other\u001b[38;5;241m.\u001b[39mis_dagger:\n\u001b[1;32m    258\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar\u001b[38;5;241m.\u001b[39mbraid(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom[\u001b[38;5;241m0\u001b[39m]), \u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom[\u001b[38;5;241m1\u001b[39m]))\n\u001b[0;32m--> 259\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/traced.py:275\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    273\u001b[0m     n \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39marg\u001b[38;5;241m.\u001b[39mdom)) \u001b[38;5;241m-\u001b[39m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom))\n\u001b[1;32m    274\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar\u001b[38;5;241m.\u001b[39mtrace(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39marg), n, left\u001b[38;5;241m=\u001b[39mother\u001b[38;5;241m.\u001b[39mleft)\n\u001b[0;32m--> 275\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/monoidal.py:1115\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m   1113\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(other, Bubble) \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar \u001b[38;5;129;01mis\u001b[39;00m Drawing:\n\u001b[1;32m   1114\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m other\u001b[38;5;241m.\u001b[39mto_drawing()\n\u001b[0;32m-> 1115\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/cat.py:912\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    910\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar\u001b[38;5;241m.\u001b[39mid(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom))\n\u001b[1;32m    911\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m box \u001b[38;5;129;01min\u001b[39;00m other\u001b[38;5;241m.\u001b[39minside:\n\u001b[0;32m--> 912\u001b[0m     result \u001b[38;5;241m=\u001b[39m result \u001b[38;5;241m>>\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mbox\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    913\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m result\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/symmetric.py:355\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    353\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(other, Swap):\n\u001b[1;32m    354\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar\u001b[38;5;241m.\u001b[39mswap(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom[\u001b[38;5;241m0\u001b[39m]), \u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom[\u001b[38;5;241m1\u001b[39m]))\n\u001b[0;32m--> 355\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/balanced.py:213\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    211\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(other, Trace):\n\u001b[1;32m    212\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m traced\u001b[38;5;241m.\u001b[39mFunctor\u001b[38;5;241m.\u001b[39m\u001b[38;5;21m__call__\u001b[39m(\u001b[38;5;28mself\u001b[39m, other)\n\u001b[0;32m--> 213\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mbraided\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mFunctor\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/braided.py:259\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    257\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(other, Braid) \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m other\u001b[38;5;241m.\u001b[39mis_dagger:\n\u001b[1;32m    258\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar\u001b[38;5;241m.\u001b[39mbraid(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom[\u001b[38;5;241m0\u001b[39m]), \u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom[\u001b[38;5;241m1\u001b[39m]))\n\u001b[0;32m--> 259\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/traced.py:275\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    273\u001b[0m     n \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39marg\u001b[38;5;241m.\u001b[39mdom)) \u001b[38;5;241m-\u001b[39m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom))\n\u001b[1;32m    274\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar\u001b[38;5;241m.\u001b[39mtrace(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39marg), n, left\u001b[38;5;241m=\u001b[39mother\u001b[38;5;241m.\u001b[39mleft)\n\u001b[0;32m--> 275\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/monoidal.py:1111\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m   1109\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m(head)\n\u001b[1;32m   1110\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m box_or_typ \u001b[38;5;129;01min\u001b[39;00m tail:\n\u001b[0;32m-> 1111\u001b[0m         result \u001b[38;5;241m=\u001b[39m result \u001b[38;5;241m@\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mbox_or_typ\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   1112\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m result\n\u001b[1;32m   1113\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(other, Bubble) \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar \u001b[38;5;129;01mis\u001b[39;00m Drawing:\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/symmetric.py:355\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    353\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(other, Swap):\n\u001b[1;32m    354\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar\u001b[38;5;241m.\u001b[39mswap(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom[\u001b[38;5;241m0\u001b[39m]), \u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom[\u001b[38;5;241m1\u001b[39m]))\n\u001b[0;32m--> 355\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/balanced.py:213\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    211\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(other, Trace):\n\u001b[1;32m    212\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m traced\u001b[38;5;241m.\u001b[39mFunctor\u001b[38;5;241m.\u001b[39m\u001b[38;5;21m__call__\u001b[39m(\u001b[38;5;28mself\u001b[39m, other)\n\u001b[0;32m--> 213\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mbraided\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mFunctor\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/braided.py:259\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    257\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(other, Braid) \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m other\u001b[38;5;241m.\u001b[39mis_dagger:\n\u001b[1;32m    258\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar\u001b[38;5;241m.\u001b[39mbraid(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom[\u001b[38;5;241m0\u001b[39m]), \u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom[\u001b[38;5;241m1\u001b[39m]))\n\u001b[0;32m--> 259\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/traced.py:275\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    273\u001b[0m     n \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39marg\u001b[38;5;241m.\u001b[39mdom)) \u001b[38;5;241m-\u001b[39m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom))\n\u001b[1;32m    274\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar\u001b[38;5;241m.\u001b[39mtrace(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39marg), n, left\u001b[38;5;241m=\u001b[39mother\u001b[38;5;241m.\u001b[39mleft)\n\u001b[0;32m--> 275\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/monoidal.py:1115\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m   1113\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(other, Bubble) \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar \u001b[38;5;129;01mis\u001b[39;00m Drawing:\n\u001b[1;32m   1114\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m other\u001b[38;5;241m.\u001b[39mto_drawing()\n\u001b[0;32m-> 1115\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/cat.py:908\u001b[0m, in \u001b[0;36mFunctor.__call__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    905\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mar[other]\n\u001b[1;32m    906\u001b[0m     \u001b[38;5;66;03m# This allows some nice syntactic sugar for the ar mapping.\u001b[39;00m\n\u001b[1;32m    907\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m result \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(result, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar)\\\n\u001b[0;32m--> 908\u001b[0m         \u001b[38;5;28;01melse\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcod\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mar\u001b[49m\u001b[43m(\u001b[49m\u001b[43mresult\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdom\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcod\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    909\u001b[0m assert_isinstance(other, Arrow)\n\u001b[1;32m    910\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcod\u001b[38;5;241m.\u001b[39mar\u001b[38;5;241m.\u001b[39mid(\u001b[38;5;28mself\u001b[39m(other\u001b[38;5;241m.\u001b[39mdom))\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/monoidal.py:522\u001b[0m, in \u001b[0;36mDiagram.__init__\u001b[0;34m(self, inside, dom, cod, _scan)\u001b[0m\n\u001b[1;32m    520\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m layer \u001b[38;5;129;01min\u001b[39;00m inside:\n\u001b[1;32m    521\u001b[0m     assert_isinstance(layer, Layer)\n\u001b[0;32m--> 522\u001b[0m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__init__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43minside\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdom\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcod\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m_scan\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m_scan\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/discopy/cat.py:235\u001b[0m, in \u001b[0;36mArrow.__init__\u001b[0;34m(self, inside, dom, cod, _scan)\u001b[0m\n\u001b[1;32m    233\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m box \u001b[38;5;129;01min\u001b[39;00m inside:\n\u001b[1;32m    234\u001b[0m     assert_isinstance(box, Box)\n\u001b[0;32m--> 235\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m f, g \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(\u001b[43m(\u001b[49m\u001b[43mId\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdom\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m+\u001b[39;49m\u001b[43m \u001b[49m\u001b[43minside\u001b[49m, inside \u001b[38;5;241m+\u001b[39m (Id(cod), )):\n\u001b[1;32m    236\u001b[0m     assert_iscomposable(f, g)\n",
-      "\u001b[0;31mTypeError\u001b[0m: can only concatenate tuple (not \"Z\") to tuple"
-     ]
-    }
-   ],
-   "source": [
-    "from optyx.core.zx import zx_to_path\n",
-    "\n",
-    "circ = zx_to_path(diagram)\n",
-    "circ.draw(draw_box_labels=False, draw_type_labels=False)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the dual rail encoding, each qubit gets mapped to 2 linear optical modes.\n",
-    "Specifically $\\ket{0}$ and $\\ket{1}$ get mapped to $\\ket{1, 0}$ and $\\ket{0, 1}$ respectively.\n",
-    "\n",
-    "Here are all the $n$ qubit dual rail states."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[[1, 0, 1, 0, 1, 0],\n",
-       " [1, 0, 1, 0, 0, 1],\n",
-       " [1, 0, 0, 1, 1, 0],\n",
-       " [1, 0, 0, 1, 0, 1],\n",
-       " [0, 1, 1, 0, 1, 0],\n",
-       " [0, 1, 1, 0, 0, 1],\n",
-       " [0, 1, 0, 1, 1, 0],\n",
-       " [0, 1, 0, 1, 0, 1]]"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "def dual_rail_states(n_qubits):\n",
-    "    strings = []\n",
-    "    def genbin(n, bs=[]):\n",
-    "        if len(bs) == 2*n:\n",
-    "            strings.append(bs)\n",
-    "        else:\n",
-    "            genbin(n, bs + [1, 0])\n",
-    "            genbin(n, bs + [0, 1])\n",
-    "    genbin(n_qubits)\n",
-    "    return strings\n",
-    "\n",
-    "dual_rail_states(3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Then we calculate amplitudes of input output pair by sampling the permenant of the unitary associated with the QPath diagram (For details see https://arxiv.org/abs/1011.3245)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def evaluate(circ, x, y):\n",
-    "    \"\"\" Evaluate the probability of <y|U_h|x> \"\"\"\n",
-    "    from optyx import Id, Create, Select\n",
-    "    inp = Id().tensor(*[Create(i) for i in x])\n",
-    "    out = Id().tensor(*[Select(i) for i in y])\n",
-    "\n",
-    "    return ((inp >> circ >> out).eval().array.flatten().item())"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[ 0.707-0.j, -0.   +0.j,  0.   +0.j,  0.707+0.j],\n",
-       "       [-0.   +0.j,  0.707+0.j,  0.707+0.j,  0.   -0.j],\n",
-       "       [-0.   -0.j,  0.707-0.j, -0.707+0.j, -0.   -0.j],\n",
-       "       [ 0.707-0.j, -0.   -0.j, -0.   -0.j, -0.707+0.j]])"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "import numpy as np\n",
-    "\n",
-    "states = dual_rail_states(len(circuit.cod))\n",
-    "array = np.array([[evaluate(circ, x, y) for x in states] for y in states])\n",
-    "np.round(array, decimals=3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "which is equal to the direct simulation of the original quantum circuit."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[ 0.707+0.j,  0.   +0.j,  0.   +0.j,  0.707+0.j],\n",
-       "       [ 0.   +0.j,  0.707+0.j,  0.707+0.j,  0.   +0.j],\n",
-       "       [ 0.   +0.j,  0.707+0.j, -0.707+0.j,  0.   +0.j],\n",
-       "       [ 0.707+0.j,  0.   +0.j,  0.   +0.j, -0.707+0.j]])"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.round(circuit.eval().array.reshape(4, 4), decimals=3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.10.12"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 4
-}
diff --git a/docs/notebooks/optyx-vqe-experiment.ipynb b/docs/notebooks/optyx-vqe-experiment.ipynb
index 67cb55b4..6d1f9176 100644
--- a/docs/notebooks/optyx-vqe-experiment.ipynb
+++ b/docs/notebooks/optyx-vqe-experiment.ipynb
@@ -32,7 +32,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 200x600 with 1 Axes>"
       ]
@@ -72,7 +72,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 200x1400 with 1 Axes>"
       ]
@@ -93,12 +93,88 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "from optyx.qubits import Circuit"
+    "from optyx.qubits import Circuit\n",
+    "from optyx.core.backends import DiscopyBackend"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 6,
+   "id": "28b96946",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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",
+      "text/plain": [
+       "<Figure size 100x100 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from optyx.qubits import Z\n",
+    "\n",
+    "Z(1, 1).dagger().draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "26ece567",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 450x2400 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "Circuit(exp).decomp().draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "768b5f7e",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 1700x5600 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "Circuit(exp).decomp().to_dual_rail().draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "0406fa28",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "path_exp = Circuit(exp).to_dual_rail()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
    "id": "b86a1407-e4ce-4776-ac0e-ce23ea5a9fff",
    "metadata": {},
    "outputs": [],
@@ -112,14 +188,24 @@
     "free_syms = exp.free_symbols\n",
     "\n",
     "path_exp = Circuit(exp).to_dual_rail()\n",
-    "f_exp = lambda xs: to_float(path_exp.lambdify(*free_syms)(*xs).double().to_tensor().eval().array[0, 0])\n",
-    "orig_f_exp = lambda xs: to_float(exp.lambdify(*free_syms)(*xs).double().to_tensor().eval().array.item())\n",
+    "\n",
+    "f_exp = lambda xs: to_float(path_exp.lambdify(*free_syms)(*xs).eval().tensor.array)\n",
+    "orig_f_exp = lambda xs: to_float(exp.lambdify(*free_syms)(*xs).eval().array.item())\n",
     "\n",
     "def d_f_exp(xs):\n",
+    "    #path_exp.grad(list(free_syms)[0]).draw()#.lambdify(*free_syms)(*xs).draw()\n",
     "    return [\n",
-    "        path_exp.grad(s).lambdify(*free_syms)(*xs).eval().array[0, 0]\n",
+    "        path_exp.grad(s).lambdify(*free_syms)(*xs).eval().tensor.array\n",
     "        for s in free_syms\n",
-    "    ]"
+    "    ]\n",
+    "\n",
+    "# def d_f_exp(xs):\n",
+    "#     grads = [path_exp.grad(s) for s in free_syms]\n",
+    "#     vals = [0] * len(grads)\n",
+    "#     for i, g in enumerate(grads):\n",
+    "#         for term in g.lambdify(*free_syms)(*xs).terms:\n",
+    "#             vals[i] += to_float(term.eval().tensor.array)\n",
+    "#     return vals"
    ]
   },
   {
@@ -132,7 +218,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 12,
    "id": "41ea980c-40c4-4bd2-8731-fc84fb110f41",
    "metadata": {},
    "outputs": [],
@@ -147,10 +233,10 @@
     "    x = x0\n",
     "\n",
     "    for _ in tqdm(range(20)):\n",
+    "        orig_fx = orig_f_exp(x)\n",
     "        fx = f_exp(x)\n",
     "        dfx = d_f_exp(x)\n",
-    "        orig_fx = orig_f_exp(x)\n",
-    "\n",
+    "        print(orig_fx)\n",
     "        # verifies that the conversion is correct\n",
     "        assert abs(orig_fx - fx) < 1e-10\n",
     "\n",
@@ -167,7 +253,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 13,
    "id": "cd5e3e93-5d75-415d-bbcc-14022c9ecf97",
    "metadata": {
     "scrolled": true
@@ -179,6 +265,42 @@
      "text": [
       "  0%|          | 0/20 [00:00<?, ?it/s]"
      ]
+    },
+    {
+     "data": {
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+      "text/plain": [
+       "<Figure size 3600x5800 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "  0%|          | 0/20 [00:02<?, ?it/s]\n"
+     ]
+    },
+    {
+     "ename": "ValueError",
+     "evalue": "too many values to unpack (expected 3)",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
+      "\u001b[31mValueError\u001b[39m                                Traceback (most recent call last)",
+      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[13]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[43moptimize\u001b[49m\u001b[43m(\u001b[49m\u001b[43m[\u001b[49m\u001b[32;43m0.1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[32;43m0.2\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n",
+      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[12]\u001b[39m\u001b[32m, line 13\u001b[39m, in \u001b[36moptimize\u001b[39m\u001b[34m(x0)\u001b[39m\n\u001b[32m     11\u001b[39m orig_fx = orig_f_exp(x)\n\u001b[32m     12\u001b[39m fx = f_exp(x)\n\u001b[32m---> \u001b[39m\u001b[32m13\u001b[39m dfx = \u001b[43md_f_exp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m     14\u001b[39m \u001b[38;5;28mprint\u001b[39m(orig_fx)\n\u001b[32m     15\u001b[39m \u001b[38;5;66;03m# verifies that the conversion is correct\u001b[39;00m\n",
+      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[11]\u001b[39m\u001b[32m, line 17\u001b[39m, in \u001b[36md_f_exp\u001b[39m\u001b[34m(xs)\u001b[39m\n\u001b[32m     14\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34md_f_exp\u001b[39m(xs):\n\u001b[32m     15\u001b[39m     path_exp.grad(\u001b[38;5;28mlist\u001b[39m(free_syms)[\u001b[32m0\u001b[39m]).draw()\u001b[38;5;66;03m#.lambdify(*free_syms)(*xs).draw()\u001b[39;00m\n\u001b[32m     16\u001b[39m     \u001b[38;5;28;01mreturn\u001b[39;00m [\n\u001b[32m---> \u001b[39m\u001b[32m17\u001b[39m         \u001b[43mpath_exp\u001b[49m\u001b[43m.\u001b[49m\u001b[43mgrad\u001b[49m\u001b[43m(\u001b[49m\u001b[43ms\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mlambdify\u001b[49m\u001b[43m(\u001b[49m\u001b[43m*\u001b[49m\u001b[43mfree_syms\u001b[49m\u001b[43m)\u001b[49m\u001b[43m(\u001b[49m\u001b[43m*\u001b[49m\u001b[43mxs\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43meval\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m.tensor.array\n\u001b[32m     18\u001b[39m         \u001b[38;5;28;01mfor\u001b[39;00m s \u001b[38;5;129;01min\u001b[39;00m free_syms\n\u001b[32m     19\u001b[39m     ]\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/optyx/optyx/core/channel.py:475\u001b[39m, in \u001b[36mDiagram.eval\u001b[39m\u001b[34m(self, backend, **kwargs)\u001b[39m\n\u001b[32m    472\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m backend \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[32m    473\u001b[39m     backend = QuimbBackend()\n\u001b[32m--> \u001b[39m\u001b[32m475\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mbackend\u001b[49m\u001b[43m.\u001b[49m\u001b[43meval\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/optyx/optyx/core/backends.py:397\u001b[39m, in \u001b[36mQuimbBackend.eval\u001b[39m\u001b[34m(self, diagram, **extra)\u001b[39m\n\u001b[32m    384\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34meval\u001b[39m(\n\u001b[32m    385\u001b[39m         \u001b[38;5;28mself\u001b[39m,\n\u001b[32m    386\u001b[39m         diagram: Diagram,\n\u001b[32m    387\u001b[39m         **extra: Any) -> EvalResult:\n\u001b[32m    388\u001b[39m \u001b[38;5;250m    \u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    389\u001b[39m \u001b[33;03m    Evaluate the diagram using Quimb.\u001b[39;00m\n\u001b[32m    390\u001b[39m \n\u001b[32m   (...)\u001b[39m\u001b[32m    395\u001b[39m \u001b[33;03m        The result of the evaluation.\u001b[39;00m\n\u001b[32m    396\u001b[39m \u001b[33;03m    \"\"\"\u001b[39;00m\n\u001b[32m--> \u001b[39m\u001b[32m397\u001b[39m     quimb_tn = \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_get_quimb_tensor\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdiagram\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m    398\u001b[39m     tensor_diagram = \u001b[38;5;28mself\u001b[39m._get_discopy_tensor(diagram)\n\u001b[32m    400\u001b[39m     \u001b[38;5;28;01mfor\u001b[39;00m t \u001b[38;5;129;01min\u001b[39;00m quimb_tn:\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/optyx/optyx/core/backends.py:320\u001b[39m, in \u001b[36mAbstractBackend._get_quimb_tensor\u001b[39m\u001b[34m(self, diagram)\u001b[39m\n\u001b[32m    313\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34m_get_quimb_tensor\u001b[39m(\n\u001b[32m    314\u001b[39m     \u001b[38;5;28mself\u001b[39m,\n\u001b[32m    315\u001b[39m     diagram: Diagram\n\u001b[32m    316\u001b[39m ) -> TensorNetwork:\n\u001b[32m    317\u001b[39m \u001b[38;5;250m    \u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    318\u001b[39m \u001b[33;03m    Get the Quimb tensor representation of the diagram.\u001b[39;00m\n\u001b[32m    319\u001b[39m \u001b[33;03m    \"\"\"\u001b[39;00m\n\u001b[32m--> \u001b[39m\u001b[32m320\u001b[39m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_get_discopy_tensor\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdiagram\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mto_quimb\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/.venv/lib/python3.12/site-packages/discopy/tensor.py:451\u001b[39m, in \u001b[36mDiagram.to_quimb\u001b[39m\u001b[34m(self, dtype)\u001b[39m\n\u001b[32m    448\u001b[39m tensors = inputs[:]\n\u001b[32m    449\u001b[39m scan = [(t, \u001b[32m1\u001b[39m) \u001b[38;5;28;01mfor\u001b[39;00m t \u001b[38;5;129;01min\u001b[39;00m inputs]\n\u001b[32m--> \u001b[39m\u001b[32m451\u001b[39m \u001b[38;5;28;01mfor\u001b[39;00m i, (box, off) \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(\u001b[38;5;28mzip\u001b[39m(\u001b[38;5;28mself\u001b[39m.boxes, \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43moffsets\u001b[49m)):\n\u001b[32m    452\u001b[39m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(box, Swap):\n\u001b[32m    453\u001b[39m         scan[off], scan[off + \u001b[32m1\u001b[39m] = scan[off + \u001b[32m1\u001b[39m], scan[off]\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/.venv/lib/python3.12/site-packages/discopy/monoidal.py:598\u001b[39m, in \u001b[36mDiagram.offsets\u001b[39m\u001b[34m(self)\u001b[39m\n\u001b[32m    595\u001b[39m \u001b[38;5;129m@property\u001b[39m\n\u001b[32m    596\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34moffsets\u001b[39m(\u001b[38;5;28mself\u001b[39m) -> \u001b[38;5;28mlist\u001b[39m[\u001b[38;5;28mint\u001b[39m]:\n\u001b[32m    597\u001b[39m \u001b[38;5;250m    \u001b[39m\u001b[33;03m\"\"\" The offset of a box is the length of the type on its left. \"\"\"\u001b[39;00m\n\u001b[32m--> \u001b[39m\u001b[32m598\u001b[39m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mlist\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mlen\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mleft\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mfor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mleft\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m_\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m_\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m)\u001b[49m\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/.venv/lib/python3.12/site-packages/discopy/monoidal.py:598\u001b[39m, in \u001b[36m<genexpr>\u001b[39m\u001b[34m(.0)\u001b[39m\n\u001b[32m    595\u001b[39m \u001b[38;5;129m@property\u001b[39m\n\u001b[32m    596\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34moffsets\u001b[39m(\u001b[38;5;28mself\u001b[39m) -> \u001b[38;5;28mlist\u001b[39m[\u001b[38;5;28mint\u001b[39m]:\n\u001b[32m    597\u001b[39m \u001b[38;5;250m    \u001b[39m\u001b[33;03m\"\"\" The offset of a box is the length of the type on its left. \"\"\"\u001b[39;00m\n\u001b[32m--> \u001b[39m\u001b[32m598\u001b[39m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mlist\u001b[39m(\u001b[38;5;28mlen\u001b[39m(left) \u001b[38;5;28;01mfor\u001b[39;00m left, _, _ \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m)\n",
+      "\u001b[31mValueError\u001b[39m: too many values to unpack (expected 3)"
+     ]
     }
    ],
    "source": [
@@ -187,7 +309,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": null,
    "id": "3a0c4436-86d9-4a16-9bc2-7eba1cc440f7",
    "metadata": {},
    "outputs": [
@@ -220,11 +342,19 @@
     "    **{f'x{i}': [v[i] for v in xs] for i in range(len(free_syms))}\n",
     "}).plot()"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c4e312d7",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": ".venv",
    "language": "python",
    "name": "python3"
   },
@@ -238,7 +368,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.12"
+   "version": "3.12.3"
   }
  },
  "nbformat": 4,
diff --git a/docs/notebooks/photon_distinguishability.ipynb b/docs/notebooks/photon_distinguishability.ipynb
index bc3e323c..6d4653d1 100644
--- a/docs/notebooks/photon_distinguishability.ipynb
+++ b/docs/notebooks/photon_distinguishability.ipynb
@@ -61,11 +61,11 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-07-11T08:56:28.547486</dc:date>\n",
+       "    <dc:date>2025-09-04T14:45:17.238229</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
-       "      <dc:title>Matplotlib v3.10.0, https://matplotlib.org/</dc:title>\n",
+       "      <dc:title>Matplotlib v3.10.5, https://matplotlib.org/</dc:title>\n",
        "     </cc:Agent>\n",
        "    </dc:creator>\n",
        "   </cc:Work>\n",
@@ -90,37 +90,37 @@
        "L 439.2 7.2 \n",
        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pce30823637)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd22800e47d)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
        "    <path d=\"M 223.2 43.2 \n",
        "Q 223.2 43.2 223.2 61.2 \n",
-       "\" clip-path=\"url(#pce30823637)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd22800e47d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 223.2 61.2 \n",
        "Q 223.2 97.2 223.2 97.2 \n",
-       "\" clip-path=\"url(#pce30823637)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd22800e47d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
        "    <path d=\"M 115.2 133.2 \n",
        "Q 115.2 169.2 115.2 169.2 \n",
-       "\" clip-path=\"url(#pce30823637)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd22800e47d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_6\">\n",
        "    <path d=\"M 331.2 133.2 \n",
        "Q 331.2 169.2 331.2 169.2 \n",
-       "\" clip-path=\"url(#pce30823637)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd22800e47d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_7\">\n",
        "    <path d=\"M 115.2 205.2 \n",
        "Q 115.2 223.2 115.2 223.2 \n",
-       "\" clip-path=\"url(#pce30823637)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd22800e47d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_8\">\n",
        "    <path d=\"M 331.2 205.2 \n",
        "Q 331.2 223.2 331.2 223.2 \n",
-       "\" clip-path=\"url(#pce30823637)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd22800e47d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_9\">\n",
        "    <path d=\"M 61.2 133.2 \n",
@@ -128,7 +128,7 @@
        "L 385.2 97.2 \n",
        "L 385.2 133.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pce30823637)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd22800e47d)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_10\">\n",
        "    <path d=\"M 61.2 205.2 \n",
@@ -136,7 +136,7 @@
        "L 169.2 169.2 \n",
        "L 169.2 205.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pce30823637)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd22800e47d)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_11\">\n",
        "    <path d=\"M 277.2 205.2 \n",
@@ -144,11 +144,11 @@
        "L 385.2 169.2 \n",
        "L 385.2 205.2 \n",
        "z\n",
-       "\" clip-path=\"url(#pce30823637)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd22800e47d)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_1\">\n",
        "    <defs>\n",
-       "     <path id=\"me13a503d70\" d=\"M 0 6.578374 \n",
+       "     <path id=\"m5994983a8f\" d=\"M 0 6.578374 \n",
        "C 1.744605 6.578374 3.417991 5.885235 4.651613 4.651613 \n",
        "C 5.885235 3.417991 6.578374 1.744605 6.578374 0 \n",
        "C 6.578374 -1.744605 5.885235 -3.417991 4.651613 -4.651613 \n",
@@ -160,8 +160,8 @@
        "z\n",
        "\" style=\"stroke: #776ff3\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#pce30823637)\">\n",
-       "     <use xlink:href=\"#me13a503d70\" x=\"223.2\" y=\"43.2\" style=\"fill: #776ff3; stroke: #776ff3\"/>\n",
+       "    <g clip-path=\"url(#pd22800e47d)\">\n",
+       "     <use xlink:href=\"#m5994983a8f\" x=\"223.2\" y=\"43.2\" style=\"fill: #776ff3; stroke: #776ff3\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
@@ -667,7 +667,7 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_9\">\n",
-       "    <g clip-path=\"url(#pce30823637)\">\n",
+       "    <g clip-path=\"url(#pd22800e47d)\">\n",
        "     <!-- Create(1) -->\n",
        "     <g transform=\"translate(194.766562 46.51125) scale(0.12 -0.12)\">\n",
        "      <defs>\n",
@@ -779,7 +779,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"pce30823637\">\n",
+       "  <clipPath id=\"pd22800e47d\">\n",
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        "  </clipPath>\n",
        " </defs>\n",
@@ -825,11 +825,11 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-07-11T08:56:28.611310</dc:date>\n",
+       "    <dc:date>2025-09-04T14:45:18.222738</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
-       "      <dc:title>Matplotlib v3.10.0, https://matplotlib.org/</dc:title>\n",
+       "      <dc:title>Matplotlib v3.10.5, https://matplotlib.org/</dc:title>\n",
        "     </cc:Agent>\n",
        "    </dc:creator>\n",
        "   </cc:Work>\n",
@@ -854,62 +854,62 @@
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+       "\" clip-path=\"url(#pe68549364e)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p7e7797de41)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -917,7 +917,7 @@
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        "z\n",
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@@ -925,7 +925,7 @@
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@@ -933,7 +933,7 @@
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@@ -941,7 +941,7 @@
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@@ -949,7 +949,7 @@
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@@ -957,7 +957,7 @@
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@@ -965,7 +965,7 @@
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        "z\n",
-       "\" clip-path=\"url(#p7e7797de41)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pe68549364e)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -1516,7 +1516,7 @@
        "  </g>\n",
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-       "  <clipPath id=\"p7e7797de41\">\n",
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@@ -1595,7 +1595,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "result = channel_BS.double().to_tensor(max_dim=3).eval().array"
+    "result = channel_BS.eval().prob_dist()"
    ]
   },
   {
@@ -1606,20 +1606,18 @@
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "{(0, 2): (0.5+0j), (2, 0): (0.5+0j)}\n"
-     ]
+     "data": {
+      "text/plain": [
+       "{(0, 2): (0.5+0j), (1, 1): (1.2325951644078304e-32+0j), (2, 0): (0.5+0j)}"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
-    "import numpy as np\n",
-    "\n",
-    "rounded_result = np.round(result, 3)\n",
-    "\n",
-    "non_zero_dict = {idx: val for idx, val in np.ndenumerate(rounded_result) if val != 0}\n",
-    "print(non_zero_dict)"
+    "result"
    ]
   },
   {
@@ -1648,6 +1646,15 @@
    "execution_count": 8,
    "metadata": {},
    "outputs": [],
+   "source": [
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "internal_state_1 = np.random.rand(2) + 1j*np.random.rand(2)\n",
     "internal_state_1 = internal_state_1 / np.linalg.norm(internal_state_1)\n",
@@ -1657,16 +1664,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([0.40967198+0.60659402j, 0.60777898+0.30792413j])"
+       "array([0.46805045+0.03203795j, 0.78186157+0.41060301j])"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1677,16 +1684,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([0.46117336+0.69994621j, 0.02085841+0.54493978j])"
+       "array([0.54051796+0.56786515j, 0.46030203+0.41652317j])"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1697,7 +1704,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1710,33 +1717,33 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [],
    "source": [
-    "result = channel_BS.double().to_tensor(max_dim=3).eval().array"
+    "result = channel_BS.eval().prob_dist()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "{(0, 2): (0.435125-0j), (1, 1): (0.129749+0j), (2, 0): (0.435125-0j)}\n"
-     ]
+     "data": {
+      "text/plain": [
+       "{(0, 2): (0.4479236685298761+1.66268625707414e-18j),\n",
+       " (1, 1): (0.10415266294024787-1.7203160321962734e-17j),\n",
+       " (2, 0): (0.4479236685298761+1.5540474064888597e-17j)}"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
-    "import numpy as np\n",
-    "\n",
-    "rounded_result = np.round(result, 6)\n",
-    "\n",
-    "non_zero_dict = {idx: val for idx, val in np.ndenumerate(rounded_result) if val != 0}\n",
-    "print(non_zero_dict)"
+    "result"
    ]
   },
   {
@@ -1748,16 +1755,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "0.1297494782905118"
+       "0.10415266294024783"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1777,7 +1784,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
@@ -1791,11 +1798,11 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-07-11T08:56:29.397725</dc:date>\n",
+       "    <dc:date>2025-09-04T14:45:30.829444</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
-       "      <dc:title>Matplotlib v3.10.0, https://matplotlib.org/</dc:title>\n",
+       "      <dc:title>Matplotlib v3.10.5, https://matplotlib.org/</dc:title>\n",
        "     </cc:Agent>\n",
        "    </dc:creator>\n",
        "   </cc:Work>\n",
@@ -1820,182 +1827,182 @@
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        "z\n",
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-       "\" clip-path=\"url(#p3ee7baf01e)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p3ee7baf01e)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p3ee7baf01e)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p3ee7baf01e)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3e57b90873)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p3ee7baf01e)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p3ee7baf01e)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p3ee7baf01e)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p3ee7baf01e)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p3ee7baf01e)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3e57b90873)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p3ee7baf01e)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -4648,72 +4655,87 @@
     "from optyx.photonic import DualRail\n",
     "from optyx.classical import PostselectBit\n",
     "from discopy.drawing import Equation\n",
+    "from optyx.core.channel import Diagram, bit, qubit, mode, qmode\n",
     "\n",
-    "bell_state = Z(0, 2) @ Scalar(0.5 ** 0.5)\n",
+    "bell_state = (Z(0, 2) @ Scalar(0.5 ** 0.5))\n",
     "dual_rail_encoding = lambda state: DualRail(1, internal_states=[state])\n",
-    "encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(internal_state_2)\n",
     "post_select = PostselectBit(1) @ PostselectBit(0)\n",
-    "experiment = bell_state @ bell_state >> Id(1) @ (encoding_layer >> fusion_channel >> post_select) @ Id(1)\n",
-    "measure = Measure(2)\n",
-    "Equation(experiment >> measure, bell_state >> measure).draw(figsize=(8, 8))"
+    "\n",
+    "def fusion(internal_state_1, internal_state_2):\n",
+    "    @Diagram.from_callable(dom=bit ** 0, cod=qubit**2)\n",
+    "    def d():\n",
+    "        a = (bell_state @ bell_state)()\n",
+    "        b = (dual_rail_encoding(internal_state_1) @ dual_rail_encoding(internal_state_2))(a[1], a[2])\n",
+    "        c = fusion_channel(*b)\n",
+    "        post_select(c[0], c[1])\n",
+    "        return a[0], a[3]\n",
+    "\n",
+    "    return d\n",
+    "\n",
+    "@Diagram.from_callable(dom=bit ** 0, cod=qubit**2)\n",
+    "def bell():\n",
+    "    a1, a2 = bell_state()\n",
+    "    return a1, a2\n",
+    "\n",
+    "Equation(fusion(internal_state_1, internal_state_2) >> Measure(2), bell >> Measure(2)).draw(figsize=(8, 8))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "0.25000000000000017"
+       "array(0.25-0.j)"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "from optyx.qubits import Discard\n",
-    "(experiment >> Discard(2)).inflate(2).double().to_tensor(max_dim=3).to_quimb()^..."
+    "(fusion(internal_state_1, internal_state_2) >> Discard(2)).inflate(2).eval().tensor.array"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [],
    "source": [
-    "fidelity = (experiment >> bell_state.dagger())\n",
+    "fidelity = (fusion(internal_state_1, internal_state_2) >> bell_state.dagger())\n",
     "\n",
-    "normalisation = (experiment >> Discard(2)).inflate(2).double().to_tensor(max_dim=3).to_quimb()^..."
+    "normalisation = (fusion(internal_state_1, internal_state_2) >> Discard(2)).inflate(2).eval().tensor.array"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {
      "data": {
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-       "1.0000000000000002"
+       "(1.0000000000000002-1.83697019872103e-16j)"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 21,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "f = fidelity.inflate(2).double().to_tensor(max_dim=3).to_quimb()^...\n",
+    "f = fidelity.inflate(2).eval().tensor.array\n",
     "f/normalisation"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -4727,7 +4749,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -4736,14 +4758,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 24,
    "metadata": {},
    "outputs": [],
    "source": [
     "inner_product_states = []\n",
     "inner_product_bell_states = []\n",
     "\n",
-    "result_bell = (bell_state.double().to_tensor().to_quimb()^...).data.flatten()\n",
+    "result_bell = bell_state.eval().tensor.array.flatten()\n",
     "result_bell = result_bell / np.linalg.norm(result_bell)\n",
     "\n",
     "for vector in unit_vectors:\n",
@@ -4751,8 +4773,8 @@
     "    experiment = bell_state @ bell_state >> Id(1) @ (encoding_layer >> fusion_channel\n",
     "                                                                                >> post_select) @ Id(1)\n",
     "\n",
-    "    f = (experiment >> bell_state.dagger()).inflate(2).double().to_tensor(max_dim=3).to_quimb()^...\n",
-    "    normalisation = (experiment >> Discard(2)).inflate(2).double().to_tensor(max_dim=3).to_quimb()^...\n",
+    "    f = (experiment >> bell_state.dagger()).inflate(2).eval().tensor.array\n",
+    "    normalisation = (experiment >> Discard(2)).inflate(2).eval().tensor.array\n",
     "\n",
     "    inner_product_states.append(np.inner(vector, internal_state_1))\n",
     "    inner_product_bell_states.append(f/normalisation)"
@@ -4760,9 +4782,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part\n",
+      "  return math.isfinite(val)\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part\n",
+      "  return np.asarray(x, float)\n"
+     ]
+    },
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        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p267996ebfb\">\n",
+       "  <clipPath id=\"p33a72152de\">\n",
        "   <rect x=\"44.103125\" y=\"22.318125\" width=\"334.8\" height=\"221.76\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -6128,7 +6160,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 26,
    "metadata": {},
    "outputs": [
     {
@@ -6142,11 +6174,11 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-07-11T08:57:34.528132</dc:date>\n",
+       "    <dc:date>2025-09-04T14:51:25.378090</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
-       "      <dc:title>Matplotlib v3.10.0, https://matplotlib.org/</dc:title>\n",
+       "      <dc:title>Matplotlib v3.10.5, https://matplotlib.org/</dc:title>\n",
        "     </cc:Agent>\n",
        "    </dc:creator>\n",
        "   </cc:Work>\n",
@@ -6178,16 +6210,16 @@
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        "      <path d=\"M 50.465625 244.078125 \n",
        "L 50.465625 22.318125 \n",
-       "\" clip-path=\"url(#p984e08da21)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p131f154857)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
        "     </g>\n",
        "     <g id=\"line2d_2\">\n",
        "      <defs>\n",
-       "       <path id=\"m94b01484e2\" d=\"M 0 0 \n",
+       "       <path id=\"mcaad2c210b\" d=\"M 0 0 \n",
        "L 0 3.5 \n",
        "\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </defs>\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m94b01484e2\" x=\"50.465625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_1\">\n",
@@ -6264,11 +6296,11 @@
        "     <g id=\"line2d_3\">\n",
        "      <path d=\"M 117.425625 244.078125 \n",
        "L 117.425625 22.318125 \n",
-       "\" clip-path=\"url(#p984e08da21)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p131f154857)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
        "     </g>\n",
        "     <g id=\"line2d_4\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m94b01484e2\" x=\"117.425625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#mcaad2c210b\" x=\"117.425625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_2\">\n",
@@ -6311,11 +6343,11 @@
        "     <g id=\"line2d_5\">\n",
        "      <path d=\"M 184.385625 244.078125 \n",
        "L 184.385625 22.318125 \n",
-       "\" clip-path=\"url(#p984e08da21)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p131f154857)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
        "     </g>\n",
        "     <g id=\"line2d_6\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m94b01484e2\" x=\"184.385625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#mcaad2c210b\" x=\"184.385625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_3\">\n",
@@ -6353,11 +6385,11 @@
        "     <g id=\"line2d_7\">\n",
        "      <path d=\"M 251.345625 244.078125 \n",
        "L 251.345625 22.318125 \n",
-       "\" clip-path=\"url(#p984e08da21)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p131f154857)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
        "     </g>\n",
        "     <g id=\"line2d_8\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m94b01484e2\" x=\"251.345625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#mcaad2c210b\" x=\"251.345625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_4\">\n",
@@ -6406,11 +6438,11 @@
        "     <g id=\"line2d_9\">\n",
        "      <path d=\"M 318.305625 244.078125 \n",
        "L 318.305625 22.318125 \n",
-       "\" clip-path=\"url(#p984e08da21)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p131f154857)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
        "     </g>\n",
        "     <g id=\"line2d_10\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m94b01484e2\" x=\"318.305625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#mcaad2c210b\" x=\"318.305625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_5\">\n",
@@ -6468,11 +6500,11 @@
        "     <g id=\"line2d_11\">\n",
        "      <path d=\"M 385.265625 244.078125 \n",
        "L 385.265625 22.318125 \n",
-       "\" clip-path=\"url(#p984e08da21)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p131f154857)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
        "     </g>\n",
        "     <g id=\"line2d_12\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m94b01484e2\" x=\"385.265625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#mcaad2c210b\" x=\"385.265625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_6\">\n",
@@ -6739,16 +6771,16 @@
        "     <g id=\"line2d_13\">\n",
        "      <path d=\"M 50.465625 244.078125 \n",
        "L 385.265625 244.078125 \n",
-       "\" clip-path=\"url(#p984e08da21)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p131f154857)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
        "     </g>\n",
        "     <g id=\"line2d_14\">\n",
        "      <defs>\n",
-       "       <path id=\"m2ab98fbcb7\" d=\"M 0 0 \n",
+       "       <path id=\"meab27b0957\" d=\"M 0 0 \n",
        "L -3.5 0 \n",
        "\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </defs>\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m2ab98fbcb7\" x=\"50.465625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#meab27b0957\" x=\"50.465625\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_8\">\n",
@@ -6765,11 +6797,11 @@
        "     <g id=\"line2d_15\">\n",
        "      <path d=\"M 50.465625 199.726125 \n",
        "L 385.265625 199.726125 \n",
-       "\" clip-path=\"url(#p984e08da21)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p131f154857)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
        "     </g>\n",
        "     <g id=\"line2d_16\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m2ab98fbcb7\" x=\"50.465625\" y=\"199.726125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#meab27b0957\" x=\"50.465625\" y=\"199.726125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_9\">\n",
@@ -6786,11 +6818,11 @@
        "     <g id=\"line2d_17\">\n",
        "      <path d=\"M 50.465625 155.374125 \n",
        "L 385.265625 155.374125 \n",
-       "\" clip-path=\"url(#p984e08da21)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p131f154857)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
        "     </g>\n",
        "     <g id=\"line2d_18\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m2ab98fbcb7\" x=\"50.465625\" y=\"155.374125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#meab27b0957\" x=\"50.465625\" y=\"155.374125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_10\">\n",
@@ -6807,11 +6839,11 @@
        "     <g id=\"line2d_19\">\n",
        "      <path d=\"M 50.465625 111.022125 \n",
        "L 385.265625 111.022125 \n",
-       "\" clip-path=\"url(#p984e08da21)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p131f154857)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
        "     </g>\n",
        "     <g id=\"line2d_20\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m2ab98fbcb7\" x=\"50.465625\" y=\"111.022125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#meab27b0957\" x=\"50.465625\" y=\"111.022125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_11\">\n",
@@ -6828,11 +6860,11 @@
        "     <g id=\"line2d_21\">\n",
        "      <path d=\"M 50.465625 66.670125 \n",
        "L 385.265625 66.670125 \n",
-       "\" clip-path=\"url(#p984e08da21)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p131f154857)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
        "     </g>\n",
        "     <g id=\"line2d_22\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m2ab98fbcb7\" x=\"50.465625\" y=\"66.670125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#meab27b0957\" x=\"50.465625\" y=\"66.670125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_12\">\n",
@@ -6849,11 +6881,11 @@
        "     <g id=\"line2d_23\">\n",
        "      <path d=\"M 50.465625 22.318125 \n",
        "L 385.265625 22.318125 \n",
-       "\" clip-path=\"url(#p984e08da21)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p131f154857)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
        "     </g>\n",
        "     <g id=\"line2d_24\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m2ab98fbcb7\" x=\"50.465625\" y=\"22.318125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#meab27b0957\" x=\"50.465625\" y=\"22.318125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_13\">\n",
@@ -7133,9 +7165,9 @@
        "L 147.479683 174.226224 \n",
        "L 75.82813 217.807169 \n",
        "L -1 263.379876 \n",
-       "\" clip-path=\"url(#p984e08da21)\" style=\"fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p131f154857)\" style=\"fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square\"/>\n",
        "    <defs>\n",
-       "     <path id=\"m2cb00b1871\" d=\"M 0 3 \n",
+       "     <path id=\"mf8a5f07f7a\" d=\"M 0 3 \n",
        "C 0.795609 3 1.55874 2.683901 2.12132 2.12132 \n",
        "C 2.683901 1.55874 3 0.795609 3 0 \n",
        "C 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \n",
@@ -7147,17 +7179,17 @@
        "z\n",
        "\" style=\"stroke: #1f77b4\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#p984e08da21)\">\n",
-       "     <use xlink:href=\"#m2cb00b1871\" x=\"385.265625\" y=\"22.318125\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
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-       "     <use xlink:href=\"#m2cb00b1871\" x=\"306.991246\" y=\"73.558312\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
-       "     <use xlink:href=\"#m2cb00b1871\" x=\"263.231\" y=\"101.676507\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
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-       "     <use xlink:href=\"#m2cb00b1871\" x=\"75.82813\" y=\"217.807169\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
-       "     <use xlink:href=\"#m2cb00b1871\" x=\"-1\" y=\"263.379876\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "    <g clip-path=\"url(#p131f154857)\">\n",
+       "     <use xlink:href=\"#mf8a5f07f7a\" x=\"385.265625\" y=\"22.318125\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "     <use xlink:href=\"#mf8a5f07f7a\" x=\"380.355495\" y=\"25.568042\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "     <use xlink:href=\"#mf8a5f07f7a\" x=\"365.639506\" y=\"35.279689\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "     <use xlink:href=\"#mf8a5f07f7a\" x=\"341.160822\" y=\"51.339207\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "     <use xlink:href=\"#mf8a5f07f7a\" x=\"306.991246\" y=\"73.558312\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "     <use xlink:href=\"#mf8a5f07f7a\" x=\"263.231\" y=\"101.676507\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "     <use xlink:href=\"#mf8a5f07f7a\" x=\"210.008442\" y=\"135.364129\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "     <use xlink:href=\"#mf8a5f07f7a\" x=\"147.479683\" y=\"174.226224\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "     <use xlink:href=\"#mf8a5f07f7a\" x=\"75.82813\" y=\"217.807169\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "     <use xlink:href=\"#mf8a5f07f7a\" x=\"-1\" y=\"263.379876\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
@@ -7399,7 +7431,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p984e08da21\">\n",
+       "  <clipPath id=\"p131f154857\">\n",
        "   <rect x=\"50.465625\" y=\"22.318125\" width=\"334.8\" height=\"221.76\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -7437,7 +7469,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": ".venv",
    "language": "python",
    "name": "python3"
   },
@@ -7451,7 +7483,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.12"
+   "version": "3.12.3"
   }
  },
  "nbformat": 4,
diff --git a/optyx/core/backends.py b/optyx/core/backends.py
index 0c46726f..9a792f41 100644
--- a/optyx/core/backends.py
+++ b/optyx/core/backends.py
@@ -392,16 +392,49 @@ def eval(
         Returns:
             The result of the evaluation.
         """
-        quimb_tn = self._get_quimb_tensor(diagram)
+
+        if hasattr(diagram, 'terms'):
+            results = sum(self._process_term(term) for term in diagram.terms)
+        else:
+            results = self._process_term(diagram)
+
+        if diagram.is_pure:
+            state_type = StateType.AMP
+        else:
+            state_type = StateType.DM
+
         tensor_diagram = self._get_discopy_tensor(diagram)
 
+        return EvalResult(
+            discopy_tensor.Box(
+                "Result",
+                tensor_diagram.dom,
+                tensor_diagram.cod,
+                results
+            ),
+            output_types=diagram.cod,
+            state_type=state_type
+        )
+
+    def _process_term(self, term: Diagram) -> np.ndarray:
+        """
+        Process a term in a diagram with multiple terms.
+
+        Args:
+            term (Diagram): The term to process.
+
+        Returns:
+            np.ndarray: The processed term as a numpy array.
+        """
+        quimb_tn = self._get_quimb_tensor(term)
+
         for t in quimb_tn:
             dt = t.data.dtype
             if dt.kind in {'i', 'u', 'b'}:
                 t.modify(data=t.data.astype(np.complex128, copy=False))
 
         if self.hyperoptimiser is None:
-            results = quimb_tn ^ ...
+            result = quimb_tn ^ ...
         else:
             is_approx = isinstance(
                 self.hyperoptimiser,
@@ -426,30 +459,16 @@ def eval(
 
             contract = quimb_tn.contract_compressed if \
                 is_approx else quimb_tn.contract
-            results = contract(
+            result = contract(
                 optimize=self.hyperoptimiser,
                 output_inds=sorted(quimb_tn.outer_inds()),
                 **self.contraction_params
             )
 
-        if not isinstance(results, (complex, float, int)):
-            results = results.data
-
-        if diagram.is_pure:
-            state_type = StateType.AMP
-        else:
-            state_type = StateType.DM
+        if not isinstance(result, (complex, float, int)):
+            result = result.data
 
-        return EvalResult(
-            discopy_tensor.Box(
-                "Result",
-                tensor_diagram.dom,
-                tensor_diagram.cod,
-                results
-            ),
-            output_types=diagram.cod,
-            state_type=state_type
-        )
+        return result
 
 
 # pylint: disable=too-few-public-methods
diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index d83c9914..db29fd64 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -108,6 +108,7 @@
 
 from __future__ import annotations
 
+import numpy as np
 from discopy import tensor
 from discopy import symmetric, frobenius, hypergraph
 from discopy.cat import factory
@@ -115,6 +116,7 @@
 from pyzx import extract_circuit
 from optyx.core import zx, diagram
 from optyx.utils.utils import explode_channel
+from optyx.core.path import Matrix
 
 
 class Ob(frobenius.Ob):
@@ -334,8 +336,7 @@ def to_path(self, dtype: type = complex):
             cod=frobenius.Category(int, path.Matrix[dtype]),
         )(self)
 
-    def _decomp(self):
-
+    def decomp(self):
         # pylint: disable=protected-access
         return frobenius.Functor(
             ob=lambda x: qubit**len(x),
@@ -590,14 +591,10 @@ def dagger(self):
             cod=self.dom,
         )
 
-    def _decomp(self):
+    def decomp(self):
         # pylint: disable=import-outside-toplevel
-        from optyx.qubits import QubitChannel
-        decomposed = zx.decomp(self.kraus)
-        return explode_channel(
-            decomposed,
-            QubitChannel,
-            Diagram
+        raise NotImplementedError(
+            "Decomposition is only implemented for ZX channels."
         )
 
     def to_dual_rail(self):
@@ -658,20 +655,65 @@ def grad(self, var, **params):
             return self.sum_factory((), self.dom, self.cod)
         return sum(term.grad(var, **params) for term in self.terms)
 
-    def eval(self, n_photons=0, permanent=None, dtype=complex):
-        """Evaluate the sum of diagrams."""
-        # we need to implement the proper sums of qpath diagrams
-        # this is only a temporary solution, so that the grad tests pass
-        if permanent is None:
-            # pylint: disable=import-outside-toplevel
-            from optyx.core.path import npperm
-
-            permanent = npperm
-        return sum(
-            term.to_path(dtype).eval(n_photons, permanent)
-            for term in self.terms
+    def get_kraus(self):
+        if len(self.terms) == 0:
+            return diagram.Scalar(0)
+
+        return diagram.Diagram.sum_factory(
+            [term.get_kraus() for term in self.terms]
         )
 
+    # def to_path(self, dtype: type = complex):
+    #     """Evaluate the sum of diagrams."""
+    #     array = 0
+    #     doms = []
+    #     cods = []
+    #     creations = []
+    #     selections = []
+    #     normalisations = []
+    #     for term in self.terms:
+    #         path_diagram = term.to_path(dtype)
+    #         array += path_diagram.array
+    #         creations.append(path_diagram.creations)
+    #         selections.append(path_diagram.selections)
+    #         doms.append(path_diagram.dom)
+    #         cods.append(path_diagram.cod)
+    #         normalisations.append(path_diagram.normalisation)
+
+    #     assert all(d == doms[0] for d in doms), "All terms must have the same dom"
+    #     assert all(c == cods[0] for c in cods), "All terms must have the same cod"
+    #     assert all(creations[0] == cr for cr in creations), "All creations tuples must be identical"
+    #     assert all(selections[0] == se for se in selections), "All selections tuples must be identical"
+    #     assert all(normalisations[0] == n for n in normalisations), "All normalisations must be identical"
+
+    #     array = array/len(self.terms)
+
+    #     dom = doms[0]
+    #     cod = cods[0]
+
+    #     return Matrix[dtype](
+    #         array,
+    #         dom,
+    #         cod,
+    #         creations=creations[0],
+    #         selections=selections[0],
+    #         normalisation=normalisations[0]
+    #     )
+
+    # def eval(self, n_photons=0, permanent=None, dtype=complex):
+    #     """Evaluate the sum of diagrams."""
+    #     # we need to implement the proper sums of qpath diagrams
+    #     # this is only a temporary solution, so that the grad tests pass
+    #     if permanent is None:
+    #         # pylint: disable=import-outside-toplevel
+    #         from optyx.core.path import npperm
+
+    #         permanent = npperm
+    #     return sum(
+    #         term.to_path(dtype).eval(n_photons, permanent)
+    #         for term in self.terms
+    #     )
+
 
 class CQMap(Diagram, frobenius.Box):
     """
diff --git a/optyx/qubits.py b/optyx/qubits.py
index d2958768..b84d69bc 100644
--- a/optyx/qubits.py
+++ b/optyx/qubits.py
@@ -265,13 +265,14 @@
 
 """  # noqa E501
 
-from typing import Literal
+from typing import Literal, Iterable
 from enum import Enum
 import numpy as np
 from pyzx.graph.base import BaseGraph
 import graphix
 from discopy import quantum as quantum_discopy
 from discopy import symmetric
+from sympy import Expr, lambdify, Symbol, Mul
 # from pytket import circuit as tket_circuit
 from optyx.utils.utils import explode_channel
 from optyx.core import (
@@ -422,22 +423,28 @@ def _to_optyx_from_graphix(cls, underlying_circuit):
 class QubitChannel(Channel):
     """Qubit channel."""
 
-    def _decomp(self):
-        decomposed = zx.decomp(self.kraus)
-        return explode_channel(
-            decomposed,
-            QubitChannel,
-            Diagram
-        )
+    # def decomp(self):
+    #     """Decompose into elementary gates."""
+    #     from optyx.utils.utils import decomp_ar
+    #     from discopy import symmetric
+    #     return symmetric.Functor(
+    #         ob=lambda x: qubit**len(x),
+    #         ar=decomp_ar,
+    #         cod=symmetric.Category(channel.Ty, channel.Diagram),
+    #     )(self)
+
+    # def to_dual_rail(self):
+    #     """Convert to dual-rail encoding."""
+    #     from optyx.utils.utils import ar_zx2path
+    #     from optyx import qmode
+    #     from discopy import symmetric
+
+    #     return symmetric.Functor(
+    #         ob=lambda x: qmode**(2 * len(x)),
+    #         ar=lambda ar : ar_zx2path(ar.decomp()),
+    #         cod=symmetric.Category(channel.Ty, channel.Diagram),
+    #     )(self)
 
-    def to_dual_rail(self):
-        """Convert to dual-rail encoding."""
-        kraus_path = zx.zx2path(self.kraus)
-        return explode_channel(
-            kraus_path,
-            Channel,
-            Diagram
-        )
 
     # pylint: disable=too-many-locals
     # pylint: disable=too-many-return-statements
@@ -605,7 +612,89 @@ def __init__(self, n_legs_in, n_legs_out, phase=0):
             qubit**n_legs_in,
             qubit**n_legs_out,
         )
+        self.data = phase
+        self.phase = phase
+
+    def lambdify(self, *symbols, **kwargs):
+        return lambda *xs: type(self)(
+            len(self.dom),
+            len(self.cod),
+            lambdify(symbols, self.phase, **kwargs)(*xs)
+        )
+
+    def decomp(self):
+        n, m = len(self.dom), len(self.cod)
+        phase = self.phase
+        rot = Id(1) if phase == 0 else Z(1, 1, phase)
+        if n == 0:
+            return X(0, 1) >> H() >> rot >> self._make_spiders(m)
+        if m == 0:
+            return X(1, 0) << H() << rot << self._make_spiders(n).dagger()
+        return self._make_spiders(n).dagger() >> rot >> self._make_spiders(m)
+
+    @staticmethod
+    def _make_spiders(n):
+        """Constructs the Z spider 1 -> n from spiders 1 -> 2.
+
+        >>> assert len(make_spiders(6)) == 5
+        """
+        from optyx import qubits
+
+        spider = qubits.Id(1)
+        for k in range(n - 1):
+            spider = spider >> qubits.Z(1, 2) @ qubits.Id(k)
+        return spider
+
+    def to_dual_rail(self):
+        """Convert to dual-rail encoding."""
+
+        from optyx import (
+            photonic,
+            qmode,
+            classical
+        )
+        from optyx.core import zw
+        create = photonic.Create(1)
+        annil = classical.Select(1)
+        comonoid = Channel("Split", zw.Split(2))
+        monoid = Channel("Merge", zw.Merge(2))
+        BS = photonic.BS
+
+        n, m = len(self.dom), len(self.cod)
+        phase = self.phase
+        if (n, m) == (0, 1):
+            return create >> comonoid
+        if (n, m) == (1, 1):
+            return qmode @ photonic.Phase(phase)
+        if (n, m, phase) == (2, 1, 0):
+            return (
+                qmode @
+                (monoid >> annil) @
+                qmode
+                )
+        if (n, m, phase) == (1, 2, 0):
+            plus = create >> comonoid
+            bot = (
+                (plus >> qmode @ plus @ qmode) @
+                (qmode @ plus @ qmode)
+            )
+            mid = qmode**2 @ BS.dagger() @ BS @ qmode**2
+            fusion = (
+                qmode @ plus.dagger() @
+                qmode >> plus.dagger()
+            )
+            return (
+                bot >> mid >> (qmode**2 @
+                               fusion @ qmode**2)
+                )
+        raise NotImplementedError(f"No translation of {self} in QPath.")
 
+    def dagger(self):
+        return type(self)(
+            len(self.cod),
+            len(self.dom),
+            -self.phase
+        )
 
 # pylint: disable=invalid-name
 class X(Channel):
@@ -623,7 +712,62 @@ def __init__(self, n_legs_in, n_legs_out, phase=0):
             qubit**n_legs_in,
             qubit**n_legs_out,
         )
+        self.data = phase
+        self.phase = phase
+
+    def lambdify(self, *symbols, **kwargs):
+        return lambda *xs: type(self)(
+            len(self.dom),
+            len(self.cod),
+            lambdify(symbols, self.phase, **kwargs)(*xs),
+        )
 
+    def decomp(self):
+        n, m = len(self.dom), len(self.cod)
+        phase = self.phase
+        if (n, m) in ((1, 0), (0, 1)):
+            return self
+        box = (
+            Id(0).tensor(*[H()] * n) >> Z(n, m, phase) >> Id(0).tensor(*[H()] * m)
+        )
+        return box.decomp()
+
+    def to_dual_rail(self):
+        """Convert to dual-rail encoding."""
+        from optyx import (
+            photonic,
+            classical
+        )
+        from optyx.core import zw
+
+        root2 = photonic.Scalar(2**0.5)
+        unit = photonic.Create(0)
+        counit = classical.Select(0)
+        create = photonic.Create(1)
+        annil = classical.Select(1)
+        BS = photonic.BS
+        n, m = len(self.dom), len(self.cod)
+        phase = 1 + self.phase if self.phase < 0 else self.phase
+        if (n, m, phase) == (0, 1, 0):
+            return create @ unit @ root2
+        if (n, m, phase) == (0, 1, 0.5):
+            return unit @ create @ root2
+        if (n, m, phase) == (1, 0, 0):
+            return annil @ counit @ root2
+        if (n, m, phase) == (1, 0, 0.5):
+            return counit @ annil @ root2
+        if (n, m, phase) == (1, 1, 0.25):
+            return BS.dagger()
+        if (n, m, phase) == (1, 1, -0.25):
+            return BS
+        raise NotImplementedError(f"No translation of {self} in QPath.")
+
+    def dagger(self):
+        return type(self)(
+            len(self.cod),
+            len(self.dom),
+            -self.phase
+        )
 
 # pylint: disable=invalid-name
 class H(Channel):
@@ -640,6 +784,16 @@ def __init__(self):
             qubit,
         )
 
+    def decomp(self):
+        return H()
+
+    def to_dual_rail(self):
+        """Convert to dual-rail encoding."""
+        from optyx import photonic
+        return photonic.HadamardBS()
+
+    def dagger(self):
+        return self
 
 class Scalar(Channel):
     """
@@ -653,7 +807,18 @@ def __init__(self, value: float):
             qubit**0,
             qubit**0,
         )
+        self.data = value
 
+    def decomp(self):
+        return Scalar(self.data)
+
+    def to_dual_rail(self):
+        """Convert to dual-rail encoding."""
+        from optyx import photonic
+        return photonic.Scalar(self.data)
+
+    def dagger(self):
+        return type(self)(np.conj(self.data))
 
 class BitFlipError(Channel):
     """

From 13b25c2a90ba0da64e7480e9a69e150087f8a537 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Fri, 5 Sep 2025 22:13:05 +0100
Subject: [PATCH 38/59] Fixing bugs with sums

---
 docs/notebooks/bosonic-vqe-2.ipynb        | 379 +++++++++++++--------
 docs/notebooks/optyx-vqe-experiment.ipynb | 384 ++++++++++++++++------
 optyx/core/backends.py                    |  12 +-
 optyx/core/channel.py                     |  36 +-
 optyx/core/diagram.py                     |  40 +--
 optyx/core/zx.py                          | 128 --------
 optyx/qubits.py                           |   2 +-
 test/grad.py                              |   2 +-
 test/qpath.py                             |  20 +-
 test/test_channel.py                      |   7 +-
 test/test_qubit.py                        |  10 +-
 11 files changed, 593 insertions(+), 427 deletions(-)

diff --git a/docs/notebooks/bosonic-vqe-2.ipynb b/docs/notebooks/bosonic-vqe-2.ipynb
index 2d28c183..3ff6d24e 100644
--- a/docs/notebooks/bosonic-vqe-2.ipynb
+++ b/docs/notebooks/bosonic-vqe-2.ipynb
@@ -17,7 +17,7 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-05T11:56:11.751703</dc:date>\n",
+       "    <dc:date>2025-09-05T20:09:47.097250</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -46,62 +46,62 @@
        "L 223.2 7.2 \n",
        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
        "    <path d=\"M 43.2 61.2 \n",
        "Q 43.2 97.2 43.2 97.2 \n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 115.2 61.2 \n",
        "Q 115.2 97.2 115.2 97.2 \n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
        "    <path d=\"M 187.2 61.2 \n",
        "Q 187.2 169.2 187.2 169.2 \n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_6\">\n",
        "    <path d=\"M 43.2 133.2 \n",
        "Q 43.2 241.2 43.2 241.2 \n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_7\">\n",
        "    <path d=\"M 115.2 133.2 \n",
        "Q 115.2 169.2 115.2 169.2 \n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_8\">\n",
        "    <path d=\"M 115.2 205.2 \n",
        "Q 115.2 241.2 115.2 241.2 \n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_9\">\n",
        "    <path d=\"M 187.2 205.2 \n",
        "Q 187.2 313.2 187.2 313.2 \n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_10\">\n",
        "    <path d=\"M 43.2 277.2 \n",
        "Q 43.2 439.2 43.2 439.2 \n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_11\">\n",
        "    <path d=\"M 115.2 277.2 \n",
        "Q 115.2 313.2 115.2 313.2 \n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_12\">\n",
        "    <path d=\"M 115.2 349.2 \n",
        "Q 115.2 439.2 115.2 439.2 \n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_13\">\n",
        "    <path d=\"M 187.2 349.2 \n",
        "Q 187.2 385.2 187.2 385.2 \n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_14\">\n",
        "    <path d=\"M 25.2 61.2 \n",
@@ -109,7 +109,7 @@
        "L 205.2 25.2 \n",
        "L 205.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_15\">\n",
        "    <path d=\"M 25.2 133.2 \n",
@@ -117,7 +117,7 @@
        "L 133.2 97.2 \n",
        "L 133.2 133.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_16\">\n",
        "    <path d=\"M 97.2 205.2 \n",
@@ -125,7 +125,7 @@
        "L 205.2 169.2 \n",
        "L 205.2 205.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   </g>\n",
        "   <g id=\"patch_17\">\n",
        "    <path d=\"M 25.2 277.2 \n",
@@ -133,7 +133,7 @@
        "L 133.2 241.2 \n",
        "L 133.2 277.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_18\">\n",
        "    <path d=\"M 97.2 349.2 \n",
@@ -141,7 +141,7 @@
        "L 205.2 313.2 \n",
        "L 205.2 349.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_19\">\n",
        "    <path d=\"M 169.2 421.2 \n",
@@ -149,7 +149,7 @@
        "L 205.2 385.2 \n",
        "L 205.2 421.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p661c0a7bc2)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#pd1650474ac)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
        "    <!-- qmode -->\n",
@@ -878,7 +878,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p661c0a7bc2\">\n",
+       "  <clipPath id=\"pd1650474ac\">\n",
        "   <rect x=\"7.2\" y=\"7.2\" width=\"216\" height=\"432\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -916,7 +916,7 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-05T11:56:11.815619</dc:date>\n",
+       "    <dc:date>2025-09-05T20:09:47.853222</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -945,87 +945,87 @@
        "L 799.2 7.2 \n",
        "L 7.2 7.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
        "    <path d=\"M 43.2 7.2 \n",
        "Q 43.2 25.2 43.2 25.2 \n",
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        "   </g>\n",
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-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
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-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   </g>\n",
        "   <g id=\"patch_6\">\n",
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-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_9\">\n",
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-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_12\">\n",
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-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_13\">\n",
        "    <path d=\"M 475.2 61.2 \n",
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-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_14\">\n",
        "    <path d=\"M 547.2 61.2 \n",
        "Q 547.2 79.2 547.2 79.2 \n",
-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_15\">\n",
        "    <path d=\"M 691.2 7.2 \n",
        "Q 691.2 25.2 691.2 25.2 \n",
-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_16\">\n",
        "    <path d=\"M 763.2 7.2 \n",
        "Q 763.2 25.2 763.2 25.2 \n",
-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_17\">\n",
        "    <path d=\"M 691.2 61.2 \n",
        "Q 691.2 79.2 691.2 79.2 \n",
-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_18\">\n",
        "    <path d=\"M 763.2 61.2 \n",
        "Q 763.2 79.2 763.2 79.2 \n",
-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_19\">\n",
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@@ -1033,7 +1033,7 @@
        "L 133.2 25.2 \n",
        "L 133.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_20\">\n",
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@@ -1041,7 +1041,7 @@
        "L 349.2 25.2 \n",
        "L 349.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_21\">\n",
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@@ -1049,7 +1049,7 @@
        "L 565.2 25.2 \n",
        "L 565.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_22\">\n",
        "    <path d=\"M 673.2 61.2 \n",
@@ -1057,11 +1057,11 @@
        "L 781.2 25.2 \n",
        "L 781.2 61.2 \n",
        "z\n",
-       "\" clip-path=\"url(#p05f3bff2b7)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p3b4158f82d)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_1\">\n",
        "    <defs>\n",
-       "     <path id=\"C0_0_f50920dcc6\" d=\"M 0 4.759202 \n",
+       "     <path id=\"C0_0_517940923d\" d=\"M 0 4.759202 \n",
        "C 1.262155 4.759202 2.472785 4.257742 3.365264 3.365264 \n",
        "C 4.257742 2.472785 4.759202 1.262155 4.759202 -0 \n",
        "C 4.759202 -1.262155 4.257742 -2.472785 3.365264 -3.365264 \n",
@@ -1073,14 +1073,14 @@
        "z\n",
        "\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#p05f3bff2b7)\">\n",
-       "     <use xlink:href=\"#C0_0_f50920dcc6\" x=\"403.2\" y=\"43.2\" style=\"fill: #ffffff; stroke: #ffffff\"/>\n",
+       "    <g clip-path=\"url(#p3b4158f82d)\">\n",
+       "     <use xlink:href=\"#C0_0_517940923d\" x=\"187.2\" y=\"43.2\" style=\"fill: #ffffff; stroke: #ffffff\"/>\n",
        "    </g>\n",
-       "    <g clip-path=\"url(#p05f3bff2b7)\">\n",
-       "     <use xlink:href=\"#C0_0_f50920dcc6\" x=\"187.2\" y=\"43.2\" style=\"fill: #ffffff; stroke: #ffffff\"/>\n",
+       "    <g clip-path=\"url(#p3b4158f82d)\">\n",
+       "     <use xlink:href=\"#C0_0_517940923d\" x=\"403.2\" y=\"43.2\" style=\"fill: #ffffff; stroke: #ffffff\"/>\n",
        "    </g>\n",
-       "    <g clip-path=\"url(#p05f3bff2b7)\">\n",
-       "     <use xlink:href=\"#C0_0_f50920dcc6\" x=\"619.2\" y=\"43.2\" style=\"fill: #ffffff; stroke: #ffffff\"/>\n",
+       "    <g clip-path=\"url(#p3b4158f82d)\">\n",
+       "     <use xlink:href=\"#C0_0_517940923d\" x=\"619.2\" y=\"43.2\" style=\"fill: #ffffff; stroke: #ffffff\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
@@ -1674,9 +1674,9 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_21\">\n",
-       "    <g clip-path=\"url(#p05f3bff2b7)\">\n",
+       "    <g clip-path=\"url(#p3b4158f82d)\">\n",
        "     <!-- + -->\n",
-       "     <g transform=\"translate(398.172188 46.51125) scale(0.12 -0.12)\">\n",
+       "     <g transform=\"translate(182.172187 46.51125) scale(0.12 -0.12)\">\n",
        "      <defs>\n",
        "       <path id=\"DejaVuSans-2b\" d=\"M 2944 4013 \n",
        "L 2944 2272 \n",
@@ -1699,15 +1699,15 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_22\">\n",
-       "    <g clip-path=\"url(#p05f3bff2b7)\">\n",
+       "    <g clip-path=\"url(#p3b4158f82d)\">\n",
        "     <!-- + -->\n",
-       "     <g transform=\"translate(182.172187 46.51125) scale(0.12 -0.12)\">\n",
+       "     <g transform=\"translate(398.172188 46.51125) scale(0.12 -0.12)\">\n",
        "      <use xlink:href=\"#DejaVuSans-2b\"/>\n",
        "     </g>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_23\">\n",
-       "    <g clip-path=\"url(#p05f3bff2b7)\">\n",
+       "    <g clip-path=\"url(#p3b4158f82d)\">\n",
        "     <!-- + -->\n",
        "     <g transform=\"translate(614.172188 46.51125) scale(0.12 -0.12)\">\n",
        "      <use xlink:href=\"#DejaVuSans-2b\"/>\n",
@@ -1717,7 +1717,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p05f3bff2b7\">\n",
+       "  <clipPath id=\"p3b4158f82d\">\n",
        "   <rect x=\"7.2\" y=\"7.2\" width=\"792\" height=\"72\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -1770,29 +1770,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
-   "id": "68041095",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Create((1, 1, 1)) >> MZI(a_0_0, b_0_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_3_0, b_3_0) >> qmode @ qmode @ Select((1,)) >> Bosonic operator >> qmode @ qmode @ Select((1,)).dagger() >> qmode @ MZI(a_3_0, b_3_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_0_0, b_0_0) @ qmode >> Create((1, 1, 1)).dagger()\n",
-      "Create((1, 1, 1)) >> MZI(a_0_0, b_0_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_3_0, b_3_0) >> qmode @ qmode @ Select((1,)) >> Bosonic operator >> qmode @ qmode @ Select((1,)).dagger() >> qmode @ MZI(a_3_0, b_3_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_0_0, b_0_0) @ qmode >> Create((1, 1, 1)).dagger()\n",
-      "Create((1, 1, 1)) >> MZI(a_0_0, b_0_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_3_0, b_3_0) >> qmode @ qmode @ Select((1,)) >> Bosonic operator >> qmode @ qmode @ Select((1,)).dagger() >> qmode @ MZI(a_3_0, b_3_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_0_0, b_0_0) @ qmode >> Create((1, 1, 1)).dagger()\n",
-      "Create((1, 1, 1)) >> MZI(a_0_0, b_0_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_3_0, b_3_0) >> qmode @ qmode @ Select((1,)) >> Bosonic operator >> qmode @ qmode @ Select((1,)).dagger() >> qmode @ MZI(a_3_0, b_3_0) >> MZI(a_2_0, b_2_0) @ qmode >> qmode @ MZI(a_1_0, b_1_0) >> MZI(a_0_0, b_0_0) @ qmode >> Create((1, 1, 1)).dagger()\n"
-     ]
-    }
-   ],
-   "source": [
-    "for i in expectation.terms:\n",
-    "    print(i)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": null,
    "id": "f4e5462d-464d-4b09-8574-6867522b61ea",
    "metadata": {},
    "outputs": [],
@@ -1807,32 +1785,18 @@
     "\n",
     "free_syms = list(expectation.free_symbols)\n",
     "\n",
-    "#f_exp = lambda xs: to_float(expectation.lambdify(*free_syms)(*xs).eval().array[0, 0])\n",
-    "\n",
-    "def f_exp(xs):\n",
-    "    val = 0\n",
-    "    for term in expectation.lambdify(*free_syms)(*xs).terms:\n",
-    "        val += to_float(term.eval().tensor.array)\n",
-    "    return val\n",
-    "\n",
-    "# def d_f_exp(xs):\n",
-    "#     return [\n",
-    "#         expectation.grad(s).lambdify(*free_syms)(*xs).eval().array[0, 0]\n",
-    "#         for s in free_syms\n",
-    "#     ]\n",
+    "f_exp = lambda xs: to_float(expectation.lambdify(*free_syms)(*xs).eval().tensor.array)\n",
     "\n",
     "def d_f_exp(xs):\n",
-    "    grads = [expectation.grad(s) for s in free_syms]\n",
-    "    vals = [0] * len(grads)\n",
-    "    for i, g in enumerate(grads):\n",
-    "        for term in g.lambdify(*free_syms)(*xs).terms:\n",
-    "            vals[i] += to_float(term.eval().tensor.array)\n",
-    "    return vals"
+    "    return [\n",
+    "        expectation.grad(s).lambdify(*free_syms)(*xs).eval().tensor.array\n",
+    "        for s in free_syms\n",
+    "    ]"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 7,
    "id": "24355282-4c9c-40b3-b643-461981f9475f",
    "metadata": {},
    "outputs": [],
@@ -1863,7 +1827,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 8,
    "id": "e96227b0-db8e-4871-8c12-b1d034a4bc86",
    "metadata": {},
    "outputs": [
@@ -1871,14 +1835,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "  0%|          | 0/10 [00:00<?, ?it/s]"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "100%|██████████| 10/10 [02:35<00:00, 15.52s/it]\n"
+      "100%|██████████| 10/10 [04:56<00:00, 29.62s/it]\n"
      ]
     }
    ],
@@ -1888,10 +1845,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 9,
    "id": "088c8fa8-76b3-45bd-a5dd-b337be0d33b1",
    "metadata": {},
    "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part\n",
+      "  return math.isfinite(val)\n",
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part\n",
+      "  return np.asarray(x, float)\n"
+     ]
+    },
     {
      "data": {
       "image/svg+xml": [
@@ -1903,7 +1870,7 @@
        "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-05T11:59:44.101867</dc:date>\n",
+       "    <dc:date>2025-09-05T20:15:39.618171</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -1938,12 +1905,12 @@
        "    <g id=\"xtick_1\">\n",
        "     <g id=\"line2d_1\">\n",
        "      <defs>\n",
-       "       <path id=\"ma382debacf\" d=\"M 0 0 \n",
+       "       <path id=\"mb60952e2f5\" d=\"M 0 0 \n",
        "L 0 3.5 \n",
        "\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </defs>\n",
        "      <g>\n",
-       "       <use xlink:href=\"#ma382debacf\" x=\"54.71554\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#mb60952e2f5\" x=\"54.71554\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_1\">\n",
@@ -1979,7 +1946,7 @@
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        "      <g>\n",
-       "       <use xlink:href=\"#ma382debacf\" x=\"119.646449\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#mb60952e2f5\" x=\"119.646449\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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@@ -2018,7 +1985,7 @@
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        "      <g>\n",
-       "       <use xlink:href=\"#ma382debacf\" x=\"184.577358\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#mb60952e2f5\" x=\"184.577358\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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@@ -2052,7 +2019,7 @@
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        "      <g>\n",
-       "       <use xlink:href=\"#ma382debacf\" x=\"249.508267\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#mb60952e2f5\" x=\"249.508267\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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@@ -2097,7 +2064,7 @@
        "    <g id=\"xtick_5\">\n",
        "     <g id=\"line2d_5\">\n",
        "      <g>\n",
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@@ -2151,7 +2118,7 @@
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        "      <g>\n",
-       "       <use xlink:href=\"#ma382debacf\" x=\"379.370085\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#mb60952e2f5\" x=\"379.370085\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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@@ -2183,12 +2150,12 @@
        "    <g id=\"ytick_1\">\n",
        "     <g id=\"line2d_7\">\n",
        "      <defs>\n",
-       "       <path id=\"m8a093308ac\" d=\"M 0 0 \n",
+       "       <path id=\"m020a1198a5\" d=\"M 0 0 \n",
        "L -3.5 0 \n",
        "\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </defs>\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m8a093308ac\" x=\"38.482813\" y=\"236.616595\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#m020a1198a5\" x=\"38.482813\" y=\"236.616595\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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@@ -2220,7 +2187,7 @@
        "    <g id=\"ytick_2\">\n",
        "     <g id=\"line2d_8\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m8a093308ac\" x=\"38.482813\" y=\"184.874401\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#m020a1198a5\" x=\"38.482813\" y=\"184.874401\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
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@@ -2236,7 +2203,7 @@
        "    <g id=\"ytick_3\">\n",
        "     <g id=\"line2d_9\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m8a093308ac\" x=\"38.482813\" y=\"133.132207\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#m020a1198a5\" x=\"38.482813\" y=\"133.132207\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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@@ -2252,7 +2219,7 @@
        "    <g id=\"ytick_4\">\n",
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-       "       <use xlink:href=\"#m8a093308ac\" x=\"38.482813\" y=\"81.390013\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#m020a1198a5\" x=\"38.482813\" y=\"81.390013\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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@@ -2267,7 +2234,7 @@
        "    <g id=\"ytick_5\">\n",
        "     <g id=\"line2d_11\">\n",
        "      <g>\n",
-       "       <use xlink:href=\"#m8a093308ac\" x=\"38.482813\" y=\"29.647819\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
+       "       <use xlink:href=\"#m020a1198a5\" x=\"38.482813\" y=\"29.647819\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
        "      </g>\n",
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        "     <g id=\"text_11\">\n",
@@ -2282,7 +2249,7 @@
        "   </g>\n",
        "   <g id=\"line2d_12\">\n",
        "    <defs>\n",
-       "     <path id=\"mcd2e95b7bb\" d=\"M 0 1.5 \n",
+       "     <path id=\"ma4aef5440d\" d=\"M 0 1.5 \n",
        "C 0.397805 1.5 0.77937 1.341951 1.06066 1.06066 \n",
        "C 1.341951 0.77937 1.5 0.397805 1.5 0 \n",
        "C 1.5 -0.397805 1.341951 -0.77937 1.06066 -1.06066 \n",
@@ -2294,18 +2261,18 @@
        "z\n",
        "\" style=\"stroke: #0000ff\"/>\n",
        "    </defs>\n",
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+       "     <use xlink:href=\"#ma4aef5440d\" x=\"184.577358\" y=\"224.024215\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#ma4aef5440d\" x=\"217.042813\" y=\"240.624501\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#ma4aef5440d\" x=\"249.508267\" y=\"251.094574\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#ma4aef5440d\" x=\"281.973722\" y=\"256.858981\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#ma4aef5440d\" x=\"314.439176\" y=\"259.810304\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#ma4aef5440d\" x=\"346.904631\" y=\"261.06328\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
+       "     <use xlink:href=\"#ma4aef5440d\" x=\"379.370085\" y=\"261.216\" style=\"fill: #0000ff; stroke: #0000ff\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
@@ -2331,7 +2298,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"paa5c911910\">\n",
+       "  <clipPath id=\"pdb3284be10\">\n",
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        "  </clipPath>\n",
        " </defs>\n",
@@ -2354,17 +2321,151 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "id": "346a4294",
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "from optyx.photonic import BBS, Create, Scalar"
+   ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
+   "id": "eea8a769",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#diagram = BBS(0.3) + BBS(0.9) + BBS(0.5)\n",
+    "#diagram.draw()\n",
+    "\n",
+    "diagram = Create(1) @ Scalar(0.34) + Create(2) @ Scalar(0.56) + Create(3) @ Scalar(0.12)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
    "id": "5e2fd068",
    "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0.  +0.j, 0.34+0.j, 0.56+0.j, 0.12+0.j])"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "diagram.eval().tensor.array"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "fa135207",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[0.  +0.j 0.34+0.j 0.  +0.j 0.  +0.j]\n",
+      "-----\n",
+      "[0.  +0.j 0.34+0.j 0.  +0.j 0.  +0.j]\n",
+      "======\n",
+      "[0.  +0.j 0.  +0.j 0.56+0.j 0.  +0.j]\n",
+      "-----\n",
+      "[0.  +0.j 0.  +0.j 0.56+0.j 0.  +0.j]\n",
+      "======\n",
+      "[0.  +0.j 0.  +0.j 0.  +0.j 0.12+0.j]\n",
+      "-----\n",
+      "[0.  +0.j 0.  +0.j 0.  +0.j 0.12+0.j]\n",
+      "======\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "for term in diagram.get_kraus().to_tensor():\n",
+    "    print((term.to_quimb()^...).data)\n",
+    "    print(\"-----\")\n",
+    "    print(term.eval().array)\n",
+    "    print(\"======\")\n",
+    "    assert np.allclose((term.to_quimb()^...).data, term.eval().array)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "f20a782f",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/discopy/matrix.py:161: ComplexWarning: Casting complex values to real discards the imaginary part\n",
+      "  self.array = np.array(array, dtype=self.dtype).reshape((dom, cod))\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "array([0, 0, 0, 0])"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "diagram.get_kraus().to_tensor().eval().array"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "abf30abe",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor.Sum(terms=(tensor.Diagram(inside=(rigid.Layer(Dim(1), tensor.Box[complex128]('Create(1)', Dim(2), Dim(1), data=array([0.+0.j, 1.+0.j])).dagger(), Dim(1)), rigid.Layer(Dim(2), tensor.Box[complex128]('scalar', Dim(1), Dim(1), data=[(0.34+0j)]), Dim(1)), rigid.Layer(Dim(1), tensor.Box[int64]('ZBox(1, 1, mode)', Dim(2), Dim(2), data=array([[1, 0],\n",
+       "       [0, 1]])), Dim(1)), rigid.Layer(Dim(1), tensor.Spider(1, 1, Dim(2)), Dim(1)), rigid.Layer(Dim(1), optyx.core.diagram.EmbeddingTensor('Embedding', Dim(2), Dim(4), data=array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+       "       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])), Dim(1))), dom=Dim(1), cod=Dim(4)), tensor.Diagram(inside=(rigid.Layer(Dim(1), tensor.Box[complex128]('Create((2,))', Dim(3), Dim(1), data=array([0.+0.j, 0.+0.j, 1.+0.j])).dagger(), Dim(1)), rigid.Layer(Dim(3), tensor.Box[complex128]('scalar', Dim(1), Dim(1), data=[(0.56+0j)]), Dim(1)), rigid.Layer(Dim(1), tensor.Box[int64]('ZBox(1, 1, mode)', Dim(3), Dim(3), data=array([[1, 0, 0],\n",
+       "       [0, 1, 0],\n",
+       "       [0, 0, 1]])), Dim(1)), rigid.Layer(Dim(1), tensor.Spider(1, 1, Dim(3)), Dim(1)), rigid.Layer(Dim(1), optyx.core.diagram.EmbeddingTensor('Embedding', Dim(3), Dim(4), data=array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+       "       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
+       "       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j]])), Dim(1))), dom=Dim(1), cod=Dim(4)), tensor.Diagram(inside=(rigid.Layer(Dim(1), tensor.Box[complex128]('Create((3,))', Dim(4), Dim(1), data=array([0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j])).dagger(), Dim(1)), rigid.Layer(Dim(4), tensor.Box[complex128]('scalar', Dim(1), Dim(1), data=[(0.12+0j)]), Dim(1)), rigid.Layer(Dim(1), tensor.Box[int64]('ZBox(1, 1, mode)', Dim(4), Dim(4), data=array([[1, 0, 0, 0],\n",
+       "       [0, 1, 0, 0],\n",
+       "       [0, 0, 1, 0],\n",
+       "       [0, 0, 0, 1]])), Dim(1)), rigid.Layer(Dim(1), tensor.Spider(1, 1, Dim(4)), Dim(1)), rigid.Layer(Dim(1), optyx.core.diagram.EmbeddingTensor('Embedding', Dim(4), Dim(4), data=array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+       "       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
+       "       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
+       "       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])), Dim(1))), dom=Dim(1), cod=Dim(4))))"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "diagram.get_kraus().to_tensor()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "554c80f7",
+   "metadata": {},
    "outputs": [],
    "source": []
   }
diff --git a/docs/notebooks/optyx-vqe-experiment.ipynb b/docs/notebooks/optyx-vqe-experiment.ipynb
index 6d1f9176..5e318c0d 100644
--- a/docs/notebooks/optyx-vqe-experiment.ipynb
+++ b/docs/notebooks/optyx-vqe-experiment.ipynb
@@ -97,74 +97,9 @@
     "from optyx.core.backends import DiscopyBackend"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "id": "28b96946",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<Figure size 100x100 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "from optyx.qubits import Z\n",
-    "\n",
-    "Z(1, 1).dagger().draw()"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "26ece567",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 450x2400 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "Circuit(exp).decomp().draw()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "id": "768b5f7e",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<Figure size 1700x5600 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "Circuit(exp).decomp().to_dual_rail().draw()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
    "id": "0406fa28",
    "metadata": {},
    "outputs": [],
@@ -193,19 +128,10 @@
     "orig_f_exp = lambda xs: to_float(exp.lambdify(*free_syms)(*xs).eval().array.item())\n",
     "\n",
     "def d_f_exp(xs):\n",
-    "    #path_exp.grad(list(free_syms)[0]).draw()#.lambdify(*free_syms)(*xs).draw()\n",
     "    return [\n",
     "        path_exp.grad(s).lambdify(*free_syms)(*xs).eval().tensor.array\n",
     "        for s in free_syms\n",
-    "    ]\n",
-    "\n",
-    "# def d_f_exp(xs):\n",
-    "#     grads = [path_exp.grad(s) for s in free_syms]\n",
-    "#     vals = [0] * len(grads)\n",
-    "#     for i, g in enumerate(grads):\n",
-    "#         for term in g.lambdify(*free_syms)(*xs).terms:\n",
-    "#             vals[i] += to_float(term.eval().tensor.array)\n",
-    "#     return vals"
+    "    ]"
    ]
   },
   {
@@ -218,7 +144,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": null,
    "id": "41ea980c-40c4-4bd2-8731-fc84fb110f41",
    "metadata": {},
    "outputs": [],
@@ -236,14 +162,12 @@
     "        orig_fx = orig_f_exp(x)\n",
     "        fx = f_exp(x)\n",
     "        dfx = d_f_exp(x)\n",
-    "        print(orig_fx)\n",
     "        # verifies that the conversion is correct\n",
     "        assert abs(orig_fx - fx) < 1e-10\n",
     "\n",
     "        xs.append(x[::])\n",
     "        fxs.append(fx)\n",
     "        dfxs.append(dfx)\n",
-    "        # print(x, fx, dfx)\n",
     "        for i, dfxx in enumerate(dfx):\n",
     "            x[i] = to_float(x[i] - 0.01 * dfxx)\n",
     "    xs.append(x[::])\n",
@@ -253,7 +177,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 10,
    "id": "cd5e3e93-5d75-415d-bbcc-14022c9ecf97",
    "metadata": {
     "scrolled": true
@@ -263,43 +187,287 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "  0%|          | 0/20 [00:00<?, ?it/s]"
+      "  5%|▌         | 1/20 [00:02<00:41,  2.20s/it]"
      ]
     },
     {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<Figure size 3600x5800 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.8385254915624215\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 10%|█         | 2/20 [00:04<00:38,  2.16s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.7711039313289111\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 15%|█▌        | 3/20 [00:06<00:36,  2.15s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.6787280203868928\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 20%|██        | 4/20 [00:08<00:33,  2.09s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.561851722253541\n"
+     ]
     },
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "  0%|          | 0/20 [00:02<?, ?it/s]\n"
+      " 25%|██▌       | 5/20 [00:10<00:31,  2.12s/it]"
      ]
     },
     {
-     "ename": "ValueError",
-     "evalue": "too many values to unpack (expected 3)",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
-      "\u001b[31mValueError\u001b[39m                                Traceback (most recent call last)",
-      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[13]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[43moptimize\u001b[49m\u001b[43m(\u001b[49m\u001b[43m[\u001b[49m\u001b[32;43m0.1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[32;43m0.2\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n",
-      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[12]\u001b[39m\u001b[32m, line 13\u001b[39m, in \u001b[36moptimize\u001b[39m\u001b[34m(x0)\u001b[39m\n\u001b[32m     11\u001b[39m orig_fx = orig_f_exp(x)\n\u001b[32m     12\u001b[39m fx = f_exp(x)\n\u001b[32m---> \u001b[39m\u001b[32m13\u001b[39m dfx = \u001b[43md_f_exp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m     14\u001b[39m \u001b[38;5;28mprint\u001b[39m(orig_fx)\n\u001b[32m     15\u001b[39m \u001b[38;5;66;03m# verifies that the conversion is correct\u001b[39;00m\n",
-      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[11]\u001b[39m\u001b[32m, line 17\u001b[39m, in \u001b[36md_f_exp\u001b[39m\u001b[34m(xs)\u001b[39m\n\u001b[32m     14\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34md_f_exp\u001b[39m(xs):\n\u001b[32m     15\u001b[39m     path_exp.grad(\u001b[38;5;28mlist\u001b[39m(free_syms)[\u001b[32m0\u001b[39m]).draw()\u001b[38;5;66;03m#.lambdify(*free_syms)(*xs).draw()\u001b[39;00m\n\u001b[32m     16\u001b[39m     \u001b[38;5;28;01mreturn\u001b[39;00m [\n\u001b[32m---> \u001b[39m\u001b[32m17\u001b[39m         \u001b[43mpath_exp\u001b[49m\u001b[43m.\u001b[49m\u001b[43mgrad\u001b[49m\u001b[43m(\u001b[49m\u001b[43ms\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mlambdify\u001b[49m\u001b[43m(\u001b[49m\u001b[43m*\u001b[49m\u001b[43mfree_syms\u001b[49m\u001b[43m)\u001b[49m\u001b[43m(\u001b[49m\u001b[43m*\u001b[49m\u001b[43mxs\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43meval\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m.tensor.array\n\u001b[32m     18\u001b[39m         \u001b[38;5;28;01mfor\u001b[39;00m s \u001b[38;5;129;01min\u001b[39;00m free_syms\n\u001b[32m     19\u001b[39m     ]\n",
-      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/optyx/optyx/core/channel.py:475\u001b[39m, in \u001b[36mDiagram.eval\u001b[39m\u001b[34m(self, backend, **kwargs)\u001b[39m\n\u001b[32m    472\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m backend \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[32m    473\u001b[39m     backend = QuimbBackend()\n\u001b[32m--> \u001b[39m\u001b[32m475\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mbackend\u001b[49m\u001b[43m.\u001b[49m\u001b[43meval\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/optyx/optyx/core/backends.py:397\u001b[39m, in \u001b[36mQuimbBackend.eval\u001b[39m\u001b[34m(self, diagram, **extra)\u001b[39m\n\u001b[32m    384\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34meval\u001b[39m(\n\u001b[32m    385\u001b[39m         \u001b[38;5;28mself\u001b[39m,\n\u001b[32m    386\u001b[39m         diagram: Diagram,\n\u001b[32m    387\u001b[39m         **extra: Any) -> EvalResult:\n\u001b[32m    388\u001b[39m \u001b[38;5;250m    \u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    389\u001b[39m \u001b[33;03m    Evaluate the diagram using Quimb.\u001b[39;00m\n\u001b[32m    390\u001b[39m \n\u001b[32m   (...)\u001b[39m\u001b[32m    395\u001b[39m \u001b[33;03m        The result of the evaluation.\u001b[39;00m\n\u001b[32m    396\u001b[39m \u001b[33;03m    \"\"\"\u001b[39;00m\n\u001b[32m--> \u001b[39m\u001b[32m397\u001b[39m     quimb_tn = \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_get_quimb_tensor\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdiagram\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m    398\u001b[39m     tensor_diagram = \u001b[38;5;28mself\u001b[39m._get_discopy_tensor(diagram)\n\u001b[32m    400\u001b[39m     \u001b[38;5;28;01mfor\u001b[39;00m t \u001b[38;5;129;01min\u001b[39;00m quimb_tn:\n",
-      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/optyx/optyx/core/backends.py:320\u001b[39m, in \u001b[36mAbstractBackend._get_quimb_tensor\u001b[39m\u001b[34m(self, diagram)\u001b[39m\n\u001b[32m    313\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34m_get_quimb_tensor\u001b[39m(\n\u001b[32m    314\u001b[39m     \u001b[38;5;28mself\u001b[39m,\n\u001b[32m    315\u001b[39m     diagram: Diagram\n\u001b[32m    316\u001b[39m ) -> TensorNetwork:\n\u001b[32m    317\u001b[39m \u001b[38;5;250m    \u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    318\u001b[39m \u001b[33;03m    Get the Quimb tensor representation of the diagram.\u001b[39;00m\n\u001b[32m    319\u001b[39m \u001b[33;03m    \"\"\"\u001b[39;00m\n\u001b[32m--> \u001b[39m\u001b[32m320\u001b[39m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_get_discopy_tensor\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdiagram\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mto_quimb\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
-      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/.venv/lib/python3.12/site-packages/discopy/tensor.py:451\u001b[39m, in \u001b[36mDiagram.to_quimb\u001b[39m\u001b[34m(self, dtype)\u001b[39m\n\u001b[32m    448\u001b[39m tensors = inputs[:]\n\u001b[32m    449\u001b[39m scan = [(t, \u001b[32m1\u001b[39m) \u001b[38;5;28;01mfor\u001b[39;00m t \u001b[38;5;129;01min\u001b[39;00m inputs]\n\u001b[32m--> \u001b[39m\u001b[32m451\u001b[39m \u001b[38;5;28;01mfor\u001b[39;00m i, (box, off) \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(\u001b[38;5;28mzip\u001b[39m(\u001b[38;5;28mself\u001b[39m.boxes, \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43moffsets\u001b[49m)):\n\u001b[32m    452\u001b[39m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(box, Swap):\n\u001b[32m    453\u001b[39m         scan[off], scan[off + \u001b[32m1\u001b[39m] = scan[off + \u001b[32m1\u001b[39m], scan[off]\n",
-      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/.venv/lib/python3.12/site-packages/discopy/monoidal.py:598\u001b[39m, in \u001b[36mDiagram.offsets\u001b[39m\u001b[34m(self)\u001b[39m\n\u001b[32m    595\u001b[39m \u001b[38;5;129m@property\u001b[39m\n\u001b[32m    596\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34moffsets\u001b[39m(\u001b[38;5;28mself\u001b[39m) -> \u001b[38;5;28mlist\u001b[39m[\u001b[38;5;28mint\u001b[39m]:\n\u001b[32m    597\u001b[39m \u001b[38;5;250m    \u001b[39m\u001b[33;03m\"\"\" The offset of a box is the length of the type on its left. \"\"\"\u001b[39;00m\n\u001b[32m--> \u001b[39m\u001b[32m598\u001b[39m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mlist\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mlen\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mleft\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mfor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mleft\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m_\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m_\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m)\u001b[49m\n",
-      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/optyx/.venv/lib/python3.12/site-packages/discopy/monoidal.py:598\u001b[39m, in \u001b[36m<genexpr>\u001b[39m\u001b[34m(.0)\u001b[39m\n\u001b[32m    595\u001b[39m \u001b[38;5;129m@property\u001b[39m\n\u001b[32m    596\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34moffsets\u001b[39m(\u001b[38;5;28mself\u001b[39m) -> \u001b[38;5;28mlist\u001b[39m[\u001b[38;5;28mint\u001b[39m]:\n\u001b[32m    597\u001b[39m \u001b[38;5;250m    \u001b[39m\u001b[33;03m\"\"\" The offset of a box is the length of the type on its left. \"\"\"\u001b[39;00m\n\u001b[32m--> \u001b[39m\u001b[32m598\u001b[39m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mlist\u001b[39m(\u001b[38;5;28mlen\u001b[39m(left) \u001b[38;5;28;01mfor\u001b[39;00m left, _, _ \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m)\n",
-      "\u001b[31mValueError\u001b[39m: too many values to unpack (expected 3)"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.4296238247323758\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 30%|███       | 6/20 [00:12<00:29,  2.13s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.29959341800206996\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 35%|███▌      | 7/20 [00:14<00:27,  2.13s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.18996344005095658\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 40%|████      | 8/20 [00:16<00:25,  2.09s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.10985803661254136\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 45%|████▌     | 9/20 [00:19<00:23,  2.11s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.057103882372305376\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 50%|█████     | 10/20 [00:21<00:21,  2.11s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.023521573022446115\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 55%|█████▌    | 11/20 [00:23<00:18,  2.08s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.000415985082452835\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 60%|██████    | 12/20 [00:25<00:16,  2.10s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "-0.01932481270375224\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 65%|██████▌   | 13/20 [00:27<00:14,  2.11s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "-0.04148099296641865\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 70%|███████   | 14/20 [00:29<00:12,  2.08s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "-0.0714343170674597\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 75%|███████▌  | 15/20 [00:31<00:10,  2.10s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "-0.11488446907551937\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 80%|████████  | 16/20 [00:33<00:08,  2.11s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "-0.17779636062909193\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 85%|████████▌ | 17/20 [00:35<00:06,  2.11s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "-0.2649466539403759\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 90%|█████████ | 18/20 [00:37<00:04,  2.09s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "-0.3766785210831544\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 95%|█████████▌| 19/20 [00:40<00:02,  2.11s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "-0.5051429153418859\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 20/20 [00:42<00:00,  2.11s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "-0.6340993442622342\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
      ]
     }
    ],
@@ -309,7 +477,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 11,
    "id": "3a0c4436-86d9-4a16-9bc2-7eba1cc440f7",
    "metadata": {},
    "outputs": [
@@ -319,13 +487,13 @@
        "<Axes: >"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
diff --git a/optyx/core/backends.py b/optyx/core/backends.py
index 9a792f41..5b8b2441 100644
--- a/optyx/core/backends.py
+++ b/optyx/core/backends.py
@@ -393,18 +393,20 @@ def eval(
             The result of the evaluation.
         """
 
+        tensor_diagram = self._get_discopy_tensor(diagram)
+
         if hasattr(diagram, 'terms'):
-            results = sum(self._process_term(term) for term in diagram.terms)
+            results = sum(
+                self._process_term(term) for term in tensor_diagram.terms
+            )
         else:
-            results = self._process_term(diagram)
+            results = self._process_term(tensor_diagram)
 
         if diagram.is_pure:
             state_type = StateType.AMP
         else:
             state_type = StateType.DM
 
-        tensor_diagram = self._get_discopy_tensor(diagram)
-
         return EvalResult(
             discopy_tensor.Box(
                 "Result",
@@ -426,7 +428,7 @@ def _process_term(self, term: Diagram) -> np.ndarray:
         Returns:
             np.ndarray: The processed term as a numpy array.
         """
-        quimb_tn = self._get_quimb_tensor(term)
+        quimb_tn = term.to_quimb()
 
         for t in quimb_tn:
             dt = t.data.dtype
diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index db29fd64..2934fdbe 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -410,16 +410,36 @@ def from_discopy(cls, discopy_circuit):
         from optyx.qubits import Circuit
         return Circuit(discopy_circuit)
 
+    # @classmethod
+    # def from_bosonic_operator(cls, n_modes, operators, scalar=1):
+    #     return Channel(
+    #         "Bosonic operator",
+    #         diagram.Diagram.from_bosonic_operator(
+    #             n_modes, operators, scalar=scalar
+    #         )
+    #     )
+
     @classmethod
     def from_bosonic_operator(cls, n_modes, operators, scalar=1):
-        """Convert from a list of bosonic operators. Based on
-        diagram.Diagram.from_bosonic_operator."""
-        return Channel(
-            "Bosonic operator",
-            diagram.Diagram.from_bosonic_operator(
-                n_modes, operators, scalar=scalar
-            )
-        )
+        """Create a :class:`zw` diagram from a bosonic operator."""
+        # pylint: disable=import-outside-toplevel
+        from optyx.core import zw
+        from optyx.photonic import Scalar
+
+        # pylint: disable=invalid-name
+        d = Diagram.id(qmode**n_modes)
+        annil = Channel("n", zw.Split(2) >> zw.Select(1) @ zw.Id(1))
+        create = annil.dagger()
+        for idx, dagger in operators:
+            if not 0 <= idx < n_modes:
+                raise ValueError(f"Index {idx} out of bounds.")
+            box = create if dagger else annil
+            d = d >> qmode**idx @ box @ qmode**(n_modes - idx - 1)
+
+        if scalar != 1:
+            # pylint: disable=invalid-name
+            d = Scalar(scalar) @ d
+        return d
 
     @classmethod
     def from_graphix(cls, measurement_pattern):
diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index 3850a210..99533074 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -394,26 +394,26 @@ def to_tensor(
         diagram >>= zboxes
         return diagram
 
-    @classmethod
-    def from_bosonic_operator(cls, n_modes, operators, scalar=1):
-        """Create a :class:`zw` diagram from a bosonic operator."""
-        # pylint: disable=import-outside-toplevel
-        from optyx.core import zw
-
-        # pylint: disable=invalid-name
-        d = cls.id(Mode(n_modes))
-        annil = zw.Split(2) >> zw.Select(1) @ zw.Id(1)
-        create = annil.dagger()
-        for idx, dagger in operators:
-            if not 0 <= idx < n_modes:
-                raise ValueError(f"Index {idx} out of bounds.")
-            box = create if dagger else annil
-            d = d >> zw.Id(idx) @ box @ zw.Id(n_modes - idx - 1)
-
-        if scalar != 1:
-            # pylint: disable=invalid-name
-            d = Scalar(scalar) @ d
-        return d
+    # @classmethod
+    # def from_bosonic_operator(cls, n_modes, operators, scalar=1):
+    #     """Create a :class:`zw` diagram from a bosonic operator."""
+    #     # pylint: disable=import-outside-toplevel
+    #     from optyx.core import zw
+
+    #     # pylint: disable=invalid-name
+    #     d = cls.id(Mode(n_modes))
+    #     annil = zw.Split(2) >> zw.Select(1) @ zw.Id(1)
+    #     create = annil.dagger()
+    #     for idx, dagger in operators:
+    #         if not 0 <= idx < n_modes:
+    #             raise ValueError(f"Index {idx} out of bounds.")
+    #         box = create if dagger else annil
+    #         d = d >> zw.Id(idx) @ box @ zw.Id(n_modes - idx - 1)
+
+    #     if scalar != 1:
+    #         # pylint: disable=invalid-name
+    #         d = Scalar(scalar) @ d
+    #     return d
 
     def to_pyzx(self):
         # pylint: disable=import-outside-toplevel
diff --git a/optyx/core/zx.py b/optyx/core/zx.py
index c52c20c3..a8753ace 100644
--- a/optyx/core/zx.py
+++ b/optyx/core/zx.py
@@ -507,139 +507,11 @@ def scalar(data):
     return diagram.Scalar(data)
 
 
-def make_spiders(n):
-    """Constructs the Z spider 1 -> n from spiders 1 -> 2.
-
-    >>> assert len(make_spiders(6)) == 5
-    """
-    spider = Id(1)
-    for k in range(n - 1):
-        spider = spider >> Z(1, 2) @ Id(k)
-    return spider
-
-
-def decomp_ar(box):
-    """
-    Decomposes a ZX diagram into Z spiders
-    with at most two inputs/outputs and hadamards.
-
-    >>> assert len(decomp(X(2, 2, 0.25))) == 7
-    """
-    n, m = len(box.dom), len(box.cod)
-    if isinstance(box, X):
-        phase = box.phase
-        if (n, m) in ((1, 0), (0, 1)):
-            return box
-        box = (
-            Id(0).tensor(*[H] * n) >> Z(n, m, phase) >> Id(0).tensor(*[H] * m)
-        )
-        return decomp(box)
-    if isinstance(box, Z):
-        phase = box.phase
-        rot = Id(1) if phase == 0 else Z(1, 1, phase)
-        if n == 0:
-            return X(0, 1) >> H >> rot >> make_spiders(m)
-        if m == 0:
-            return X(1, 0) << H << rot << make_spiders(n).dagger()
-        return make_spiders(n).dagger() >> rot >> make_spiders(m)
-    return box
-
-
-decomp = symmetric.Functor(
-    ob=lambda x: diagram.Bit(len(x)),
-    ar=decomp_ar,
-    cod=symmetric.Category(diagram.Bit, diagram.Diagram),
-)
-
-
 def Id(n):
     return diagram.Diagram.id(n) if isinstance(n, diagram.Ty) \
           else diagram.Diagram.id(diagram.Bit(n))
 
 
-def ar_zx2path(box):
-    """Mapping from ZX generators to QPath diagrams
-
-    >>> zx2path(decomp(X(0, 1) @ X(0, 1) >> Z(2, 1))).to_path().eval()
-    Amplitudes([2.+0.j, 0.+0.j], dom=1, cod=2)
-    """
-    # pylint: disable=import-outside-toplevel
-    from optyx.photonic import HadamardBS, Phase, BS
-
-    unit = zw.Create(0)
-    counit = zw.Select(0)
-    create = zw.Create(1)
-    annil = zw.Select(1)
-    comonoid = zw.Split(2)
-    monoid = zw.Merge(2)
-    BS = BS.get_kraus()
-
-    n, m = len(box.dom), len(box.cod)
-    if isinstance(box, diagram.Scalar):
-        return diagram.Scalar(box.data)
-    if isinstance(box, X):
-        phase = 1 + box.phase if box.phase < 0 else box.phase
-        if (n, m, phase) == (0, 1, 0):
-            return create @ unit @ root2
-        if (n, m, phase) == (0, 1, 0.5):
-            return unit @ create @ root2
-        if (n, m, phase) == (1, 0, 0):
-            return annil @ counit @ root2
-        if (n, m, phase) == (1, 0, 0.5):
-            return counit @ annil @ root2
-        if (n, m, phase) == (1, 1, 0.25):
-            return BS.dagger()
-        if (n, m, phase) == (1, 1, -0.25):
-            return BS
-    if isinstance(box, Z):
-        phase = box.phase
-        if (n, m) == (0, 1):
-            return create >> comonoid
-        if (n, m) == (1, 1):
-            return Id(diagram.Mode(1)) @ Phase(phase).get_kraus()
-        if (n, m, phase) == (2, 1, 0):
-            return (
-                Id(diagram.Mode(1)) @
-                (monoid >> annil) @
-                Id(diagram.Mode(1))
-                )
-        if (n, m, phase) == (1, 2, 0):
-            plus = create >> comonoid
-            bot = (
-                (plus >> Id(diagram.Mode(1)) @ plus @ Id(diagram.Mode(1))) @
-                (Id(diagram.Mode(1)) @ plus @ Id(diagram.Mode(1)))
-            )
-            mid = Id(diagram.Mode(2)) @ BS.dagger() @ BS @ Id(diagram.Mode(2))
-            fusion = (
-                Id(diagram.Mode(1)) @ plus.dagger() @
-                Id(diagram.Mode(1)) >> plus.dagger()
-            )
-            return (
-                bot >> mid >> (Id(diagram.Mode(2)) @
-                               fusion @ Id(diagram.Mode(2)))
-                )
-    if box == H:
-        return HadamardBS().get_kraus()
-    raise NotImplementedError(f"No translation of {box} in QPath.")
-
-
-zx2path = symmetric.Functor(
-    ob=lambda x: diagram.Mode(2 * len(x)),
-    ar=ar_zx2path,
-    cod=symmetric.Category(diagram.Mode, diagram.Diagram),
-)
-
-
-def zx_to_path(diagram: diagram.Diagram) -> diagram.Diagram:
-    """
-    Dual-rail encoding of any ZX diagram as a QPath diagram.
-    """
-    return zx2path(decomp(diagram))
-
-
-root2 = scalar(2**0.5)
-
-
 H = ZXBox("H", 1, 1)
 H.draw_as_spider = False
 (H.drawing_name, H.tikzstyle_name,) = (
diff --git a/optyx/qubits.py b/optyx/qubits.py
index b84d69bc..bd3dc07a 100644
--- a/optyx/qubits.py
+++ b/optyx/qubits.py
@@ -636,7 +636,7 @@ def decomp(self):
     def _make_spiders(n):
         """Constructs the Z spider 1 -> n from spiders 1 -> 2.
 
-        >>> assert len(make_spiders(6)) == 5
+        >>> assert len(Z._make_spiders(6)) == 5
         """
         from optyx import qubits
 
diff --git a/test/grad.py b/test/grad.py
index cfd82a4f..f9005ff5 100644
--- a/test/grad.py
+++ b/test/grad.py
@@ -23,7 +23,7 @@
 @pytest.mark.parametrize("circ, value", product(param_circuits, values))
 def test_daggers_cancel(circ, value):
     d = circ >> circ.dagger()
-    out = d.grad(psi).subs((psi, value)).eval(2).array
+    out = d.grad(psi).subs((psi, value)).eval().tensor.array
     assert np.allclose(out, np.zeros(shape=out.shape))
 
 
diff --git a/test/qpath.py b/test/qpath.py
index 810ea16c..bd795640 100644
--- a/test/qpath.py
+++ b/test/qpath.py
@@ -27,16 +27,16 @@ def test_dilate():
         assert np.allclose(unitary.eval(3).array, matrix.eval(3).array)
 
 
-def test_bosonic_operator():
-    d1 = Diagram.from_bosonic_operator(
-        n_modes= 2,
-        operators=((0, False), (1, False), (0, True)),
-        scalar=2.1
-    )
+# def test_bosonic_operator():
+#     d1 = Diagram.from_bosonic_operator(
+#         n_modes= 2,
+#         operators=((0, False), (1, False), (0, True)),
+#         scalar=2.1
+#     )
 
-    annil = Split(2) >> Select(1) @ Id(Mode(1))
-    create = annil.dagger()
+#     annil = Split(2) >> Select(1) @ Id(Mode(1))
+#     create = annil.dagger()
 
-    d2 = Scalar(2.1) @ annil @ Id(Mode(1)) >> Id(Mode(1)) @ annil >> create @ Id(Mode(1))
+#     d2 = Scalar(2.1) @ annil @ Id(Mode(1)) >> Id(Mode(1)) @ annil >> create @ Id(Mode(1))
 
-    assert d1 == d2
\ No newline at end of file
+#     assert d1 == d2
\ No newline at end of file
diff --git a/test/test_channel.py b/test/test_channel.py
index 9d07de6c..34d220c9 100644
--- a/test/test_channel.py
+++ b/test/test_channel.py
@@ -57,5 +57,8 @@ def test_from_bosonic_op():
             terms.append(term)
 
     hamiltonian = Diagram.sum_factory(terms)
-    sum_1 = hamiltonian.eval()
-    assert np.allclose(sum_1.array, 0.0)
\ No newline at end of file
+
+    sum_1 = np.sign(hamiltonian.get_kraus().to_tensor().eval().array)
+    sum_2 = np.sign(hamiltonian.eval().tensor.array) # bug in discopy.tensor.Tensor.eval() for Sums (?)
+
+    assert np.allclose(sum_2, sum_1)
\ No newline at end of file
diff --git a/test/test_qubit.py b/test/test_qubit.py
index 003f08df..345383ec 100644
--- a/test/test_qubit.py
+++ b/test/test_qubit.py
@@ -94,11 +94,11 @@ def test_pure_double_kraus():
 
     assert qubits.Circuit(g).get_kraus() == qubits.Circuit(g).get_kraus()
 
-def test_to_dual_rail():
-    circuit = qubits.Z(1, 2) >> qubits.H() @ qubits.H()
-    dr_1 = qubits.Circuit(circuit).to_dual_rail().get_kraus()
-    dr_2 = zx.zx2path(circuit.get_kraus())
-    assert dr_1 == dr_2
+# def test_to_dual_rail():
+#     circuit = qubits.Z(1, 2) >> qubits.H() @ qubits.H()
+#     dr_1 = qubits.Circuit(circuit).to_dual_rail().get_kraus()
+#     dr_2 = zx.zx2path(circuit.get_kraus())
+#     assert dr_1 == dr_2
 
 def test_discard_qubits():
     a = (qubits.Discard(2).double().to_tensor().to_quimb() ^ ...).data

From 45bada4c2bad0b65f6b3b34b580da80cb423c4e8 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Sat, 6 Sep 2025 12:51:57 +0100
Subject: [PATCH 39/59] dual rail and decomp fixed

---
 optyx/core/channel.py | 46 ++++++++++++++++++++++++++++++++++++++++---
 optyx/core/diagram.py | 20 -------------------
 optyx/photonic.py     |  6 +++---
 optyx/qubits.py       | 16 +++++++--------
 4 files changed, 54 insertions(+), 34 deletions(-)

diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index 2934fdbe..2237fd88 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -104,6 +104,46 @@
 >>> lossy_prob = (state >> lossy_channel >> effect).double(\\
 ...     ).to_tensor().eval().array
 >>> assert np.allclose(lossy_prob, prob * (eff ** 2))
+
+**Diagrams from Bosonic Operators**
+
+The :code:`from_bosonic_operator` method
+supports creating :class:`path` diagrams:
+
+>>> from optyx.core.zw import Split, Select, Id
+>>> from optyx.core.diagram import Mode
+>>> from optyx.photonic import Scalar
+>>> d1 = Diagram.from_bosonic_operator(
+...     n_modes=2,
+...     operators=((0, False), (1, False), (0, True)),
+...     scalar=2.1
+... )
+
+>>> annil = Channel(
+...     "annil", Split(2) >> Select(1) @ Id(Mode(1))
+... )
+>>> create = annil.dagger()
+
+>>> d2 = Scalar(2.1) @ annil @ qmode >> \\
+... qmode @ annil >> create @ qmode
+
+>>> assert d1 == d2
+
+We can map ZX diagrams to :class:`path` diagrams using
+dual-rail encoding. For example, we can create a GHZ state:
+
+>>> from discopy.drawing import Equation
+>>> from optyx.qubits import Z
+>>> from optyx.photonic import DualRail
+>>> ghz = Z(0, 3)
+>>> ghz_path = ghz.to_dual_rail()
+>>> Equation(ghz >> DualRail(3), ghz_path, \\
+... symbol="$\\mapsto$").draw(figsize=(10, 10), \\
+... path="docs/_static/ghz_dr.svg")
+
+.. image:: /_static/ghz_dr.svg
+    :align: center
+
 """
 
 from __future__ import annotations
@@ -428,7 +468,7 @@ def from_bosonic_operator(cls, n_modes, operators, scalar=1):
 
         # pylint: disable=invalid-name
         d = Diagram.id(qmode**n_modes)
-        annil = Channel("n", zw.Split(2) >> zw.Select(1) @ zw.Id(1))
+        annil = Channel("annil", zw.Split(2) >> zw.Select(1) @ zw.Id(1))
         create = annil.dagger()
         for idx, dagger in operators:
             if not 0 <= idx < n_modes:
@@ -611,13 +651,13 @@ def dagger(self):
             cod=self.dom,
         )
 
-    def decomp(self):
+    def _decomp(self):
         # pylint: disable=import-outside-toplevel
         raise NotImplementedError(
             "Decomposition is only implemented for ZX channels."
         )
 
-    def to_dual_rail(self):
+    def _to_dual_rail(self):
         raise TypeError(
             "Only ZX channels can be converted to dual rail."
             )
diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index 99533074..58d6b346 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -149,26 +149,6 @@
 ...             Hong_Ou_Mandel.to_tensor().eval().array,\\
 ...             np.array([0]))
 
-**:class:`zw` diagrams from Bosonic Operators**
-
-The :code:`from_bosonic_operator` method
-supports creating :class:`path` diagrams:
-
->>> from optyx.core.zw import Split, Select, Id
->>> d1 = Diagram.from_bosonic_operator(
-...     n_modes= 2,
-...     operators=((0, False), (1, False), (0, True)),
-...     scalar=2.1
-... )
-
->>> annil = Split(2) >> Select(1) @ Id(Mode(1))
->>> create = annil.dagger()
-
->>> d2 = Scalar(2.1) @ annil @ Id(Mode(1)) >> \\
-... Id(Mode(1)) @ annil >> create @ Id(Mode(1))
-
->>> assert d1 == d2
-
 **Permanent evaluation for QPath diagrams**
 
 The :code:`to_path` method supports evaluation by
diff --git a/optyx/photonic.py b/optyx/photonic.py
index 6641fd55..8f3e17cf 100644
--- a/optyx/photonic.py
+++ b/optyx/photonic.py
@@ -929,7 +929,7 @@ class FusionTypeI(Diagram):
 
     **Codomain**
         ``qmode ** 2 @ bit ** 2``
-        – the surviving dual-rail qubit followed by two classical bits
+        - the surviving dual-rail qubit followed by two classical bits
         ``[s, k]`` where
 
         * ``s`` is the parity (success) bit
@@ -1071,8 +1071,8 @@ class FusionTypeII(Diagram):
         ``bit ** 2``
         containing
 
-        * ``s`` – success / parity bit
-        * ``k`` – Pauli-correction bit (applied to neighbouring nodes).
+        * ``s`` - success / parity bit
+        * ``k`` - Pauli-correction bit (applied to neighbouring nodes).
 
     Notes
     -----
diff --git a/optyx/qubits.py b/optyx/qubits.py
index bd3dc07a..5e2ad95e 100644
--- a/optyx/qubits.py
+++ b/optyx/qubits.py
@@ -622,7 +622,7 @@ def lambdify(self, *symbols, **kwargs):
             lambdify(symbols, self.phase, **kwargs)(*xs)
         )
 
-    def decomp(self):
+    def _decomp(self):
         n, m = len(self.dom), len(self.cod)
         phase = self.phase
         rot = Id(1) if phase == 0 else Z(1, 1, phase)
@@ -645,7 +645,7 @@ def _make_spiders(n):
             spider = spider >> qubits.Z(1, 2) @ qubits.Id(k)
         return spider
 
-    def to_dual_rail(self):
+    def _to_dual_rail(self):
         """Convert to dual-rail encoding."""
 
         from optyx import (
@@ -722,7 +722,7 @@ def lambdify(self, *symbols, **kwargs):
             lambdify(symbols, self.phase, **kwargs)(*xs),
         )
 
-    def decomp(self):
+    def _decomp(self):
         n, m = len(self.dom), len(self.cod)
         phase = self.phase
         if (n, m) in ((1, 0), (0, 1)):
@@ -732,7 +732,7 @@ def decomp(self):
         )
         return box.decomp()
 
-    def to_dual_rail(self):
+    def _to_dual_rail(self):
         """Convert to dual-rail encoding."""
         from optyx import (
             photonic,
@@ -784,10 +784,10 @@ def __init__(self):
             qubit,
         )
 
-    def decomp(self):
+    def _decomp(self):
         return H()
 
-    def to_dual_rail(self):
+    def _to_dual_rail(self):
         """Convert to dual-rail encoding."""
         from optyx import photonic
         return photonic.HadamardBS()
@@ -809,10 +809,10 @@ def __init__(self, value: float):
         )
         self.data = value
 
-    def decomp(self):
+    def _decomp(self):
         return Scalar(self.data)
 
-    def to_dual_rail(self):
+    def _to_dual_rail(self):
         """Convert to dual-rail encoding."""
         from optyx import photonic
         return photonic.Scalar(self.data)

From f6a9cda9caba19d616599de4eec8dc4d954d3913 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Sat, 6 Sep 2025 12:52:18 +0100
Subject: [PATCH 40/59] remove notes from notebooks

---
 docs/notebooks/bosonic-vqe-2.ipynb | 150 -----------------------------
 1 file changed, 150 deletions(-)

diff --git a/docs/notebooks/bosonic-vqe-2.ipynb b/docs/notebooks/bosonic-vqe-2.ipynb
index 3ff6d24e..d028b85c 100644
--- a/docs/notebooks/bosonic-vqe-2.ipynb
+++ b/docs/notebooks/bosonic-vqe-2.ipynb
@@ -2318,156 +2318,6 @@
     "plt.plot(range(len(xs)),fxs,'b.')\n",
     "plt.show()"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "id": "346a4294",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from optyx.photonic import BBS, Create, Scalar"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "id": "eea8a769",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "#diagram = BBS(0.3) + BBS(0.9) + BBS(0.5)\n",
-    "#diagram.draw()\n",
-    "\n",
-    "diagram = Create(1) @ Scalar(0.34) + Create(2) @ Scalar(0.56) + Create(3) @ Scalar(0.12)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "id": "5e2fd068",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0.  +0.j, 0.34+0.j, 0.56+0.j, 0.12+0.j])"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "diagram.eval().tensor.array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "id": "fa135207",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[0.  +0.j 0.34+0.j 0.  +0.j 0.  +0.j]\n",
-      "-----\n",
-      "[0.  +0.j 0.34+0.j 0.  +0.j 0.  +0.j]\n",
-      "======\n",
-      "[0.  +0.j 0.  +0.j 0.56+0.j 0.  +0.j]\n",
-      "-----\n",
-      "[0.  +0.j 0.  +0.j 0.56+0.j 0.  +0.j]\n",
-      "======\n",
-      "[0.  +0.j 0.  +0.j 0.  +0.j 0.12+0.j]\n",
-      "-----\n",
-      "[0.  +0.j 0.  +0.j 0.  +0.j 0.12+0.j]\n",
-      "======\n"
-     ]
-    }
-   ],
-   "source": [
-    "import numpy as np\n",
-    "\n",
-    "for term in diagram.get_kraus().to_tensor():\n",
-    "    print((term.to_quimb()^...).data)\n",
-    "    print(\"-----\")\n",
-    "    print(term.eval().array)\n",
-    "    print(\"======\")\n",
-    "    assert np.allclose((term.to_quimb()^...).data, term.eval().array)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "id": "f20a782f",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/discopy/matrix.py:161: ComplexWarning: Casting complex values to real discards the imaginary part\n",
-      "  self.array = np.array(array, dtype=self.dtype).reshape((dom, cod))\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 0, 0, 0])"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "diagram.get_kraus().to_tensor().eval().array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "id": "abf30abe",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "tensor.Sum(terms=(tensor.Diagram(inside=(rigid.Layer(Dim(1), tensor.Box[complex128]('Create(1)', Dim(2), Dim(1), data=array([0.+0.j, 1.+0.j])).dagger(), Dim(1)), rigid.Layer(Dim(2), tensor.Box[complex128]('scalar', Dim(1), Dim(1), data=[(0.34+0j)]), Dim(1)), rigid.Layer(Dim(1), tensor.Box[int64]('ZBox(1, 1, mode)', Dim(2), Dim(2), data=array([[1, 0],\n",
-       "       [0, 1]])), Dim(1)), rigid.Layer(Dim(1), tensor.Spider(1, 1, Dim(2)), Dim(1)), rigid.Layer(Dim(1), optyx.core.diagram.EmbeddingTensor('Embedding', Dim(2), Dim(4), data=array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
-       "       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])), Dim(1))), dom=Dim(1), cod=Dim(4)), tensor.Diagram(inside=(rigid.Layer(Dim(1), tensor.Box[complex128]('Create((2,))', Dim(3), Dim(1), data=array([0.+0.j, 0.+0.j, 1.+0.j])).dagger(), Dim(1)), rigid.Layer(Dim(3), tensor.Box[complex128]('scalar', Dim(1), Dim(1), data=[(0.56+0j)]), Dim(1)), rigid.Layer(Dim(1), tensor.Box[int64]('ZBox(1, 1, mode)', Dim(3), Dim(3), data=array([[1, 0, 0],\n",
-       "       [0, 1, 0],\n",
-       "       [0, 0, 1]])), Dim(1)), rigid.Layer(Dim(1), tensor.Spider(1, 1, Dim(3)), Dim(1)), rigid.Layer(Dim(1), optyx.core.diagram.EmbeddingTensor('Embedding', Dim(3), Dim(4), data=array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
-       "       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
-       "       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j]])), Dim(1))), dom=Dim(1), cod=Dim(4)), tensor.Diagram(inside=(rigid.Layer(Dim(1), tensor.Box[complex128]('Create((3,))', Dim(4), Dim(1), data=array([0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j])).dagger(), Dim(1)), rigid.Layer(Dim(4), tensor.Box[complex128]('scalar', Dim(1), Dim(1), data=[(0.12+0j)]), Dim(1)), rigid.Layer(Dim(1), tensor.Box[int64]('ZBox(1, 1, mode)', Dim(4), Dim(4), data=array([[1, 0, 0, 0],\n",
-       "       [0, 1, 0, 0],\n",
-       "       [0, 0, 1, 0],\n",
-       "       [0, 0, 0, 1]])), Dim(1)), rigid.Layer(Dim(1), tensor.Spider(1, 1, Dim(4)), Dim(1)), rigid.Layer(Dim(1), optyx.core.diagram.EmbeddingTensor('Embedding', Dim(4), Dim(4), data=array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
-       "       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
-       "       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
-       "       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])), Dim(1))), dom=Dim(1), cod=Dim(4))))"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "diagram.get_kraus().to_tensor()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "554c80f7",
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {

From c8da03f40f6739b138e26b1f1309ee115affc6f9 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Mon, 8 Sep 2025 13:48:48 +0100
Subject: [PATCH 41/59] flake8

---
 optyx/core/channel.py | 52 -------------------------------------------
 optyx/core/zx.py      |  1 -
 optyx/qubits.py       | 14 +++++++-----
 test/test_channel.py  |  2 +-
 4 files changed, 10 insertions(+), 59 deletions(-)

diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index 2237fd88..26a58fc4 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -148,7 +148,6 @@
 
 from __future__ import annotations
 
-import numpy as np
 from discopy import tensor
 from discopy import symmetric, frobenius, hypergraph
 from discopy.cat import factory
@@ -723,57 +722,6 @@ def get_kraus(self):
             [term.get_kraus() for term in self.terms]
         )
 
-    # def to_path(self, dtype: type = complex):
-    #     """Evaluate the sum of diagrams."""
-    #     array = 0
-    #     doms = []
-    #     cods = []
-    #     creations = []
-    #     selections = []
-    #     normalisations = []
-    #     for term in self.terms:
-    #         path_diagram = term.to_path(dtype)
-    #         array += path_diagram.array
-    #         creations.append(path_diagram.creations)
-    #         selections.append(path_diagram.selections)
-    #         doms.append(path_diagram.dom)
-    #         cods.append(path_diagram.cod)
-    #         normalisations.append(path_diagram.normalisation)
-
-    #     assert all(d == doms[0] for d in doms), "All terms must have the same dom"
-    #     assert all(c == cods[0] for c in cods), "All terms must have the same cod"
-    #     assert all(creations[0] == cr for cr in creations), "All creations tuples must be identical"
-    #     assert all(selections[0] == se for se in selections), "All selections tuples must be identical"
-    #     assert all(normalisations[0] == n for n in normalisations), "All normalisations must be identical"
-
-    #     array = array/len(self.terms)
-
-    #     dom = doms[0]
-    #     cod = cods[0]
-
-    #     return Matrix[dtype](
-    #         array,
-    #         dom,
-    #         cod,
-    #         creations=creations[0],
-    #         selections=selections[0],
-    #         normalisation=normalisations[0]
-    #     )
-
-    # def eval(self, n_photons=0, permanent=None, dtype=complex):
-    #     """Evaluate the sum of diagrams."""
-    #     # we need to implement the proper sums of qpath diagrams
-    #     # this is only a temporary solution, so that the grad tests pass
-    #     if permanent is None:
-    #         # pylint: disable=import-outside-toplevel
-    #         from optyx.core.path import npperm
-
-    #         permanent = npperm
-    #     return sum(
-    #         term.to_path(dtype).eval(n_photons, permanent)
-    #         for term in self.terms
-    #     )
-
 
 class CQMap(Diagram, frobenius.Box):
     """
diff --git a/optyx/core/zx.py b/optyx/core/zx.py
index a8753ace..71c524a7 100644
--- a/optyx/core/zx.py
+++ b/optyx/core/zx.py
@@ -127,7 +127,6 @@
 from typing import List
 
 import numpy as np
-from discopy import symmetric
 from discopy import cat
 from discopy.utils import factory_name
 from discopy.frobenius import Dim
diff --git a/optyx/qubits.py b/optyx/qubits.py
index 5e2ad95e..647ed2d3 100644
--- a/optyx/qubits.py
+++ b/optyx/qubits.py
@@ -265,14 +265,14 @@
 
 """  # noqa E501
 
-from typing import Literal, Iterable
+from typing import Literal
 from enum import Enum
 import numpy as np
 from pyzx.graph.base import BaseGraph
 import graphix
 from discopy import quantum as quantum_discopy
 from discopy import symmetric
-from sympy import Expr, lambdify, Symbol, Mul
+from sympy import lambdify
 # from pytket import circuit as tket_circuit
 from optyx.utils.utils import explode_channel
 from optyx.core import (
@@ -445,7 +445,6 @@ class QubitChannel(Channel):
     #         cod=symmetric.Category(channel.Ty, channel.Diagram),
     #     )(self)
 
-
     # pylint: disable=too-many-locals
     # pylint: disable=too-many-return-statements
     # pylint: disable=too-many-branches
@@ -696,6 +695,7 @@ def dagger(self):
             -self.phase
         )
 
+
 # pylint: disable=invalid-name
 class X(Channel):
     """X spider."""
@@ -728,7 +728,9 @@ def _decomp(self):
         if (n, m) in ((1, 0), (0, 1)):
             return self
         box = (
-            Id(0).tensor(*[H()] * n) >> Z(n, m, phase) >> Id(0).tensor(*[H()] * m)
+            Id(0).tensor(*[H()] * n) >>
+            Z(n, m, phase) >>
+            Id(0).tensor(*[H()] * m)
         )
         return box.decomp()
 
@@ -738,7 +740,6 @@ def _to_dual_rail(self):
             photonic,
             classical
         )
-        from optyx.core import zw
 
         root2 = photonic.Scalar(2**0.5)
         unit = photonic.Create(0)
@@ -769,6 +770,7 @@ def dagger(self):
             -self.phase
         )
 
+
 # pylint: disable=invalid-name
 class H(Channel):
     """Hadamard gate."""
@@ -795,6 +797,7 @@ def _to_dual_rail(self):
     def dagger(self):
         return self
 
+
 class Scalar(Channel):
     """
     Scalar.
@@ -820,6 +823,7 @@ def _to_dual_rail(self):
     def dagger(self):
         return type(self)(np.conj(self.data))
 
+
 class BitFlipError(Channel):
     """
     Represents a bit-flip error channel.
diff --git a/test/test_channel.py b/test/test_channel.py
index 34d220c9..b926f20b 100644
--- a/test/test_channel.py
+++ b/test/test_channel.py
@@ -1,7 +1,7 @@
 import pytest
 
 from optyx.core.channel import *
-from optyx.core import diagram
+from optyx.core import diagram, zx
 import numpy as np
 
 bell_density_re = np.array([

From 93dbb18ce7d341f09c0936f74ec0c817724a46a3 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Wed, 10 Sep 2025 16:31:12 +0100
Subject: [PATCH 42/59] testing_some_extra_functions

---
 examples/test_light_cones.ipynb | 16828 ++++++++++++++++++++++++++++++
 1 file changed, 16828 insertions(+)
 create mode 100644 examples/test_light_cones.ipynb

diff --git a/examples/test_light_cones.ipynb b/examples/test_light_cones.ipynb
new file mode 100644
index 00000000..408ebc05
--- /dev/null
+++ b/examples/test_light_cones.ipynb
@@ -0,0 +1,16828 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 186,
+   "id": "31149112",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from __future__ import annotations\n",
+    "\n",
+    "from typing import List, Tuple\n",
+    "from optyx.core.diagram import Box, Diagram, Spider, Swap\n",
+    "from optyx.core import zw\n",
+    "\n",
+    "LO_ELEMENTS = (\n",
+    "    zw.Create,\n",
+    "    zw.W,\n",
+    "    zw.Select,\n",
+    "    zw.Add,\n",
+    "    zw.Endo\n",
+    ")\n",
+    "\n",
+    "def update_connections(\n",
+    "    wires_in_light_cone: List[bool],\n",
+    "    previous_left_offset: int,\n",
+    "    previous_box: Box,\n",
+    "    previous_right_offset: int,\n",
+    ") -> List[bool]:\n",
+    "    \"\"\"\n",
+    "    Replace the previous box's COD segment in the light-cone by a DOM-length\n",
+    "    segment that is either all True (if connected) or all False.\n",
+    "    This pulls the cone one layer backward.\n",
+    "    \"\"\"\n",
+    "    connected = is_previous_box_connected_to_current_box(\n",
+    "        wires_in_light_cone,\n",
+    "        previous_left_offset,\n",
+    "        len(previous_box.cod),\n",
+    "        previous_right_offset,\n",
+    "    )\n",
+    "\n",
+    "    start = previous_left_offset\n",
+    "    end = len(wires_in_light_cone) - previous_right_offset\n",
+    "\n",
+    "    # replace cod slice with a dom-length slice of the same boolean\n",
+    "    return (\n",
+    "        wires_in_light_cone[:start]\n",
+    "        + [connected] * len(previous_box.dom)\n",
+    "        + wires_in_light_cone[end:]\n",
+    "    )\n",
+    "\n",
+    "def calculate_right_offset(total_wires: int, left_offset: int, span_len: int) -> int:\n",
+    "    \"\"\"Right offset = number of wires to the right of a span.\"\"\"\n",
+    "    return total_wires - span_len - left_offset\n",
+    "\n",
+    "def is_previous_box_connected_to_current_box(\n",
+    "    wires_in_light_cone: List[bool],\n",
+    "    previous_left_offset: int,\n",
+    "    previous_box_cod_len: int,\n",
+    "    previous_right_offset: int,\n",
+    ") -> bool:\n",
+    "    \"\"\"\n",
+    "    Do the current light-cone wires intersect the COD of the previous box?\n",
+    "    \"\"\"\n",
+    "    mask = (\n",
+    "        [False] * previous_left_offset\n",
+    "        + [True] * previous_box_cod_len\n",
+    "        + [False] * previous_right_offset\n",
+    "    )\n",
+    "    # lengths should match by construction\n",
+    "    assert len(mask) == len(wires_in_light_cone), (\n",
+    "        f\"Mask/wires length mismatch: {len(mask)} != {len(wires_in_light_cone)}\"\n",
+    "    )\n",
+    "\n",
+    "    return any(w and m for w, m in zip(wires_in_light_cone, mask))\n",
+    "\n",
+    "def get_previous_box_cod_index_in_light_cone(\n",
+    "    wires_in_light_cone: List[bool],\n",
+    "    previous_left_offset: int,\n",
+    "    previous_box_cod_len: int,\n",
+    "    previous_right_offset: int,\n",
+    ") -> List[int]:\n",
+    "    \"\"\"\n",
+    "    Get the indices of the COD of the previous box that are in the current light-cone.\n",
+    "    \"\"\"\n",
+    "    mask = (\n",
+    "        [False] * previous_left_offset\n",
+    "        + [True] * previous_box_cod_len\n",
+    "        + [False] * previous_right_offset\n",
+    "    )\n",
+    "    # lengths should match by construction\n",
+    "    assert len(mask) == len(wires_in_light_cone), (\n",
+    "        f\"Mask/wires length mismatch: {len(mask)} != {len(wires_in_light_cone)}\"\n",
+    "    )\n",
+    "\n",
+    "    return [\n",
+    "        i - previous_left_offset for i, (w, m) in enumerate(zip(wires_in_light_cone, mask))\n",
+    "        if w and m\n",
+    "    ]\n",
+    "\n",
+    "\n",
+    "def get_max_dim_for_box(\n",
+    "    left_offset: int,\n",
+    "    box: Box,\n",
+    "    right_offset: int,\n",
+    "    input_dims: List[int],\n",
+    "    prev_layers: List[Tuple[int, Box]],\n",
+    "):\n",
+    "\n",
+    "    if len(box.dom) == 0 or isinstance(box, Swap):\n",
+    "        return 1e20\n",
+    "\n",
+    "    dim_for_box = 0\n",
+    "\n",
+    "    # light-cone at the current layer inputs\n",
+    "    wires_in_light_cone: List[bool] = (\n",
+    "        [False] * left_offset\n",
+    "        + [True] * len(box.dom)\n",
+    "        + [False] * right_offset\n",
+    "    )\n",
+    "\n",
+    "    for previous_left_offset, previous_box in prev_layers[::-1]:\n",
+    "        previous_right_offset = calculate_right_offset(\n",
+    "            len(wires_in_light_cone), previous_left_offset, len(previous_box.cod)\n",
+    "        )\n",
+    "\n",
+    "        if is_previous_box_connected_to_current_box(\n",
+    "            wires_in_light_cone,\n",
+    "            previous_left_offset,\n",
+    "            len(previous_box.cod),\n",
+    "            previous_right_offset,\n",
+    "        ):\n",
+    "\n",
+    "            if isinstance(previous_box, zw.Create):\n",
+    "                idxs = get_previous_box_cod_index_in_light_cone(\n",
+    "                    wires_in_light_cone,\n",
+    "                    previous_left_offset,\n",
+    "                    len(previous_box.cod),\n",
+    "                    previous_right_offset,\n",
+    "                )\n",
+    "                dim_for_box += sum(previous_box.photons[i] for i in idxs)\n",
+    "\n",
+    "        wires_in_light_cone = update_connections(\n",
+    "            wires_in_light_cone,\n",
+    "            previous_left_offset,\n",
+    "            previous_box,\n",
+    "            previous_right_offset,\n",
+    "        )\n",
+    "\n",
+    "    dim_for_box += sum(2*dim for wire, dim in zip(wires_in_light_cone, input_dims) if wire) + 1\n",
+    "    return dim_for_box\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 147,
+   "id": "e97d833d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.photonic import ansatz, Create\n",
+    "import numpy as np\n",
+    "from optyx import qmode\n",
+    "\n",
+    "def chip_mzi(w, l):\n",
+    "    ansatz_ = ansatz(w, l)\n",
+    "    symbs = list(ansatz_.free_symbols)\n",
+    "    s = [(i, np.random.uniform(0, 1)) for i in symbs]\n",
+    "    return ansatz_.subs(*s)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5e3c7ea2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from optyx.core import zw\n",
+    "from optyx import Channel\n",
+    "\n",
+    "def _number_operator():\n",
+    "    return (\n",
+    "        zw.W(2) >>\n",
+    "        zw.Select(1) @ zw.Id(1) >>\n",
+    "        zw.Create(1) @ zw.Id(1) >>\n",
+    "        zw.W(2).dagger()\n",
+    "    )\n",
+    "\n",
+    "def _monomial_number_operator(power):\n",
+    "    diag = zw.Id(1)\n",
+    "    for i in range(power):\n",
+    "        diag = diag >> _number_operator()\n",
+    "    return diag\n",
+    "\n",
+    "def _get_monomial_layer(powers):\n",
+    "    monomial_layer = zw.Id(0)\n",
+    "    for power in powers:\n",
+    "        monomial_layer = monomial_layer @ _monomial_number_operator(power)\n",
+    "\n",
+    "    return Channel(\"l\", monomial_layer)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fc152566",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 190,
+   "id": "353c0a1c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from discopy import tensor\n",
+    "from optyx.core.diagram import Dim, modify_io_dims_against_max_dim\n",
+    "\n",
+    "# pylint: disable=too-many-locals\n",
+    "def to_tensor(\n",
+    "    self, input_dims: list = None\n",
+    ") -> tensor.Diagram:\n",
+    "    \"\"\"Returns a :class:`tensor.Diagram` for evaluation\"\"\"\n",
+    "    from optyx.core import zw\n",
+    "\n",
+    "    prev_layers: List[Tuple[int, Box]] = []\n",
+    "\n",
+    "    # pylint: disable=import-outside-toplevel\n",
+    "    def list_to_dim(dims: np.ndarray | list) -> Dim:\n",
+    "        \"\"\"Converts a list of dimensions to a Dim object\"\"\"\n",
+    "        return Dim(*[int(i) for i in dims])\n",
+    "\n",
+    "    number_of_input_layer_wires = len(self.dom)\n",
+    "\n",
+    "    if input_dims is None:\n",
+    "        layer_dims = [2 for _ in range(len(self.dom))]\n",
+    "    else:\n",
+    "        assert len(self.dom) == len(input_dims), (\n",
+    "            f\"Input dims length {len(input_dims)} does not match number of input wires {len(self.dom)}\"\n",
+    "        )\n",
+    "        layer_dims = input_dims\n",
+    "\n",
+    "    if len(self.boxes) == 0 and len(self.offsets) == 0:\n",
+    "        return tensor.Diagram.id(list_to_dim(layer_dims))\n",
+    "\n",
+    "    for i, (box, left_offset) in enumerate(zip(self.boxes, self.offsets)):\n",
+    "        right_offset = calculate_right_offset(\n",
+    "            number_of_input_layer_wires, left_offset, len(box.dom)\n",
+    "        )\n",
+    "\n",
+    "        max_dim = get_max_dim_for_box(\n",
+    "            left_offset,\n",
+    "            box,\n",
+    "            right_offset,\n",
+    "            layer_dims,\n",
+    "            prev_layers\n",
+    "        )\n",
+    "\n",
+    "        dims_in = layer_dims[left_offset:left_offset + len(box.dom)]\n",
+    "        dims_out, _ = modify_io_dims_against_max_dim(\n",
+    "            box.determine_output_dimensions(dims_in),\n",
+    "            None,\n",
+    "            max_dim\n",
+    "            )\n",
+    "        if isinstance(box, LO_ELEMENTS):\n",
+    "            prev_layers.append((left_offset, box))\n",
+    "        else:\n",
+    "            prev_layers.append(\n",
+    "                (left_offset, zw.Select(*dims_in) >> zw.Create(*dims_out))\n",
+    "            )\n",
+    "\n",
+    "        left = Dim()\n",
+    "        if left_offset > 0:\n",
+    "            left = list_to_dim(layer_dims[0:left_offset])\n",
+    "        right = Dim()\n",
+    "        if left_offset + len(box.dom) < number_of_input_layer_wires:\n",
+    "            right = list_to_dim(\n",
+    "                layer_dims[left_offset + len(box.dom): number_of_input_layer_wires]\n",
+    "            )\n",
+    "\n",
+    "        number_of_input_layer_wires += -len(box.dom) + len(box.cod)\n",
+    "        cod_layer_dims = (\n",
+    "            layer_dims[0:left_offset]\n",
+    "            + dims_out\n",
+    "            + layer_dims[left_offset + len(box.dom):]\n",
+    "        )\n",
+    "\n",
+    "        diagram_ = left @ box.truncation(dims_in, dims_out) @ right\n",
+    "        if i == 0:\n",
+    "            diagram = diagram_\n",
+    "        else:\n",
+    "            diagram = diagram >> diagram_\n",
+    "\n",
+    "        layer_dims = cod_layer_dims\n",
+    "\n",
+    "    zboxes = tensor.Id(Dim(1))\n",
+    "\n",
+    "    # pylint: disable=invalid-name\n",
+    "    for c in diagram.cod:\n",
+    "        zboxes @= zw.ZBox(1, 1, lambda i: 1).truncation(\n",
+    "            input_dims=[int(c.inside[0])], output_dims=[int(c.inside[0])]\n",
+    "        )\n",
+    "    diagram >>= zboxes\n",
+    "    return diagram\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e19e4271",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 160,
+   "id": "e6a63953",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "d = _get_monomial_layer([2, 0, 1, 3]).get_kraus()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 161,
+   "id": "cc6faece",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#d.to_tensor().foliation().draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 162,
+   "id": "88f71084",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#to_tensor(d).foliation().draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 154,
+   "id": "19729f78",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/svg+xml": [
+       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
+       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
+       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
+       "<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1181.4375pt\" height=\"3758.4pt\" viewBox=\"0 0 1181.4375 3758.4\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
+       " <metadata>\n",
+       "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
+       "   <cc:Work>\n",
+       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
+       "    <dc:date>2025-09-10T16:05:26.720705</dc:date>\n",
+       "    <dc:format>image/svg+xml</dc:format>\n",
+       "    <dc:creator>\n",
+       "     <cc:Agent>\n",
+       "      <dc:title>Matplotlib v3.10.5, https://matplotlib.org/</dc:title>\n",
+       "     </cc:Agent>\n",
+       "    </dc:creator>\n",
+       "   </cc:Work>\n",
+       "  </rdf:RDF>\n",
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+      "text/plain": [
+       "<Figure size 1600x5200 with 1 Axes>"
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+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "chip = chip_mzi(8, 2)\n",
+    "(Create(*[1]*8) >> chip).get_kraus().to_tensor().foliation().draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 188,
+   "id": "4e128eb7",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
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+    "to_tensor((Create(*[1]*8) >> chip).get_kraus()).foliation().draw()"
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+  },
+  {
+   "cell_type": "code",
+   "execution_count": 191,
+   "id": "896f5f67",
+   "metadata": {},
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+    "to_tensor((Create(*[1]*8) >> chip).get_kraus()).foliation().draw()"
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+   "cell_type": "code",
+   "execution_count": 192,
+   "id": "07abf735",
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+       "   </g>\n",
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+       "    <!-- ZBox(1, 1, mode) -->\n",
+       "    <g transform=\"translate(1051.2 3573.959375) scale(0.1 -0.1)\">\n",
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+       "     <use xlink:href=\"#DejaVuSans-29\" transform=\"translate(831.347656 0)\"/>\n",
+       "    </g>\n",
+       "   </g>\n",
+       "  </g>\n",
+       " </g>\n",
+       " <defs>\n",
+       "  <clipPath id=\"p33214988cf\">\n",
+       "   <rect x=\"14.71875\" y=\"7.2\" width=\"1152\" height=\"3672\"/>\n",
+       "  </clipPath>\n",
+       " </defs>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 1600x5100 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "to_tensor((chip).get_kraus()).foliation().draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5ca90920",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "335306fa",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "893f207e",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "517b6976",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "51635d8f",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9f89239e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# IF THE DIAGRAM IS ONLY COMPOSED OF LO BOXES\n",
+    "def dims_for_lo_boxes(diagram: Diagram, input_dims: List[int]) -> List[Tuple[Box, int]]:\n",
+    "    prev_layers: List[Tuple[int, Box]] = []\n",
+    "    dims_for_boxes: List[Tuple[Box, int]] = []\n",
+    "\n",
+    "\n",
+    "    assert len(diagram.dom) == len(input_dims), (\n",
+    "        f\"Input dims length {len(input_dims)} does not match number of input wires {len(diagram.dom)}\"\n",
+    "    )\n",
+    "    number_of_input_layer_wires = len(diagram.dom)\n",
+    "\n",
+    "    #post_selections = get_postselections(diagram)\n",
+    "\n",
+    "    for box, left_offset in zip(\n",
+    "        diagram.boxes,\n",
+    "        diagram.offsets,\n",
+    "        #post_selections\n",
+    "    ):\n",
+    "        right_offset = calculate_right_offset(\n",
+    "            number_of_input_layer_wires, left_offset, len(box.dom)\n",
+    "        )\n",
+    "\n",
+    "        # light-cone at the current layer inputs\n",
+    "        wires_in_light_cone: List[bool] = (\n",
+    "            [False] * left_offset\n",
+    "            + [True] * len(box.dom)\n",
+    "            + [False] * right_offset\n",
+    "        )\n",
+    "\n",
+    "        dim_for_box = 0\n",
+    "\n",
+    "        # walk backwards through previous layers\n",
+    "        #used_ps = []\n",
+    "\n",
+    "        for previous_left_offset, previous_box in prev_layers[::-1]:\n",
+    "            previous_right_offset = calculate_right_offset(\n",
+    "                len(wires_in_light_cone), previous_left_offset, len(previous_box.cod)\n",
+    "            )\n",
+    "\n",
+    "            if is_previous_box_connected_to_current_box(\n",
+    "                wires_in_light_cone,\n",
+    "                previous_left_offset,\n",
+    "                len(previous_box.cod),\n",
+    "                previous_right_offset,\n",
+    "            ):\n",
+    "\n",
+    "                if isinstance(previous_box, zw.Create):\n",
+    "                    idxs = get_previous_box_cod_index_in_light_cone(\n",
+    "                        wires_in_light_cone,\n",
+    "                        previous_left_offset,\n",
+    "                        len(previous_box.cod),\n",
+    "                        previous_right_offset,\n",
+    "                    )\n",
+    "                    dim_for_box += sum(previous_box.photons[i] for i in idxs)\n",
+    "\n",
+    "            # for p in ps:\n",
+    "            #     if p[0] not in used_ps:\n",
+    "            #         dim_for_box -= p[1]\n",
+    "            #         used_ps.append(p[0])\n",
+    "\n",
+    "            wires_in_light_cone = update_connections(\n",
+    "                wires_in_light_cone,\n",
+    "                previous_left_offset,\n",
+    "                previous_box,\n",
+    "                previous_right_offset,\n",
+    "            )\n",
+    "\n",
+    "        dim_for_box += sum(1*dim for wire, dim in zip(wires_in_light_cone, input_dims) if wire)\n",
+    "\n",
+    "        dims_for_boxes.append((box, dim_for_box + 1))\n",
+    "        if isinstance(box, LO_ELEMENTS):\n",
+    "            prev_layers.append((left_offset, box))\n",
+    "        else:\n",
+    "            pass\n",
+    "\n",
+    "        number_of_input_layer_wires += -len(box.dom) + len(box.cod)\n",
+    "\n",
+    "    return dims_for_boxes"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4d726481",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# IF THE DIAGRAM IS ONLY COMPOSED OF LO BOXES\n",
+    "def get_postselections(diagram: Diagram) -> List[Tuple[Box, int]]:\n",
+    "    diagram = diagram.dagger()\n",
+    "    prev_layers: List[Tuple[int, Box]] = []\n",
+    "    postselection_for_boxes: List[Tuple[Box, int]] = []\n",
+    "\n",
+    "    number_of_input_layer_wires = len(diagram.dom)\n",
+    "\n",
+    "    for box, left_offset in zip(diagram.boxes, diagram.offsets):\n",
+    "        right_offset = calculate_right_offset(\n",
+    "            number_of_input_layer_wires, left_offset, len(box.dom)\n",
+    "        )\n",
+    "\n",
+    "        # light-cone at the current layer inputs\n",
+    "        wires_in_light_cone: List[bool] = (\n",
+    "            [False] * left_offset\n",
+    "            + [True] * len(box.dom)\n",
+    "            + [False] * right_offset\n",
+    "        )\n",
+    "\n",
+    "        postselections_for_box = []\n",
+    "\n",
+    "        # walk backwards through previous layers\n",
+    "        for previous_left_offset, previous_box in prev_layers[::-1]:\n",
+    "            previous_right_offset = calculate_right_offset(\n",
+    "                len(wires_in_light_cone), previous_left_offset, len(previous_box.cod)\n",
+    "            )\n",
+    "\n",
+    "            if is_previous_box_connected_to_current_box(\n",
+    "                wires_in_light_cone,\n",
+    "                previous_left_offset,\n",
+    "                len(previous_box.cod),\n",
+    "                previous_right_offset,\n",
+    "            ):\n",
+    "\n",
+    "                if isinstance(previous_box, zw.Create):\n",
+    "                    idxs = get_previous_box_cod_index_in_light_cone(\n",
+    "                        wires_in_light_cone,\n",
+    "                        previous_left_offset,\n",
+    "                        len(previous_box.cod),\n",
+    "                        previous_right_offset,\n",
+    "                    )\n",
+    "                    postselections_for_box.append(\n",
+    "                        (id(previous_box), sum(previous_box.photons[i] for i in idxs))\n",
+    "                    )\n",
+    "\n",
+    "            wires_in_light_cone = update_connections(\n",
+    "                wires_in_light_cone,\n",
+    "                previous_left_offset,\n",
+    "                previous_box,\n",
+    "                previous_right_offset,\n",
+    "            )\n",
+    "\n",
+    "        postselection_for_boxes.append((postselections_for_box))\n",
+    "        if isinstance(box, LO_ELEMENTS):\n",
+    "            prev_layers.append((left_offset, box))\n",
+    "        else:\n",
+    "            pass\n",
+    "\n",
+    "        number_of_input_layer_wires += -len(box.dom) + len(box.cod)\n",
+    "\n",
+    "    return postselection_for_boxes[::-1]"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": ".venv",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

From 19b80169ed44083e7a6ffc57b5d24a1f5ddf60fe Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Fri, 19 Sep 2025 12:19:05 +0100
Subject: [PATCH 43/59] fix tests

---
 optyx/core/channel.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index 26a58fc4..577d6e21 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -390,9 +390,9 @@ def to_dual_rail(self):
 
         return frobenius.Functor(
             ob=lambda x: qmode**(2*len(x)),
-            ar=lambda arr: arr.to_dual_rail(),
+            ar=lambda arr: arr._to_dual_rail(),
             cod=frobenius.Category(Ty, Diagram),
-        )(self._decomp())
+        )(self.decomp())
 
     def to_tket(self):
         """

From 82a33a43f3b5d80f0d042c8890519465387d20a1 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Wed, 24 Sep 2025 18:45:03 +0100
Subject: [PATCH 44/59] remove debugging code

---
 optyx/core/diagram.py | 40 ++++++++++++++++++++--------------------
 1 file changed, 20 insertions(+), 20 deletions(-)

diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index 58d6b346..e1ea90ab 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -374,26 +374,26 @@ def to_tensor(
         diagram >>= zboxes
         return diagram
 
-    # @classmethod
-    # def from_bosonic_operator(cls, n_modes, operators, scalar=1):
-    #     """Create a :class:`zw` diagram from a bosonic operator."""
-    #     # pylint: disable=import-outside-toplevel
-    #     from optyx.core import zw
-
-    #     # pylint: disable=invalid-name
-    #     d = cls.id(Mode(n_modes))
-    #     annil = zw.Split(2) >> zw.Select(1) @ zw.Id(1)
-    #     create = annil.dagger()
-    #     for idx, dagger in operators:
-    #         if not 0 <= idx < n_modes:
-    #             raise ValueError(f"Index {idx} out of bounds.")
-    #         box = create if dagger else annil
-    #         d = d >> zw.Id(idx) @ box @ zw.Id(n_modes - idx - 1)
-
-    #     if scalar != 1:
-    #         # pylint: disable=invalid-name
-    #         d = Scalar(scalar) @ d
-    #     return d
+    @classmethod
+    def from_bosonic_operator(cls, n_modes, operators, scalar=1):
+        """Create a :class:`zw` diagram from a bosonic operator."""
+        # pylint: disable=import-outside-toplevel
+        from optyx.core import zw
+
+        # pylint: disable=invalid-name
+        d = cls.id(Mode(n_modes))
+        annil = zw.Split(2) >> zw.Select(1) @ zw.Id(1)
+        create = annil.dagger()
+        for idx, dagger in operators:
+            if not 0 <= idx < n_modes:
+                raise ValueError(f"Index {idx} out of bounds.")
+            box = create if dagger else annil
+            d = d >> zw.Id(idx) @ box @ zw.Id(n_modes - idx - 1)
+
+        if scalar != 1:
+            # pylint: disable=invalid-name
+            d = Scalar(scalar) @ d
+        return d
 
     def to_pyzx(self):
         # pylint: disable=import-outside-toplevel

From 67f588b06f901bd1e937927cebd168316bdd19f8 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Mon, 6 Oct 2025 11:16:38 +0100
Subject: [PATCH 45/59] new readme

---
 README.md                                     |  770 +++++++-
 docs/notebooks/readme_example.ipynb           |  949 +++++-----
 .../readme_example_33_0.svg                   | 1685 +++++++++++++++++
 .../readme_example_38_2.svg                   | 1226 ++++++++++++
 .../readme_example_42_2.svg                   | 1128 +++++++++++
 .../readme_example_47_0.svg                   | 1573 +++++++++++++++
 .../readme_example_52_0.svg                   | 1309 +++++++++++++
 .../readme_example_55_1.svg                   |  830 ++++++++
 .../readme_example_5_0.svg                    |  368 ++++
 .../readme_example_61_0.svg                   |  200 ++
 .../readme_example_6_0.svg                    |  535 ++++++
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diff --git a/README.md b/README.md
index 228b0c0c..c7e63af1 100644
--- a/README.md
+++ b/README.md
@@ -1,37 +1,777 @@
-# optyx
+# Optyx: A ZX-based Python library for networked quantum architectures
 
-Compiler for photonics technologies
+Optyx is an open-source Python library for designing, simulating, and optimizing networked, hybrid qubit–photon architectures. It offers a compositional, ZX/ZW-based string-diagram front end (built within the DisCoPy ecosystem) that lets you specify experiments mixing qubit registers with discrete-variable photonic modes, lossy channels, heralded measurements, and classical/quantum feedback. Optyx compiles these diagrams to optimized tensor networks and executes them with state-of-the-art contraction backends (Quimb + Cotengra), delivering substantial speedups on low-depth circuits. The result is an end-to-end workflow—from high-level syntax to numerics—well-suited for rapid prototyping of qubit-photon experiments.
 
-# Development
+## Basic Optyx syntax: the Hong-Ou-Mandel effect
 
-## Format the code
+We will present the basics of Optyx with a simple example from linear optics.
 
+The Hong–Ou–Mandel (HOM) effect is a two-photon interference phenomenon where indistinguishable photons entering a 50:50 beamsplitter “bunch” and exit together through the same port. When their temporal, spectral, polarization, and spatial modes overlap perfectly, destructive interference suppresses the outcome with one photon in each output. This effect is a standard benchmark for photon indistinguishability and alignment in photonic experiments.
+
+### Experiment definition
+
+Circuits in Optyx are diagrams made of typed wires (qubits, photonic modes, classical bits) and generators (gates, sources, optics, measurements). You build them by connecting outputs to inputs (sequence) and placing blocks side-by-side (parallel); types must match at every connection. Generators carry parameters and labels; measurements produce classical wires you can route into later blocks. A circuit is just the set of generators plus the wiring between their ports.
+
+Let us build a diagram to study the HOM effect.
+
+
+```python
+from optyx.photonic import BBS
+
+# diagram generators:
+# beam-splitter
+beam_splitter = BBS(0)
+beam_splitter.draw()
+```
+
+
+
+![svg](./docs/notebooks/readme_example_files/readme_example_5_0.svg)
+
+
+
+
+```python
+from optyx.photonic import Create
+
+# diagram composition with monoidal syntax
+# create two single-photon states and send them to a beam-splitter
+hong_ou_mandel = (
+    Create(1) @ Create(1) >>
+    beam_splitter
+)
+
+hong_ou_mandel.draw()
+```
+
+
+
+![svg](./docs/notebooks/readme_example_files/readme_example_6_0.svg)
+
+
+
+The result of this experiment should be a zero probability of having single photons in two output modes:
+
+ ![HOM](./docs/notebooks/hom.png "Hong-Ou-Mandel Effect")
+
+### Diagram evaluation
+
+Call `diagram.eval()` to evaluate a diagram (Quimb backend by default). It returns an evaluated object; use `.tensor.array` to extract the numeric tensor/array, or `.prob_dist()` to get an outcome distribution. You can chain it inline, e.g., `(...).eval().tensor.array`.
+
+
+```python
+# an amplitude (raw result of tensor contraction)
+from optyx.classical import Select
+(
+    hong_ou_mandel >> Select(1, 1)
+).eval().tensor.array
+```
+
+
+
+
+    array(-0.+0.j)
+
+
+
+
+```python
+hong_ou_mandel.eval().prob_dist()
+```
+
+
+
+
+    {(0, 2): 0.5, (1, 1): 4.9303806576313227e-32, (2, 0): 0.5}
+
+
+
+## Function syntax and backends: qubit teleportation
+
+Quantum teleportation transfers an unknown qubit state from sender (Alice) to receiver (Bob) using shared entanglement and two classical bits. Alice performs a joint Bell-state measurement on the unknown qubit and her half of an entangled pair, which projects Bob’s distant qubit into a state related to the original. She sends the two-bit outcome to Bob, who applies a corresponding Pauli correction (I, X, Z, or XZ) to recover the exact state. No information travels faster than light and the original is destroyed by measurement, so the state is relocated—not copied.
+
+https://en.wikipedia.org/wiki/Quantum_teleportation#/media/File:Quantum_teleportation_circuit.svg :
+
+<img src="./docs/notebooks/teleport.svg" alt="Teleportation Protocol" width="800" style="max-width:100%;">
+
+
+```python
+from optyx import qubit, bit
+from optyx.qubits import Scalar
+
+from optyx import Channel
+from optyx.qubits import Z, X, H, Measure, Scalar, qubit, bit
+from optyx.classical import BitControlledGate
+```
+
+### Define the protocol
+
+
+Instead of wiring generators together with sequential (`>>`) and parallel (`@`) composition (which we call the monoidal syntax), you can treat each generator as a **function on its domain wires**. You **label the wires** and then **call generators with those labels**, which lets you feed specific wires directly into the right box without inserting explicit `Swap`s to reorder them. This makes complex diagrams easier to read and write, and mirrors the style used in **Guppy**; it’s an alternative surface syntax that’s equivalent to the usual `>>`/`@` composition.
+
+
+
+```python
+# function syntax
+# CNOT from ZX generators
+
+@Channel.from_callable(
+  dom=qubit @ qubit, cod=qubit @ qubit
+)
+def cnot(a, b):
+  c, d = Z(1, 2)(a)
+  Scalar(2 ** 0.5)()
+  return c, X(2, 1)(d, b)
+```
+
+
+```python
+bell = Scalar(0.5 ** 0.5) @ Z(0, 2)
+
+@Channel.from_callable(
+  dom=qubit, cod=qubit
+)
+def teleportation(c):
+  a, b = bell()
+  cc, aa = cnot(c, a)
+  c_ = Measure(1)(H()(cc))
+  a_ = Measure(1)(aa)
+  bb = BitControlledGate(X(1, 1, 0.5))(a_, b)
+  return BitControlledGate(Z(1, 1, 0.5))(c_, bb)
+```
+
+
+```python
+# function syntax avoids explicit swaps and identity wires
+# this is the equivalent monoidal syntax:
+
+teleportation_monoidal_syntax = (
+    qubit @ bell >>
+    cnot @ qubit >>
+    H() @ qubit ** 2 >>
+    Measure(1) @ Measure(1) @ qubit >>
+    bit @ BitControlledGate(X(1, 1, 0.5)) >>
+    BitControlledGate(Z(1, 1, 0.5))
+)
+```
+
+### Verify the protocol
+
+
+```python
+import numpy as np
+from optyx.qubits import Id
+
+# both implementations are equivalent
+np.allclose(
+    teleportation.eval().tensor.array,
+    teleportation_monoidal_syntax.eval().tensor.array,
+    Id(1).double().to_tensor().eval().array
+)
+```
+
+
+
+
+    True
+
+
+
+Optyx evaluates diagrams via pluggable backends. By default it compiles a diagram to a tensor network, optimizes a contraction path with **cotengra**, and contracts it with **quimb** (CPU/GPU; dense/sparse). For linear-optical circuits, Optyx also exposes a **Perceval** backend using permanent-based algorithms, and a tensor-network-based **DisCoPy** backend; you can choose among these depending on the task.
+
+
+
+```python
+# backends (Perceval, Discopy, Quimb)
+
+from optyx.core.backends import (
+    DiscopyBackend,
+    QuimbBackend
+)
+
+np.allclose(
+    teleportation.eval(DiscopyBackend()).tensor.array,
+    teleportation.eval(QuimbBackend()).tensor.array
+)
 ```
-black optyx/
+
+
+
+
+    True
+
+
+
+## Approximate contraction and photon loss: fusion teleportation
+
+Teleportation with **fusion measurements** uses a Bell pair of dual-rail qubits as the channel: Alice fuses the input with her half using a Type-II fusion, reads the classical outcomes, and Bob applies the corresponding correction. In the **success** branch, the overall map is the **identity** on the teleported qubit up to a known Pauli byproduct, which Bob removes with a conditioned \(X\) correction. In the **failure** branch, the input is effectively measured and the opposite state is prepared at the output. For the standard Type-II scheme this yields identity with probability \(1/2\), and failure otherwise; the paper’s diagrams show both branches explicitly and how the correction restores the state.
+
+
+Ursin, R., Jennewein, T., Aspelmeyer, M. et al. Quantum teleportation across the Danube. Nature 430, 849 (2004). https://doi.org/10.1038/430849a :
+
+<img src="./docs/notebooks/teleportation_danube.png" alt="Fusion teleportation across the Danube" width="1150px">
+
+Graphically, the fusion measurement we would like to use, takes the following form:
+
+<img src="./docs/notebooks/fusion_ii.png" alt="Fusion measurement" width="1200px">
+
+
+where $\underline{a}, \underline{b}, \underline{c}, \underline{d}$ are the measurement outcomes as the measured photon numbers.
+
+$\underline{s} = \underline{a} \oplus \underline{b}$
+
+$\underline{k} = \underline{s} (\underline{b} + \underline{d}) + \neg \underline s (1 - \frac{\underline{a} + \underline{b}}{2})$
+
+### Define the protocol
+
+
+```python
+from optyx.photonic import DualRail
+
+dual_rail_encoded_bell = (
+    bell >>
+    DualRail(1) @ DualRail(1)
+)
 ```
 
-## Lint the code
 
+```python
+from optyx.classical import PostselectBit, BitControlledGate
+from optyx.photonic import Phase
+from optyx.photonic import HadamardBS, qmode
+
+# postselect on fusion success
+fusion_failure_processing = PostselectBit(1)
+
+# apply the box if the control bit is 1, otherwise apply an identity channel
+correction = BitControlledGate(
+    HadamardBS() >>
+    (Phase(0.5) @ qmode) >>
+    HadamardBS()
+)
 ```
-pflake8 optyx/
-pylint optyx/
+
+
+```python
+from optyx.photonic import FusionTypeII
+
+@Channel.from_callable(
+    dom=qubit, cod=qmode @ qmode
+)
+def fusion_teleportation(a):
+    dual_rail_encoded_input = DualRail(1)(a)
+    b, c, d, e = dual_rail_encoded_bell()
+    s, k = FusionTypeII()(*dual_rail_encoded_input, b, c)
+    fusion_failure_processing(s)
+    dr_output_1, dr_output_2 = correction(k, d, e)
+    return dr_output_1, dr_output_2
 ```
 
-## Test the code
+
+```python
+from optyx.photonic import FusionTypeII
+
+fusion_teleportation_monoidal_syntax = (
+    DualRail(1) @ dual_rail_encoded_bell >>
+    FusionTypeII() @ qmode**2 >>
+    fusion_failure_processing @ correction
+)
+
+fusion_teleportation_monoidal_syntax.foliation().draw(figsize=(8, 8))
 
 ```
-pytest .
+
+
+
+![svg](./docs/notebooks/readme_example_files/readme_example_33_0.svg)
+
+
+
+### Verify the protocol
+
+
+```python
+import numpy as np
+from optyx.photonic import Id
+
+array_teleportation = fusion_teleportation_monoidal_syntax.eval().tensor.array
+array_dr = (DualRail(1) @ Scalar(0.5**0.5)).double().to_tensor().eval().array
+
+np.allclose(array_teleportation[:, :, :2, :2, :2, :2], array_dr)
+
 ```
 
-## Test the code and produce coverage statistics
 
+
+
+    True
+
+
+
+### Approximate contraction with Quimb and Cotengra
+
+Approximate contraction in Optyx uses cotengra to plan a low-cost contraction with memory-aware slicing, then executes it in quimb with optional compression of intermediates. Instead of multiplying tensors exactly, large merges are factorized and truncated (e.g., SVD) so only the dominant singular components are kept; you trade speed and memory for a controlled approximation error. Tightening the truncation tolerance (or increasing the allowed bond size) yields higher accuracy at higher cost, while more aggressive truncation/slicing gives faster, lower-memory contractions with small, quantifiable loss in fidelity.
+
+
+```python
+def _flat(x):
+    return np.asarray(x, dtype=complex).ravel()
+
+def cosine_similarity(SU, SV):
+    a, b = _flat(SU), _flat(SV)
+    num = abs(np.vdot(a, b))
+    den = np.linalg.norm(a) * np.linalg.norm(b)
+    if den == 0:
+        return 0.0
+    return float(num / den)
 ```
-coverage run -m pytest .
-coverage report --fail-under=95 --show-missing
+
+
+```python
+from cotengra import HyperCompressedOptimizer
+
+# cosine similarity between the result of exact contaction and approximate contraction for different chis
+errors = []
+for chi in range(1, 6):
+    optimiser = HyperCompressedOptimizer(
+        chi=chi
+    )
+    error_for_chi = []
+    for _ in range(10):
+         error_for_chi.append(
+             cosine_similarity(
+                 fusion_teleportation.eval(QuimbBackend(optimiser)).tensor.array,
+                 array_teleportation
+             )
+         )
+    errors.append(np.median(error_for_chi))
+
+import matplotlib.pyplot as plt
+plt.plot(range(1, 6), errors, marker='o')
+plt.grid()
+plt.xlabel('Chi')
+plt.ylabel('Average cosine similarity')
+plt.title('Fusion-based Teleportation similarity vs Contraction Chi')
+
 ```
 
-## Build the documentation
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
 
+
+
+
+
+    Text(0.5, 1.0, 'Fusion-based Teleportation similarity vs Contraction Chi')
+
+
+
+
+
+![svg](./docs/notebooks/readme_example_files/readme_example_38_2.svg)
+
+
+
+### Photon loss and channel fidelity
+
+Photon loss is when a photon that should arrive simply doesn’t, so counts drop and patterns get noisier. In Optyx, you model this by placing a dedicated loss generator exactly where the loss occurs; its single parameter is the photon survival probability. Photon loss is the primary failure mode for photonic qubits. In photonic computing it breaks multi-photon interference and reduces the success of fusion/measurement steps. That’s why if we want to study architectures, thresholds, and mitigation (repeaters, multiplexing, loss-tolerant encodings), we need to be able to model photon loss accurately.
+
+
+```python
+from optyx.photonic import FusionTypeII, PhotonLoss
+
+# photo loss is one of the main error sources in photonic quantum computing
+def fusion_teleportation_with_photon_loss(p):
+    @Channel.from_callable(
+        dom=qubit, cod=qmode**2
+    )
+    def fusion_teleportation(a):
+        dr_input_1, dr_input_2 = DualRail(1)(a)
+        b, c, d, e = dual_rail_encoded_bell()
+        # apply photon loss to all modes here:
+        #-----------------------------------
+        dr_input_1_loss, dr_input_2_loss, b_loss, c_loss, d_loss, e_loss = (
+            PhotonLoss(p)(dr_input_1), PhotonLoss(p)(dr_input_2),
+            PhotonLoss(p)(b), PhotonLoss(p)(c),
+            PhotonLoss(p)(d), PhotonLoss(p)(e)
+        )
+        #-----------------------------------
+        s, k = FusionTypeII()(dr_input_1_loss, dr_input_2_loss, b_loss, c_loss)
+        fusion_failure_processing(s)
+        output_rail_1, output_rail = correction(k, d_loss, e_loss)
+        return output_rail_1, output_rail
+    return fusion_teleportation
 ```
-sphinx-build docs docs/_build/html
+
+
+```python
+from optyx.core.channel import Spider, Diagram
+
+def get_perm(n):
+    return sorted(sorted(list(range(n))), key=lambda i: i % 2)
+
+def channel_fidelity(diagram_1, diagram_2):
+    bell_1 = Channel.tensor(*[Spider(0, 2, ty) for ty in diagram_1.dom])
+    permutation_1 = Diagram.permutation(get_perm(len(bell_1.cod)), bell_1.cod)
+
+    bell_2 = Channel.tensor(*[Spider(0, 2, ty) for ty in diagram_2.dom])
+    permutation_2 = Diagram.permutation(get_perm(len(bell_2.cod)), bell_2.cod)
+
+    choi_1 = bell_1 >> permutation_1 >> (diagram_1 @ diagram_1.dom)
+    choi_2 = bell_2 >> permutation_2 >> (diagram_2 @ diagram_2.dom)
+
+    return (choi_1 >> choi_2.dagger()).eval().tensor.array
+
+```
+
+
+```python
+import numpy as np
+import matplotlib.pyplot as plt
+
+ps = np.linspace(0.0, 1.0, 20)
+
+# compute fidelity for different photon loss probabilities
+F_avg_vals = []
+succ_probs = []
+for p in ps:
+    S_impl = fusion_teleportation_with_photon_loss(p)
+    S_tgt  = fusion_teleportation_monoidal_syntax
+    s = channel_fidelity(S_impl, S_tgt)
+
+    succ_probs.append(s)
+
+plt.figure()
+plt.plot(ps, succ_probs, marker='o')
+plt.grid(True)
+plt.xlabel('Photon Survival Probability (p)')
+plt.ylabel('Fidelity')
+plt.title('Fusion-based Teleportation: Photon Survival Probability vs Fidelity')
+
+```
+
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part
+      return math.isfinite(val)
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part
+      return np.asarray(x, float)
+
+
+
+
+
+    Text(0.5, 1.0, 'Fusion-based Teleportation: Photon Survival Probability vs Fidelity')
+
+
+
+
+
+![svg](./docs/notebooks/readme_example_files/readme_example_42_2.svg)
+
+
+
+## Photon distinguishability: distributed entanglement generation
+
+Distributed entanglement generation links two distant quantum nodes (A and B) by creating a shared entangled pair. Each node emits a photon that travels to a shared site, where the photons interfere and a joint (Bell-state) detection flags success — instantly projecting A and B into an entangled state. Because attempts often fail due to loss, the process is repeated-until-success with timing. This is the core primitive behind quantum networks and repeaters, enabling long-distance QKD, teleportation, and multi-node protocols.
+
+Main, D., Drmota, P., Nadlinger, D.P. et al. Distributed quantum computing across an optical network link. Nature 638, 383–388 (2025). https://doi.org/10.1038/s41586-024-08404-x~ :
+
+![Distributed entanglement](./docs/notebooks/distributed_entanglement.png "An example of distributed entanglement generation")
+
+
+
+### Fusion and photon distinguishability
+
+#### Define the protocol
+
+
+```python
+from optyx.qubits import Z, Scalar, Id, Measure
+from optyx.photonic import DualRail
+from optyx.classical import PostselectBit
+from discopy.drawing import Equation
+
+bell_state = Z(0, 2) @ Scalar(0.5 ** 0.5)
+
+# generators introducing new qubits accepting internal states
+internal_state_1 = [1, 0]
+internal_state_2 = [0, 1]
+dual_rail_encoding = lambda state: DualRail(1, internal_states=[state])
+encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(internal_state_2)
+
+# postselect on fusion success and no errors
+post_select = PostselectBit(1) @ PostselectBit(0)
+
+protocol = (
+    bell_state @ bell_state >>
+    Id(1) @ (encoding_layer >> FusionTypeII() >> post_select) @ Id(1)
+)
+measure = Measure(2)
+
+Equation(protocol >> measure, bell_state >> measure).draw(figsize=(8, 8))
+```
+
+
+
+![svg](./docs/notebooks/readme_example_files/readme_example_47_0.svg)
+
+
+
+#### Define a set of internal states with varying degrees of distinguishability
+
+We test how partial photon distinguishability affects a heralded entanglement link. The experiment uses the overlap between two internal two-mode states (`rotated_unit_vectors`), encodes them into dual-rail photons (`dual_rail_encoding`), and performs a Type-II fusion with postselection (`FusionTypeII() >> post_select`). We then project onto the target Bell state (`... >> bell_state.dagger()`) to read off the heralded-state quality, and use a discard step (`... >> Discard(2)`) to extract the success probability. Plotting these versus the state overlap reveals how distinguishability simultaneously degrades fidelity and lowers the entanglement generation rate.
+
+
+
+```python
+import math
+
+# internal states - 2 dimensional - move further and further apart
+def rotated_unit_vectors(n: int = 10):
+    for i in range(n):
+        theta = i * (math.pi / 2) / (n - 1)
+        yield (math.cos(theta), math.sin(theta))
+
+unit_vectors = list(rotated_unit_vectors(15))
+```
+
+#### Run the experiments
+
+
+```python
+from optyx.qubits import Discard
+
+inner_product_states = []
+inner_product_bell_states = []
+
+result_bell = bell_state.eval().tensor.array.flatten()
+result_bell = result_bell / np.linalg.norm(result_bell)
+
+for vector in unit_vectors:
+    encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(vector)
+    experiment = bell_state @ bell_state >> Id(1) @ (encoding_layer >> FusionTypeII()
+                                                                                >> post_select) @ Id(1)
+
+    f = (experiment >> bell_state.dagger()).inflate(2).eval().tensor.array
+    normalisation = (experiment >> Discard(2)).inflate(2).eval().tensor.array
+
+    inner_product_states.append(np.inner(vector, internal_state_1))
+    inner_product_bell_states.append(f/normalisation)
+```
+
+
+```python
+import matplotlib.pyplot as plt
+
+plt.figure(figsize=(6, 4))
+plt.plot(inner_product_states, inner_product_bell_states, marker='o')
+plt.xlabel('<Internal state 1 | Internal state 2>')
+plt.ylabel('<Result | Bell State> (fidelity)')
+plt.title('Fidelity of the resulting state with the perfect Bell state')
+plt.grid(True)
+plt.show()
+```
+
+
+
+![svg](./docs/notebooks/readme_example_files/readme_example_52_0.svg)
+
+
+
+## Interfacing with external libraries
+
+### Graphix
+
+Open graphs supported only for now (graph + measurements; desire to implement deterministically - no corrections)
+
+
+```python
+import graphix
+
+circuit = graphix.Circuit(2)
+circuit.cnot(0, 1)
+
+pattern = circuit.transpile().pattern
+
+pattern.draw_graph()
+```
+
+    The pattern is not consistent with flow or gflow structure.
+
+
+
+
+![svg](./docs/notebooks/readme_example_files/readme_example_55_1.svg)
+
+
+
+
+```python
+simulator = graphix.simulator.PatternSimulator(pattern, backend="statevector")
+graphix_result = simulator.run().psi.conj()
+```
+
+
+```python
+from optyx import qubits
+
+optyx_zx = qubits.Circuit(pattern)
+
+optyx_res = (
+    qubits.Ket("+")**2 >> optyx_zx
+).eval().amplitudes()
+```
+
+
+```python
+for keys in optyx_res.keys():
+    assert np.isclose(optyx_res[keys], graphix_result[keys], atol=1e-6)
+```
+
+### Perceval circuits and processors
+
+#### Define the protocol in Perceval
+
+
+```python
+import perceval as pcvl
+
+p = pcvl.Processor("SLOS", 6)
+p.add(0, pcvl.catalog["postprocessed cnot"].build_processor())
+
+p.add(0, pcvl.BS.H())
+p.add(0, pcvl.Detector.pnr())
+p.add(1, pcvl.Detector.pnr())
+p.add(2, pcvl.Detector.pnr())
+p.add(3, pcvl.Detector.pnr())
+
+ff_X = pcvl.FFCircuitProvider(
+  2, 0, pcvl.Circuit(2)
+)
+ff_X.add_configuration(
+  [0, 1], pcvl.PERM([1, 0])
+)
+p.add(2, ff_X)
+
+phi = pcvl.P("phi")
+ff_Z = pcvl.FFConfigurator(
+  2, 3,
+  pcvl.PS(phi),
+  {"phi": 0}
+).add_configuration(
+  [0, 1],
+  {"phi": np.pi}
+)
+p.add(0, ff_Z)
+
+pcvl.pdisplay(p, recursive=True)
+```
+
+
+
+
+
+![svg](./docs/notebooks/readme_example_files/readme_example_61_0.svg)
+
+
+
+
+
+```python
+from optyx.qubits import Ket
+
+state = Ket("+") >> Z(1, 1, 0.3)
+state_array = state.eval().tensor.array
+state_array = state_array / np.linalg.norm(state_array)
+```
+
+#### Evaluate the protocol in Perceval
+
+
+```python
+to_transmit = (complex(state_array[0])*pcvl.BasicState([1, 0]) +
+               complex(state_array[1])*pcvl.BasicState([0, 1]))
+
+sg = pcvl.StateGenerator(pcvl.Encoding.DUAL_RAIL)
+bell_state = sg.bell_state("phi+")
+
+input_state = to_transmit * bell_state
+p.min_detected_photons_filter(2)
+
+input_state *= pcvl.BasicState([0, 0])
+
+p.with_input(input_state)
+```
+
+
+```python
+result_perceval = p.probs()
+```
+
+#### Convert to Optyx and simulate
+
+
+```python
+from optyx import Channel
+
+optyx_diagram = Channel.from_perceval(p)
+```
+
+
+```python
+from optyx.qubits import Scalar, Ket
+from optyx.photonic import DualRail
+
+bell_state = Z(0, 2) @ Scalar(0.5**0.5)
+transmit = Ket("+") >> Z(1, 1, 0.3)
+
+input_state = transmit @ bell_state
+
+protocol = (
+    input_state >>
+    DualRail(3) >>
+    Channel.from_perceval(p)
+)
+```
+
+
+```python
+result_optyx = protocol.eval().prob_dist()
+```
+
+
+```python
+def check_dict_agreement(d1, d2, rtol=1e-5, atol=1e-8):
+    for key in d1.keys() - d2.keys():
+        assert np.isclose(d1[key], 0, rtol=rtol, atol=atol)
+    for key in d2.keys() - d1.keys():
+        assert np.isclose(d2[key], 0, rtol=rtol, atol=atol)
+    for key in d1.keys() & d2.keys():
+        assert np.isclose(d1[key], d2[key], rtol=rtol, atol=atol)
+```
+
+
+```python
+check_dict_agreement(
+    {tuple(k): v for k, v in dict(result_perceval["results"]).items()},
+    result_optyx
+)
+```
+
+
+```python
+
 ```
diff --git a/docs/notebooks/readme_example.ipynb b/docs/notebooks/readme_example.ipynb
index c05af05a..af001cb4 100644
--- a/docs/notebooks/readme_example.ipynb
+++ b/docs/notebooks/readme_example.ipynb
@@ -8,12 +8,30 @@
     "# Optyx: A ZX-based Python library for networked quantum architectures"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "6613f207",
+   "metadata": {},
+   "source": [
+    "Optyx is an open-source Python library for designing, simulating, and optimizing networked, hybrid qubit–photon architectures. It offers a compositional, ZX/ZW-based string-diagram front end (built within the DisCoPy ecosystem) that lets you specify experiments mixing qubit registers with discrete-variable photonic modes, lossy channels, heralded measurements, and classical/quantum feedback. Optyx compiles these diagrams to optimized tensor networks and executes them with state-of-the-art contraction backends (Quimb + Cotengra), delivering substantial speedups on low-depth circuits. The result is an end-to-end workflow—from high-level syntax to numerics—well-suited for rapid prototyping of qubit-photon experiments."
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "b1adf8d9",
    "metadata": {},
    "source": [
-    "## Hong-Ou-Mandel effect"
+    "## Basic Optyx syntax: the Hong-Ou-Mandel effect"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "89511ebf",
+   "metadata": {},
+   "source": [
+    "We will present the basics of Optyx with a simple example from linear optics. \n",
+    "\n",
+    "The Hong–Ou–Mandel (HOM) effect is a two-photon interference phenomenon where indistinguishable photons entering a 50:50 beamsplitter “bunch” and exit together through the same port. When their temporal, spectral, polarization, and spatial modes overlap perfectly, destructive interference suppresses the outcome with one photon in each output. This effect is a standard benchmark for photon indistinguishability and alignment in photonic experiments."
    ]
   },
   {
@@ -21,12 +39,16 @@
    "id": "6f3dab5d",
    "metadata": {},
    "source": [
-    "### Experiment definition"
+    "### Experiment definition\n",
+    "\n",
+    "Circuits in Optyx are diagrams made of typed wires (qubits, photonic modes, classical bits) and generators (gates, sources, optics, measurements). You build them by connecting outputs to inputs (sequence) and placing blocks side-by-side (parallel); types must match at every connection. Generators carry parameters and labels; measurements produce classical wires you can route into later blocks. A circuit is just the set of generators plus the wiring between their ports.\n",
+    "\n",
+    "Let us build a diagram to study the HOM effect."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 3,
    "id": "13dbbb3a",
    "metadata": {},
    "outputs": [
@@ -41,7 +63,7 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-23T09:38:17.988554</dc:date>\n",
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@@ -70,27 +92,27 @@
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        "z\n",
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        "Q 43.2 25.2 43.2 25.2 \n",
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        "    <path d=\"M 115.2 7.2 \n",
        "Q 115.2 25.2 115.2 25.2 \n",
-       "\" clip-path=\"url(#pcb02312399)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_5\">\n",
        "    <path d=\"M 43.2 61.2 \n",
        "Q 43.2 79.2 43.2 79.2 \n",
-       "\" clip-path=\"url(#pcb02312399)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
+       "\" clip-path=\"url(#p7ec12db398)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "   <g id=\"patch_6\">\n",
        "    <path d=\"M 115.2 61.2 \n",
        "Q 115.2 79.2 115.2 79.2 \n",
-       "\" clip-path=\"url(#pcb02312399)\" style=\"fill: none; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -98,7 +120,7 @@
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        "z\n",
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@@ -396,7 +418,7 @@
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        " </g>\n",
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        "  </clipPath>\n",
        " </defs>\n",
@@ -421,7 +443,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 4,
    "id": "79ab4b08",
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        "z\n",
-       "\" clip-path=\"url(#pb5ed9dbb53)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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        "z\n",
-       "\" clip-path=\"url(#pb5ed9dbb53)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -509,7 +531,7 @@
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        "z\n",
-       "\" clip-path=\"url(#pb5ed9dbb53)\" style=\"fill: #ffffff; stroke: #000000; stroke-linejoin: miter\"/>\n",
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@@ -958,7 +980,7 @@
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        " </g>\n",
        " <defs>\n",
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        " </defs>\n",
@@ -976,6 +998,7 @@
     "from optyx.photonic import Create\n",
     "\n",
     "# diagram composition with monoidal syntax\n",
+    "# create two single-photon states and send them to a beam-splitter\n",
     "hong_ou_mandel = (\n",
     "    Create(1) @ Create(1) >>\n",
     "    beam_splitter\n",
@@ -984,6 +1007,14 @@
     "hong_ou_mandel.draw()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "dbdb1109",
+   "metadata": {},
+   "source": [
+    "The result of this experiment should be a zero probability of having single photons in two output modes:"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "a869643c",
@@ -997,12 +1028,14 @@
    "id": "94bfc225",
    "metadata": {},
    "source": [
-    "### Diagram evaluation"
+    "### Diagram evaluation\n",
+    "\n",
+    "Call `diagram.eval()` to evaluate a diagram (Quimb backend by default). It returns an evaluated object; use `.tensor.array` to extract the numeric tensor/array, or `.prob_dist()` to get an outcome distribution. You can chain it inline, e.g., `(...).eval().tensor.array`."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 5,
    "id": "f1478f68",
    "metadata": {},
    "outputs": [
@@ -1012,7 +1045,7 @@
        "array(-0.+0.j)"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1027,7 +1060,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 6,
    "id": "801f0884",
    "metadata": {},
    "outputs": [
@@ -1037,7 +1070,7 @@
        "{(0, 2): 0.5, (1, 1): 4.9303806576313227e-32, (2, 0): 0.5}"
       ]
      },
-     "execution_count": 4,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1051,12 +1084,24 @@
    "id": "b1f34bd2",
    "metadata": {},
    "source": [
-    "## Qubit teleportation - function syntax and backends"
+    "## Function syntax and backends: qubit teleportation\n",
+    "\n",
+    "Quantum teleportation transfers an unknown qubit state from sender (Alice) to receiver (Bob) using shared entanglement and two classical bits. Alice performs a joint Bell-state measurement on the unknown qubit and her half of an entangled pair, which projects Bob’s distant qubit into a state related to the original. She sends the two-bit outcome to Bob, who applies a corresponding Pauli correction (I, X, Z, or XZ) to recover the exact state. No information travels faster than light and the original is destroyed by measurement, so the state is relocated—not copied."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "668cadf7",
+   "metadata": {},
+   "source": [
+    "https://en.wikipedia.org/wiki/Quantum_teleportation#/media/File:Quantum_teleportation_circuit.svg :\n",
+    "\n",
+    "<img src=\"teleport.svg\" alt=\"Teleportation Protocol\" width=\"800\" style=\"max-width:100%;\">"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "id": "47e64a7d",
    "metadata": {},
    "outputs": [],
@@ -1074,7 +1119,10 @@
    "id": "748d7e3d",
    "metadata": {},
    "source": [
-    "### Define the protocol"
+    "### Define the protocol\n",
+    "\n",
+    "\n",
+    "Instead of wiring generators together with sequential (`>>`) and parallel (`@`) composition (which we call the monoidal syntax), you can treat each generator as a **function on its domain wires**. You **label the wires** and then **call generators with those labels**, which lets you feed specific wires directly into the right box without inserting explicit `Swap`s to reorder them. This makes complex diagrams easier to read and write, and mirrors the style used in **Guppy**; it’s an alternative surface syntax that’s equivalent to the usual `>>`/`@` composition.\n"
    ]
   },
   {
@@ -1096,17 +1144,9 @@
     "  return c, X(2, 1)(d, b)"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "668cadf7",
-   "metadata": {},
-   "source": [
-    "<img src=\"teleport.svg\" alt=\"Teleportation Protocol\" width=\"800\" style=\"max-width:100%;\">\n"
-   ]
-  },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 9,
    "id": "8c0301af",
    "metadata": {},
    "outputs": [],
@@ -1127,12 +1167,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 10,
    "id": "174c4713",
    "metadata": {},
    "outputs": [],
    "source": [
     "# function syntax avoids explicit swaps and identity wires\n",
+    "# this is the equivalent monoidal syntax:\n",
     "\n",
     "teleportation_monoidal_syntax = (\n",
     "    qubit @ bell >>\n",
@@ -1154,7 +1195,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 11,
    "id": "bb29783a",
    "metadata": {},
    "outputs": [
@@ -1164,7 +1205,7 @@
        "True"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1181,9 +1222,17 @@
     ")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "3b8a1829",
+   "metadata": {},
+   "source": [
+    "Optyx evaluates diagrams via pluggable backends. By default it compiles a diagram to a tensor network, optimizes a contraction path with **cotengra**, and contracts it with **quimb** (CPU/GPU; dense/sparse). For linear-optical circuits, Optyx also exposes a **Perceval** backend using permanent-based algorithms, and a tensor-network-based **DisCoPy** backend; you can choose among these depending on the task.\n"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 12,
    "id": "25af2db6",
    "metadata": {},
    "outputs": [
@@ -1193,7 +1242,7 @@
        "True"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1217,7 +1266,15 @@
    "id": "36241fe2",
    "metadata": {},
    "source": [
-    "## Fusion teleportation"
+    "## Approximate contraction and photon loss: fusion teleportation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8959a31b",
+   "metadata": {},
+   "source": [
+    "Teleportation with **fusion measurements** uses a Bell pair of dual-rail qubits as the channel: Alice fuses the input with her half using a Type-II fusion, reads the classical outcomes, and Bob applies the corresponding correction. In the **success** branch, the overall map is the **identity** on the teleported qubit up to a known Pauli byproduct, which Bob removes with a conditioned \\(X\\) correction. In the **failure** branch, the input is effectively measured and the opposite state is prepared at the output. For the standard Type-II scheme this yields identity with probability \\(1/2\\), and failure otherwise; the paper’s diagrams show both branches explicitly and how the correction restores the state.\n"
    ]
   },
   {
@@ -1225,7 +1282,7 @@
    "id": "7043700a",
    "metadata": {},
    "source": [
-    "Ursin, R., Jennewein, T., Aspelmeyer, M. et al. Quantum teleportation across the Danube. Nature 430, 849 (2004). https://doi.org/10.1038/430849a\n",
+    "Ursin, R., Jennewein, T., Aspelmeyer, M. et al. Quantum teleportation across the Danube. Nature 430, 849 (2004). https://doi.org/10.1038/430849a :\n",
     "\n",
     "<img src=\"./teleportation_danube.png\" alt=\"Fusion teleportation across the Danube\" width=\"1150px\">"
    ]
@@ -1268,7 +1325,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 13,
    "id": "c557c4b8",
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    "outputs": [],
@@ -1283,7 +1340,7 @@
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-   "execution_count": 16,
+   "execution_count": 14,
    "id": "a1764edb",
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@@ -1305,15 +1362,7 @@
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   {
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-   "execution_count": null,
-   "id": "e83e3857",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 15,
    "id": "7bb5e46f",
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    "outputs": [],
@@ -1334,7 +1383,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 16,
    "id": "4b5ee771",
    "metadata": {},
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    "source": [
-    "### Approximate contraction with Quimb and Cotengra"
+    "### Approximate contraction with Quimb and Cotengra\n",
+    "\n",
+    "Approximate contraction in Optyx uses cotengra to plan a low-cost contraction with memory-aware slicing, then executes it in quimb with optional compression of intermediates. Instead of multiplying tensors exactly, large merges are factorized and truncated (e.g., SVD) so only the dominant singular components are kept; you trade speed and memory for a controlled approximation error. Tightening the truncation tolerance (or increasing the allowed bond size) yields higher accuracy at higher cost, while more aggressive truncation/slicing gives faster, lower-memory contractions with small, quantifiable loss in fidelity."
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    "id": "351608f0",
    "metadata": {},
    "source": [
-    "### Photon loss and channel fidelity"
+    "### Photon loss and channel fidelity\n",
+    "\n",
+    "Photon loss is when a photon that should arrive simply doesn’t, so counts drop and patterns get noisier. In Optyx, you model this by placing a dedicated loss generator exactly where the loss occurs; its single parameter is the photon survival probability. Photon loss is the primary failure mode for photonic qubits. In photonic computing it breaks multi-photon interference and reduces the success of fusion/measurement steps. That’s why if we want to study architectures, thresholds, and mitigation (repeaters, multiplexing, loss-tolerant encodings), we need to be able to model photon loss accurately."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 20,
    "id": "ac439493",
    "metadata": {},
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@@ -4440,7 +4493,9 @@
     "        # apply photon loss to all modes here:\n",
     "        #-----------------------------------\n",
     "        dr_input_1_loss, dr_input_2_loss, b_loss, c_loss, d_loss, e_loss = (\n",
-    "            PhotonLoss(p)(dr_input_1), PhotonLoss(p)(dr_input_2), PhotonLoss(p)(b), PhotonLoss(p)(c), PhotonLoss(p)(d), PhotonLoss(p)(e)\n",
+    "            PhotonLoss(p)(dr_input_1), PhotonLoss(p)(dr_input_2),\n",
+    "            PhotonLoss(p)(b), PhotonLoss(p)(c),\n",
+    "            PhotonLoss(p)(d), PhotonLoss(p)(e)\n",
     "        )\n",
     "        #-----------------------------------\n",
     "        s, k = FusionTypeII()(dr_input_1_loss, dr_input_2_loss, b_loss, c_loss)\n",
@@ -4452,7 +4507,7 @@
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    "id": "7e1a2957",
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    "id": "07c143a0",
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    "source": [
-    "## Distributed entanglement generation"
+    "## Photon distinguishability: distributed entanglement generation\n",
+    "\n",
+    "Distributed entanglement generation links two distant quantum nodes (A and B) by creating a shared entangled pair. Each node emits a photon that travels to a shared site, where the photons interfere and a joint (Bell-state) detection flags success — instantly projecting A and B into an entangled state. Because attempts often fail due to loss, the process is repeated-until-success with timing. This is the core primitive behind quantum networks and repeaters, enabling long-distance QKD, teleportation, and multi-node protocols."
    ]
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   {
@@ -5678,9 +5735,9 @@
    "id": "9fa0ec11",
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    "source": [
-    "![Distributed entanglement](./distributed_entanglement.png \"An example of distributed entanglement generation\")\n",
+    "Main, D., Drmota, P., Nadlinger, D.P. et al. Distributed quantum computing across an optical network link. Nature 638, 383–388 (2025). https://doi.org/10.1038/s41586-024-08404-x~ :\n",
     "\n",
-    "Main, D., Drmota, P., Nadlinger, D.P. et al. Distributed quantum computing across an optical network link. Nature 638, 383–388 (2025). https://doi.org/10.1038/s41586-024-08404-x~\n",
+    "![Distributed entanglement](./distributed_entanglement.png \"An example of distributed entanglement generation\")\n",
     "\n"
    ]
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+   "execution_count": 23,
    "id": "bdb9611d",
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    "id": "eb9f34b3",
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    "source": [
-    "#### Define a set of internal states with varying degrees of distinguishability"
+    "#### Define a set of internal states with varying degrees of distinguishability\n",
+    "\n",
+    "We test how partial photon distinguishability affects a heralded entanglement link. The experiment uses the overlap between two internal two-mode states (`rotated_unit_vectors`), encodes them into dual-rail photons (`dual_rail_encoding`), and performs a Type-II fusion with postselection (`FusionTypeII() >> post_select`). We then project onto the target Bell state (`... >> bell_state.dagger()`) to read off the heralded-state quality, and use a discard step (`... >> Discard(2)`) to extract the success probability. Plotting these versus the state overlap reveals how distinguishability simultaneously degrades fidelity and lowers the entanglement generation rate.\n"
    ]
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-   "execution_count": 27,
+   "execution_count": 24,
    "id": "9e5c4078",
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    "id": "1c50f388",
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-       "     <use xlink:href=\"#md08248b788\" x=\"59.321307\" y=\"233.998125\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
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+       "     <use xlink:href=\"#m63e40f92a1\" x=\"249.08893\" y=\"155.628235\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "     <use xlink:href=\"#m63e40f92a1\" x=\"221.252524\" y=\"176.933606\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
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+       "     <use xlink:href=\"#m63e40f92a1\" x=\"93.399222\" y=\"231.470859\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
+       "     <use xlink:href=\"#m63e40f92a1\" x=\"59.321307\" y=\"233.998125\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
@@ -8691,7 +8750,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p428f56623c\">\n",
+       "  <clipPath id=\"p762c8ca300\">\n",
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@@ -8732,12 +8791,12 @@
    "source": [
     "### Graphix\n",
     "\n",
-    "Open graphs only for now (graph + measurements; desire to implement deterministically - no corrections)"
+    "Open graphs supported only for now (graph + measurements; desire to implement deterministically - no corrections)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 27,
    "id": "79f358ae",
    "metadata": {},
    "outputs": [
@@ -8759,7 +8818,7 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-09-23T09:47:43.571420</dc:date>\n",
+       "    <dc:date>2025-10-06T10:54:29.815082</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
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+       "\" clip-path=\"url(#p4ee765351d)\" style=\"fill: none; stroke-dasharray: 3.7,1.6; stroke-dashoffset: 0; stroke: #000000; stroke-opacity: 0.7\"/>\n",
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+       "\" clip-path=\"url(#p4ee765351d)\" style=\"fill: none; stroke-dasharray: 3.7,1.6; stroke-dashoffset: 0; stroke: #000000; stroke-opacity: 0.7\"/>\n",
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+       "\" clip-path=\"url(#p4ee765351d)\" style=\"fill: none; stroke-dasharray: 3.7,1.6; stroke-dashoffset: 0; stroke: #000000; stroke-opacity: 0.7\"/>\n",
        "   </g>\n",
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        "Q 106.042743 90.36 170.400086 90.36 \n",
-       "\" clip-path=\"url(#p1fd742a0aa)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
+       "\" clip-path=\"url(#p4ee765351d)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
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        "L 166.400086 92.36 \n",
-       "\" clip-path=\"url(#p1fd742a0aa)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
+       "\" clip-path=\"url(#p4ee765351d)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"M 40.024391 87.326433 \n",
        "Q 106.045262 62.640169 171.018913 38.345478 \n",
-       "\" clip-path=\"url(#p1fd742a0aa)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
+       "\" clip-path=\"url(#p4ee765351d)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
        "    <path d=\"M 166.571796 37.873085 \n",
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        "L 167.972729 41.619735 \n",
-       "\" clip-path=\"url(#p1fd742a0aa)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
+       "\" clip-path=\"url(#p4ee765351d)\" style=\"fill: none; stroke: #2ca02c; stroke-linecap: round\"/>\n",
        "   </g>\n",
        "   <g id=\"matplotlib.axis_1\">\n",
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@@ -8940,11 +8999,11 @@
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        "L 170.382137 33.454569 \n",
-       "\" clip-path=\"url(#p1fd742a0aa)\" style=\"fill: none; stroke: #d62728; stroke-linecap: square\"/>\n",
+       "\" clip-path=\"url(#p4ee765351d)\" style=\"fill: none; stroke: #d62728; stroke-linecap: square\"/>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_1\">\n",
        "    <defs>\n",
-       "     <path id=\"md7200e9114\" d=\"M 0 9.354143 \n",
+       "     <path id=\"mc24ce6cc0d\" d=\"M 0 9.354143 \n",
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        "C 9.354143 -2.480748 8.368532 -4.860225 6.614378 -6.614378 \n",
@@ -8956,13 +9015,13 @@
        "z\n",
        "\" style=\"stroke: #ff0000\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#p1fd742a0aa)\">\n",
-       "     <use xlink:href=\"#md7200e9114\" x=\"180.18\" y=\"90.36\" style=\"fill: #d3d3d3; stroke: #ff0000\"/>\n",
+       "    <g clip-path=\"url(#p4ee765351d)\">\n",
+       "     <use xlink:href=\"#mc24ce6cc0d\" x=\"180.18\" y=\"90.36\" style=\"fill: #d3d3d3; stroke: #ff0000\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_2\">\n",
        "    <defs>\n",
-       "     <path id=\"mfd441f340e\" d=\"M 0 9.354143 \n",
+       "     <path id=\"ma19c386aa9\" d=\"M 0 9.354143 \n",
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@@ -8974,13 +9033,13 @@
        "z\n",
        "\" style=\"stroke: #ff0000\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#p1fd742a0aa)\">\n",
-       "     <use xlink:href=\"#mfd441f340e\" x=\"31.911429\" y=\"90.36\" style=\"fill: #add8e6; stroke: #ff0000\"/>\n",
+       "    <g clip-path=\"url(#p4ee765351d)\">\n",
+       "     <use xlink:href=\"#ma19c386aa9\" x=\"31.911429\" y=\"90.36\" style=\"fill: #add8e6; stroke: #ff0000\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_3\">\n",
        "    <defs>\n",
-       "     <path id=\"mbf47868017\" d=\"M 0 9.354143 \n",
+       "     <path id=\"mf334e1dfe0\" d=\"M 0 9.354143 \n",
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@@ -8992,13 +9051,13 @@
        "z\n",
        "\" style=\"stroke: #000000\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#p1fd742a0aa)\">\n",
-       "     <use xlink:href=\"#mbf47868017\" x=\"31.911429\" y=\"34.92\" style=\"fill: #add8e6; stroke: #000000\"/>\n",
+       "    <g clip-path=\"url(#p4ee765351d)\">\n",
+       "     <use xlink:href=\"#mf334e1dfe0\" x=\"31.911429\" y=\"34.92\" style=\"fill: #add8e6; stroke: #000000\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"PathCollection_4\">\n",
        "    <defs>\n",
-       "     <path id=\"m544421308b\" d=\"M 0 9.354143 \n",
+       "     <path id=\"m0ee7112f5b\" d=\"M 0 9.354143 \n",
        "C 2.480748 9.354143 4.860225 8.368532 6.614378 6.614378 \n",
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@@ -9010,8 +9069,8 @@
        "z\n",
        "\" style=\"stroke: #000000\"/>\n",
        "    </defs>\n",
-       "    <g clip-path=\"url(#p1fd742a0aa)\">\n",
-       "     <use xlink:href=\"#m544421308b\" x=\"180.18\" y=\"34.92\" style=\"fill: #d3d3d3; stroke: #000000\"/>\n",
+       "    <g clip-path=\"url(#p4ee765351d)\">\n",
+       "     <use xlink:href=\"#m0ee7112f5b\" x=\"180.18\" y=\"34.92\" style=\"fill: #d3d3d3; stroke: #000000\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"line2d_2\"/>\n",
@@ -9048,7 +9107,7 @@
        "\" style=\"fill: none; stroke: #d62728; stroke-linecap: round\"/>\n",
        "   </g>\n",
        "   <g id=\"text_1\">\n",
-       "    <g clip-path=\"url(#p1fd742a0aa)\">\n",
+       "    <g clip-path=\"url(#p4ee765351d)\">\n",
        "     <!-- 0 -->\n",
        "     <g transform=\"translate(176.3625 93.67125) scale(0.12 -0.12)\">\n",
        "      <defs>\n",
@@ -9079,7 +9138,7 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_2\">\n",
-       "    <g clip-path=\"url(#p1fd742a0aa)\">\n",
+       "    <g clip-path=\"url(#p4ee765351d)\">\n",
        "     <!-- 1 -->\n",
        "     <g transform=\"translate(28.093929 93.67125) scale(0.12 -0.12)\">\n",
        "      <defs>\n",
@@ -9103,7 +9162,7 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_3\">\n",
-       "    <g clip-path=\"url(#p1fd742a0aa)\">\n",
+       "    <g clip-path=\"url(#p4ee765351d)\">\n",
        "     <!-- 2 -->\n",
        "     <g transform=\"translate(28.093929 38.23125) scale(0.12 -0.12)\">\n",
        "      <defs>\n",
@@ -9137,7 +9196,7 @@
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"text_4\">\n",
-       "    <g clip-path=\"url(#p1fd742a0aa)\">\n",
+       "    <g clip-path=\"url(#p4ee765351d)\">\n",
        "     <!-- 3 -->\n",
        "     <g transform=\"translate(176.3625 38.23125) scale(0.12 -0.12)\">\n",
        "      <defs>\n",
@@ -9576,7 +9635,7 @@
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
-       "  <clipPath id=\"p1fd742a0aa\">\n",
+       "  <clipPath id=\"p4ee765351d\">\n",
        "   <rect x=\"7.2\" y=\"7.2\" width=\"345.96\" height=\"110.88\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
@@ -9603,7 +9662,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 28,
    "id": "bff50dee",
    "metadata": {},
    "outputs": [],
@@ -9614,7 +9673,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 29,
    "id": "bf2d9106",
    "metadata": {},
    "outputs": [],
@@ -9630,7 +9689,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 30,
    "id": "908e477d",
    "metadata": {},
    "outputs": [],
@@ -9657,7 +9716,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 31,
    "id": "988c9618",
    "metadata": {},
    "outputs": [
@@ -9866,10 +9925,10 @@
        "</svg>"
       ],
       "text/plain": [
-       "<drawsvg.drawing.Drawing at 0x77ef9ee5ac00>"
+       "<drawsvg.drawing.Drawing at 0x7626025b0860>"
       ]
      },
-     "execution_count": 35,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -9910,7 +9969,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 32,
    "id": "96d5bf6b",
    "metadata": {},
    "outputs": [],
@@ -9932,7 +9991,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 33,
    "id": "bce649df",
    "metadata": {},
    "outputs": [],
@@ -9953,7 +10012,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 34,
    "id": "f0c1fbf3",
    "metadata": {},
    "outputs": [],
@@ -9971,7 +10030,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 35,
    "id": "463bcb6f",
    "metadata": {},
    "outputs": [],
@@ -9983,7 +10042,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 36,
    "id": "3f3fca2d",
    "metadata": {},
    "outputs": [],
@@ -10005,7 +10064,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 37,
    "id": "54633b7a",
    "metadata": {},
    "outputs": [],
@@ -10015,7 +10074,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": 38,
    "id": "e019251e",
    "metadata": {},
    "outputs": [],
@@ -10031,7 +10090,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": 39,
    "id": "ca6102c5",
    "metadata": {},
    "outputs": [],
diff --git a/docs/notebooks/readme_example_files/readme_example_33_0.svg b/docs/notebooks/readme_example_files/readme_example_33_0.svg
new file mode 100644
index 00000000..50bef7f0
--- /dev/null
+++ b/docs/notebooks/readme_example_files/readme_example_33_0.svg
@@ -0,0 +1,1685 @@
+<?xml version="1.0" encoding="utf-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="629.467969pt" height="590.4pt" viewBox="0 0 629.467969 590.4" xmlns="http://www.w3.org/2000/svg" version="1.1">
+ <metadata>
+  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
+   <cc:Work>
+    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+    <dc:date>2025-10-06T10:51:59.571927</dc:date>
+    <dc:format>image/svg+xml</dc:format>
+    <dc:creator>
+     <cc:Agent>
+      <dc:title>Matplotlib v3.10.5, https://matplotlib.org/</dc:title>
+     </cc:Agent>
+    </dc:creator>
+   </cc:Work>
+  </rdf:RDF>
+ </metadata>
+ <defs>
+  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
+ </defs>
+ <g id="figure_1">
+  <g id="patch_1">
+   <path d="M 0 590.4 
+L 629.467969 590.4 
+L 629.467969 0 
+L 0 0 
+z
+" style="fill: #ffffff"/>
+  </g>
+  <g id="axes_1">
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new file mode 100644
index 00000000..7d4c313c
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From 9ba6f39c9e00cbae9b7aba06bf72bc394b87be22 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Mon, 6 Oct 2025 11:31:27 +0100
Subject: [PATCH 46/59] edit README

---
 README.md | 44 --------------------------------------------
 1 file changed, 44 deletions(-)

diff --git a/README.md b/README.md
index c7e63af1..03432c34 100644
--- a/README.md
+++ b/README.md
@@ -354,34 +354,6 @@ plt.ylabel('Average cosine similarity')
 plt.title('Fusion-based Teleportation similarity vs Contraction Chi')
 
 ```
-
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-
-
-
-
-
-    Text(0.5, 1.0, 'Fusion-based Teleportation similarity vs Contraction Chi')
-
-
-
-
-
 ![svg](./docs/notebooks/readme_example_files/readme_example_38_2.svg)
 
 
@@ -463,22 +435,6 @@ plt.ylabel('Fidelity')
 plt.title('Fusion-based Teleportation: Photon Survival Probability vs Fidelity')
 
 ```
-
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part
-      return math.isfinite(val)
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part
-      return np.asarray(x, float)
-
-
-
-
-
-    Text(0.5, 1.0, 'Fusion-based Teleportation: Photon Survival Probability vs Fidelity')
-
-
-
-
-
 ![svg](./docs/notebooks/readme_example_files/readme_example_42_2.svg)
 
 

From 2579896dcd3e7026a2776376d5219d7c7dfa418b Mon Sep 17 00:00:00 2001
From: Mateusz Kupper <mateusz.kupper@gmail.com>
Date: Mon, 6 Oct 2025 11:35:26 +0100
Subject: [PATCH 47/59] Update README with clearer explanations

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 03432c34..7c21e36b 100644
--- a/README.md
+++ b/README.md
@@ -6,7 +6,7 @@ Optyx is an open-source Python library for designing, simulating, and optimizing
 
 We will present the basics of Optyx with a simple example from linear optics.
 
-The Hong–Ou–Mandel (HOM) effect is a two-photon interference phenomenon where indistinguishable photons entering a 50:50 beamsplitter “bunch” and exit together through the same port. When their temporal, spectral, polarization, and spatial modes overlap perfectly, destructive interference suppresses the outcome with one photon in each output. This effect is a standard benchmark for photon indistinguishability and alignment in photonic experiments.
+The Hong–Ou–Mandel (HOM) effect is a two-photon interference phenomenon where indistinguishable photons entering a 50:50 beamsplitter “bunch” and exit together through the same output register. When their temporal, spectral, polarization, and spatial modes overlap perfectly, destructive interference suppresses the outcome with one photon in each output. This effect is a standard benchmark for photon indistinguishability in photonic experiments.
 
 ### Experiment definition
 
@@ -360,7 +360,7 @@ plt.title('Fusion-based Teleportation similarity vs Contraction Chi')
 
 ### Photon loss and channel fidelity
 
-Photon loss is when a photon that should arrive simply doesn’t, so counts drop and patterns get noisier. In Optyx, you model this by placing a dedicated loss generator exactly where the loss occurs; its single parameter is the photon survival probability. Photon loss is the primary failure mode for photonic qubits. In photonic computing it breaks multi-photon interference and reduces the success of fusion/measurement steps. That’s why if we want to study architectures, thresholds, and mitigation (repeaters, multiplexing, loss-tolerant encodings), we need to be able to model photon loss accurately.
+Photon loss is when a photon that should arrive simply doesn’t. In Optyx, you model this by placing a dedicated loss generator exactly where the loss occurs; its single parameter is the photon survival probability. Photon loss is the primary failure mode for photonic qubits. In photonic computing it breaks multi-photon interference and reduces the success of fusion/measurement steps. That’s why if we want to study architectures, thresholds, and mitigation (repeaters, multiplexing, loss-tolerant encodings), we need to be able to model photon loss accurately.
 
 
 ```python

From 4400c20efb8b1563f7e811c0b6e1192f2b59a707 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Mon, 6 Oct 2025 13:39:17 +0100
Subject: [PATCH 48/59] pyzx in readme

---
 docs/notebooks/readme_example.ipynb           | 2725 ++++++++++++++---
 docs/notebooks/readme_example.md              | 1163 +++++++
 .../readme_example_25_0.svg                   | 1229 ++++++++
 .../readme_example_40_0.svg                   | 1685 ++++++++++
 .../readme_example_45_2.svg                   | 1310 ++++++++
 .../readme_example_49_2.svg                   | 1128 +++++++
 .../readme_example_54_0.svg                   | 1573 ++++++++++
 .../readme_example_59_0.svg                   | 1309 ++++++++
 .../readme_example_5_0.svg                    |   16 +-
 .../readme_example_62_1.svg                   |  830 +++++
 .../readme_example_68_0.svg                   |  200 ++
 .../readme_example_6_0.svg                    |   20 +-
 optyx/core/zx.py                              |   30 +-
 13 files changed, 12699 insertions(+), 519 deletions(-)
 create mode 100644 docs/notebooks/readme_example.md
 create mode 100644 docs/notebooks/readme_example_files/readme_example_25_0.svg
 create mode 100644 docs/notebooks/readme_example_files/readme_example_40_0.svg
 create mode 100644 docs/notebooks/readme_example_files/readme_example_45_2.svg
 create mode 100644 docs/notebooks/readme_example_files/readme_example_49_2.svg
 create mode 100644 docs/notebooks/readme_example_files/readme_example_54_0.svg
 create mode 100644 docs/notebooks/readme_example_files/readme_example_59_0.svg
 create mode 100644 docs/notebooks/readme_example_files/readme_example_62_1.svg
 create mode 100644 docs/notebooks/readme_example_files/readme_example_68_0.svg

diff --git a/docs/notebooks/readme_example.ipynb b/docs/notebooks/readme_example.ipynb
index af001cb4..3dd8ef0d 100644
--- a/docs/notebooks/readme_example.ipynb
+++ b/docs/notebooks/readme_example.ipynb
@@ -31,7 +31,7 @@
    "source": [
     "We will present the basics of Optyx with a simple example from linear optics. \n",
     "\n",
-    "The Hong–Ou–Mandel (HOM) effect is a two-photon interference phenomenon where indistinguishable photons entering a 50:50 beamsplitter “bunch” and exit together through the same port. When their temporal, spectral, polarization, and spatial modes overlap perfectly, destructive interference suppresses the outcome with one photon in each output. This effect is a standard benchmark for photon indistinguishability and alignment in photonic experiments."
+    "The Hong–Ou–Mandel (HOM) effect is a two-photon interference phenomenon where indistinguishable photons entering a 50:50 beamsplitter “bunch” and exit together through the same output register. When their temporal, spectral, polarization, and spatial modes overlap perfectly, destructive interference suppresses the outcome with one photon in each output. This effect is a standard benchmark for photon indistinguishability in photonic experiments."
    ]
   },
   {
@@ -48,7 +48,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 1,
    "id": "13dbbb3a",
    "metadata": {},
    "outputs": [
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   },
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@@ -1045,7 +1045,7 @@
        "array(-0.+0.j)"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1060,7 +1060,7 @@
   },
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+   "execution_count": 4,
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@@ -1070,7 +1070,7 @@
        "{(0, 2): 0.5, (1, 1): 4.9303806576313227e-32, (2, 0): 0.5}"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 4,
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     }
@@ -1101,7 +1101,7 @@
   },
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+   "execution_count": 5,
    "id": "47e64a7d",
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    "outputs": [],
@@ -1111,7 +1111,8 @@
     "\n",
     "from optyx import Channel\n",
     "from optyx.qubits import Z, X, H, Measure, Scalar, qubit, bit\n",
-    "from optyx.classical import BitControlledGate"
+    "from optyx.classical import BitControlledGate\n",
+    "from optyx.core import zx, diagram"
    ]
   },
   {
@@ -1127,7 +1128,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 6,
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    "outputs": [],
@@ -1146,13 +1147,30 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 7,
    "id": "8c0301af",
    "metadata": {},
    "outputs": [],
    "source": [
     "bell = Scalar(0.5 ** 0.5) @ Z(0, 2)\n",
     "\n",
+    "controlled_X = Channel(\n",
+    "  \"Controlled-X\",\n",
+    "  zx.X(2, 1) @ diagram.Scalar(2 ** 0.5),\n",
+    "  dom = bit @ qubit,\n",
+    "  cod = qubit\n",
+    ")\n",
+    "\n",
+    "controlled_Z = Channel(\n",
+    "  \"Controlled-Z\",\n",
+    "  (\n",
+    "    zx.H @ diagram.bit >>\n",
+    "    zx.Z(2, 1) @ diagram.Scalar(2 ** 0.5)\n",
+    "  ),\n",
+    "  dom = bit @ qubit,\n",
+    "  cod = qubit\n",
+    ")\n",
+    "\n",
     "@Channel.from_callable(\n",
     "  dom=qubit, cod=qubit\n",
     ")\n",
@@ -1161,104 +1179,1755 @@
     "  cc, aa = cnot(c, a)\n",
     "  c_ = Measure(1)(H()(cc))\n",
     "  a_ = Measure(1)(aa)\n",
-    "  bb = BitControlledGate(X(1, 1, 0.5))(a_, b)\n",
-    "  return BitControlledGate(Z(1, 1, 0.5))(c_, bb)"
+    "  bb = controlled_X(a_, b)\n",
+    "  return controlled_Z(c_, bb)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "174c4713",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# function syntax avoids explicit swaps and identity wires\n",
+    "# this is the equivalent monoidal syntax:\n",
+    "\n",
+    "teleportation_monoidal_syntax = (\n",
+    "    qubit @ bell >>\n",
+    "    cnot @ qubit >>\n",
+    "    H() @ qubit ** 2 >>\n",
+    "    Measure(1) @ Measure(1) @ qubit >>\n",
+    "    bit @ controlled_X >>\n",
+    "    controlled_Z\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7fcce92a",
+   "metadata": {},
+   "source": [
+    "### Verify the protocol"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "bb29783a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "from optyx.qubits import Id\n",
+    "\n",
+    "# both implementations are equivalent\n",
+    "np.allclose(\n",
+    "    teleportation.eval().tensor.array,\n",
+    "    teleportation_monoidal_syntax.eval().tensor.array,\n",
+    "    Id(1).double().to_tensor().eval().array\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a24d31ac",
+   "metadata": {},
+   "source": [
+    "Optyx evaluates diagrams via pluggable backends. By default it compiles a diagram to a tensor network, optimizes a contraction path with **cotengra**, and contracts it with **quimb** (CPU/GPU; dense/sparse). For linear-optical circuits, Optyx also exposes a **Perceval** backend using permanent-based algorithms, and a tensor-network-based **DisCoPy** backend; you can choose among these depending on the task.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "ddf6db65",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# backends (Perceval, Discopy, Quimb)\n",
+    "\n",
+    "from optyx.core.backends import (\n",
+    "    DiscopyBackend,\n",
+    "    QuimbBackend\n",
+    ")\n",
+    "\n",
+    "np.allclose(\n",
+    "    teleportation.eval(DiscopyBackend()).tensor.array,\n",
+    "    teleportation.eval(QuimbBackend()).tensor.array\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "984a7c1f",
+   "metadata": {},
+   "source": [
+    "### Verify with PyZX"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "80e3231d",
+   "metadata": {},
+   "source": [
+    "We can obtain the underlying CPTP map by doubling (CP-construction) an Optyx diagram:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "226da509",
+   "metadata": {},
+   "outputs": [
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+       "   </g>\n",
+       "  </g>\n",
+       " </g>\n",
+       " <defs>\n",
+       "  <clipPath id=\"p897823fc32\">\n",
+       "   <rect x=\"7.2\" y=\"7.2\" width=\"576\" height=\"576\"/>\n",
+       "  </clipPath>\n",
+       " </defs>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<Figure size 800x800 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "teleportation_monoidal_syntax.double().draw(figsize=(8, 8))"
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": 10,
-   "id": "174c4713",
+   "cell_type": "markdown",
+   "id": "a405228c",
    "metadata": {},
-   "outputs": [],
    "source": [
-    "# function syntax avoids explicit swaps and identity wires\n",
-    "# this is the equivalent monoidal syntax:\n",
-    "\n",
-    "teleportation_monoidal_syntax = (\n",
-    "    qubit @ bell >>\n",
-    "    cnot @ qubit >>\n",
-    "    H() @ qubit ** 2 >>\n",
-    "    Measure(1) @ Measure(1) @ qubit >>\n",
-    "    bit @ BitControlledGate(X(1, 1, 0.5)) >>\n",
-    "    BitControlledGate(Z(1, 1, 0.5))\n",
-    ")"
+    "This way we can use PyZX and its optimisation/simplifications functionalities:"
    ]
   },
   {
-   "cell_type": "markdown",
-   "id": "7fcce92a",
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "b3db33f9",
    "metadata": {},
+   "outputs": [],
    "source": [
-    "### Verify the protocol"
+    "import pyzx\n",
+    "pyzx_graph = teleportation_monoidal_syntax.double().to_pyzx()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
-   "id": "bb29783a",
+   "execution_count": 13,
+   "id": "9574fa05",
    "metadata": {},
    "outputs": [
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+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
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+       "    else if (t == 3) return \"gray\";\n",
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+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
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+       "\n",
+       "        context.moveTo(0,-s);\n",
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+       "    // SETUP SVG ITEMS\n",
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+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
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+       "        .attr(\"class\", \"selectable\");\n",
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+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
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+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
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+       "\n",
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+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
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+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
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+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
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+       "\n",
+       "    function update_hboxes() {\n",
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+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
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+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
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+       "                    }\n",
+       "                    d.x = x;\n",
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+       "        .attr(\"x2\", function(d) { return d.target.x; })\n",
+       "        .attr(\"y2\", function(d) { return d.target.y; });\n",
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+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
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+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"x1\", function(d) { return d.source.x; })\n",
+       "                .attr(\"y1\", function(d) { return d.source.y; });\n",
+       "\n",
+       "            link.filter(function(d) { return d.target.selected ||\n",
+       "                    (auto_hbox && d.target.t == 3); })\n",
+       "                .attr(\"x2\", function(d) { return d.target.x; })\n",
+       "                .attr(\"y2\", function(d) { return d.target.y; });\n",
+       "\n",
+       "            // text.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"x\", function(d) { return d.x; })\n",
+       "            //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-I4zCJPnC',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 200, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 150, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"18\", \"t\": 2}, {\"source\": \"1\", \"target\": \"19\", \"t\": 2}, {\"source\": \"16\", \"target\": \"20\", \"t\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 2}, {\"source\": \"19\", \"target\": \"21\", \"t\": 2}]}'), 250, 200, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
       "text/plain": [
-       "True"
+       "<IPython.core.display.HTML object>"
       ]
      },
-     "execution_count": 11,
      "metadata": {},
-     "output_type": "execute_result"
+     "output_type": "display_data"
     }
    ],
    "source": [
-    "import numpy as np\n",
-    "from optyx.qubits import Id\n",
-    "\n",
-    "# both implementations are equivalent\n",
-    "np.allclose(\n",
-    "    teleportation.eval().tensor.array,\n",
-    "    teleportation_monoidal_syntax.eval().tensor.array,\n",
-    "    Id(1).double().to_tensor().eval().array\n",
-    ")"
+    "pyzx.full_reduce(pyzx_graph, quiet=True)\n",
+    "pyzx_graph.normalize()\n",
+    "pyzx.draw(pyzx_graph)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3b8a1829",
-   "metadata": {},
-   "source": [
-    "Optyx evaluates diagrams via pluggable backends. By default it compiles a diagram to a tensor network, optimizes a contraction path with **cotengra**, and contracts it with **quimb** (CPU/GPU; dense/sparse). For linear-optical circuits, Optyx also exposes a **Perceval** backend using permanent-based algorithms, and a tensor-network-based **DisCoPy** backend; you can choose among these depending on the task.\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "id": "25af2db6",
+   "id": "8ae0bfcb",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
    "source": [
-    "# backends (Perceval, Discopy, Quimb)\n",
-    "\n",
-    "from optyx.core.backends import (\n",
-    "    DiscopyBackend,\n",
-    "    QuimbBackend\n",
-    ")\n",
-    "\n",
-    "np.allclose(\n",
-    "    teleportation.eval(DiscopyBackend()).tensor.array,\n",
-    "    teleportation.eval(QuimbBackend()).tensor.array\n",
-    ")"
+    "The diagram is a double identity diagram."
    ]
   },
   {
@@ -1325,7 +2994,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 14,
    "id": "c557c4b8",
    "metadata": {},
    "outputs": [],
@@ -1340,7 +3009,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 15,
    "id": "a1764edb",
    "metadata": {},
    "outputs": [],
@@ -1362,7 +3031,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 16,
    "id": "7bb5e46f",
    "metadata": {},
    "outputs": [],
@@ -1383,7 +3052,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 17,
    "id": "4b5ee771",
    "metadata": {},
    "outputs": [
@@ -1398,7 +3067,7 @@
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        "   <cc:Work>\n",
        "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
-       "    <dc:date>2025-10-06T10:51:59.571927</dc:date>\n",
+       "    <dc:date>2025-10-06T13:32:08.799221</dc:date>\n",
        "    <dc:format>image/svg+xml</dc:format>\n",
        "    <dc:creator>\n",
        "     <cc:Agent>\n",
@@ -1427,217 +3096,217 @@
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+   "execution_count": 18,
    "id": "c19354d7",
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    "id": "fb497580",
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    "source": [
     "### Photon loss and channel fidelity\n",
     "\n",
-    "Photon loss is when a photon that should arrive simply doesn’t, so counts drop and patterns get noisier. In Optyx, you model this by placing a dedicated loss generator exactly where the loss occurs; its single parameter is the photon survival probability. Photon loss is the primary failure mode for photonic qubits. In photonic computing it breaks multi-photon interference and reduces the success of fusion/measurement steps. That’s why if we want to study architectures, thresholds, and mitigation (repeaters, multiplexing, loss-tolerant encodings), we need to be able to model photon loss accurately."
+    "Photon loss is when a photon that should arrive simply doesn’t. In Optyx, you model this by placing a dedicated loss generator exactly where the loss occurs; its single parameter is the photon survival probability. Photon loss is the primary failure mode for photonic qubits. In photonic computing it breaks multi-photon interference and reduces the success of fusion/measurement steps. That’s why if we want to study architectures, thresholds, and mitigation (repeaters, multiplexing, loss-tolerant encodings), we need to be able to model photon loss accurately."
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@@ -5759,7 +7512,7 @@
   },
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+   "execution_count": 24,
    "id": "bdb9611d",
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-       "    <g clip-path=\"url(#p575c286d36)\">\n",
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@@ -7331,10 +9073,21 @@
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@@ -7386,7 +9139,7 @@
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+   "execution_count": 25,
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    "outputs": [],
@@ -7412,7 +9165,7 @@
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+   "execution_count": 26,
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    "outputs": [],
@@ -7439,7 +9192,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 27,
    "id": "1c50f388",
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    "outputs": [
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-       "    <dc:date>2025-10-06T10:54:29.717692</dc:date>\n",
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        "    <dc:format>image/svg+xml</dc:format>\n",
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-       "\" clip-path=\"url(#p762c8ca300)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
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-       "       <use xlink:href=\"#mf50ca26f6c\" x=\"302.812216\" y=\"244.078125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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-       "\" clip-path=\"url(#p762c8ca300)\" style=\"fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square\"/>\n",
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@@ -9716,7 +11469,7 @@
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        "</svg>"
       ],
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       ]
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+     "execution_count": 32,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -9969,7 +11722,7 @@
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@@ -10030,7 +11783,7 @@
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    "metadata": {},
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@@ -10042,7 +11795,7 @@
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    "id": "3f3fca2d",
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@@ -10064,7 +11817,7 @@
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    "cell_type": "code",
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+   "execution_count": 38,
    "id": "54633b7a",
    "metadata": {},
    "outputs": [],
@@ -10074,7 +11827,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 39,
    "id": "e019251e",
    "metadata": {},
    "outputs": [],
@@ -10090,7 +11843,7 @@
   },
   {
    "cell_type": "code",
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+   "execution_count": 40,
    "id": "ca6102c5",
    "metadata": {},
    "outputs": [],
diff --git a/docs/notebooks/readme_example.md b/docs/notebooks/readme_example.md
new file mode 100644
index 00000000..511bbd3d
--- /dev/null
+++ b/docs/notebooks/readme_example.md
@@ -0,0 +1,1163 @@
+# Optyx: A ZX-based Python library for networked quantum architectures
+
+Optyx is an open-source Python library for designing, simulating, and optimizing networked, hybrid qubit–photon architectures. It offers a compositional, ZX/ZW-based string-diagram front end (built within the DisCoPy ecosystem) that lets you specify experiments mixing qubit registers with discrete-variable photonic modes, lossy channels, heralded measurements, and classical/quantum feedback. Optyx compiles these diagrams to optimized tensor networks and executes them with state-of-the-art contraction backends (Quimb + Cotengra), delivering substantial speedups on low-depth circuits. The result is an end-to-end workflow—from high-level syntax to numerics—well-suited for rapid prototyping of qubit-photon experiments.
+
+## Basic Optyx syntax: the Hong-Ou-Mandel effect
+
+We will present the basics of Optyx with a simple example from linear optics. 
+
+The Hong–Ou–Mandel (HOM) effect is a two-photon interference phenomenon where indistinguishable photons entering a 50:50 beamsplitter “bunch” and exit together through the same output register. When their temporal, spectral, polarization, and spatial modes overlap perfectly, destructive interference suppresses the outcome with one photon in each output. This effect is a standard benchmark for photon indistinguishability in photonic experiments.
+
+### Experiment definition
+
+Circuits in Optyx are diagrams made of typed wires (qubits, photonic modes, classical bits) and generators (gates, sources, optics, measurements). You build them by connecting outputs to inputs (sequence) and placing blocks side-by-side (parallel); types must match at every connection. Generators carry parameters and labels; measurements produce classical wires you can route into later blocks. A circuit is just the set of generators plus the wiring between their ports.
+
+Let us build a diagram to study the HOM effect.
+
+
+```python
+from optyx.photonic import BBS
+
+# diagram generators:
+# beam-splitter
+beam_splitter = BBS(0)
+beam_splitter.draw()
+```
+
+
+    
+![svg](readme_example_files/readme_example_5_0.svg)
+    
+
+
+
+```python
+from optyx.photonic import Create
+
+# diagram composition with monoidal syntax
+# create two single-photon states and send them to a beam-splitter
+hong_ou_mandel = (
+    Create(1) @ Create(1) >>
+    beam_splitter
+)
+
+hong_ou_mandel.draw()
+```
+
+
+    
+![svg](readme_example_files/readme_example_6_0.svg)
+    
+
+
+The result of this experiment should be a zero probability of having single photons in two output modes:
+
+ ![HOM](./hom.png "Hong-Ou-Mandel Effect")
+
+### Diagram evaluation
+
+Call `diagram.eval()` to evaluate a diagram (Quimb backend by default). It returns an evaluated object; use `.tensor.array` to extract the numeric tensor/array, or `.prob_dist()` to get an outcome distribution. You can chain it inline, e.g., `(...).eval().tensor.array`.
+
+
+```python
+# an amplitude (raw result of tensor contraction)
+from optyx.classical import Select
+(
+    hong_ou_mandel >> Select(1, 1)
+).eval().tensor.array
+```
+
+
+
+
+    array(-0.+0.j)
+
+
+
+
+```python
+hong_ou_mandel.eval().prob_dist()
+```
+
+
+
+
+    {(0, 2): 0.5, (1, 1): 4.9303806576313227e-32, (2, 0): 0.5}
+
+
+
+## Function syntax and backends: qubit teleportation
+
+Quantum teleportation transfers an unknown qubit state from sender (Alice) to receiver (Bob) using shared entanglement and two classical bits. Alice performs a joint Bell-state measurement on the unknown qubit and her half of an entangled pair, which projects Bob’s distant qubit into a state related to the original. She sends the two-bit outcome to Bob, who applies a corresponding Pauli correction (I, X, Z, or XZ) to recover the exact state. No information travels faster than light and the original is destroyed by measurement, so the state is relocated—not copied.
+
+https://en.wikipedia.org/wiki/Quantum_teleportation#/media/File:Quantum_teleportation_circuit.svg :
+
+<img src="teleport.svg" alt="Teleportation Protocol" width="800" style="max-width:100%;">
+
+
+```python
+from optyx import qubit, bit
+from optyx.qubits import Scalar
+
+from optyx import Channel
+from optyx.qubits import Z, X, H, Measure, Scalar, qubit, bit
+from optyx.classical import BitControlledGate
+from optyx.core import zx, diagram
+```
+
+### Define the protocol
+
+
+Instead of wiring generators together with sequential (`>>`) and parallel (`@`) composition (which we call the monoidal syntax), you can treat each generator as a **function on its domain wires**. You **label the wires** and then **call generators with those labels**, which lets you feed specific wires directly into the right box without inserting explicit `Swap`s to reorder them. This makes complex diagrams easier to read and write, and mirrors the style used in **Guppy**; it’s an alternative surface syntax that’s equivalent to the usual `>>`/`@` composition.
+
+
+
+```python
+# function syntax
+# CNOT from ZX generators
+
+@Channel.from_callable(
+  dom=qubit @ qubit, cod=qubit @ qubit
+)
+def cnot(a, b):
+  c, d = Z(1, 2)(a)
+  Scalar(2 ** 0.5)()
+  return c, X(2, 1)(d, b)
+```
+
+
+```python
+bell = Scalar(0.5 ** 0.5) @ Z(0, 2)
+
+controlled_X = Channel(
+  "Controlled-X",
+  zx.X(2, 1) @ diagram.Scalar(2 ** 0.5),
+  dom = bit @ qubit,
+  cod = qubit
+)
+
+controlled_Z = Channel(
+  "Controlled-Z",
+  (
+    zx.H @ diagram.bit >>
+    zx.Z(2, 1) @ diagram.Scalar(2 ** 0.5)
+  ),
+  dom = bit @ qubit,
+  cod = qubit
+)
+
+@Channel.from_callable(
+  dom=qubit, cod=qubit
+)
+def teleportation(c):
+  a, b = bell()
+  cc, aa = cnot(c, a)
+  c_ = Measure(1)(H()(cc))
+  a_ = Measure(1)(aa)
+  bb = controlled_X(a_, b)
+  return controlled_Z(c_, bb)
+```
+
+
+```python
+# function syntax avoids explicit swaps and identity wires
+# this is the equivalent monoidal syntax:
+
+teleportation_monoidal_syntax = (
+    qubit @ bell >>
+    cnot @ qubit >>
+    H() @ qubit ** 2 >>
+    Measure(1) @ Measure(1) @ qubit >>
+    bit @ controlled_X >>
+    controlled_Z
+)
+```
+
+### Verify the protocol
+
+
+```python
+import numpy as np
+from optyx.qubits import Id
+
+# both implementations are equivalent
+np.allclose(
+    teleportation.eval().tensor.array,
+    teleportation_monoidal_syntax.eval().tensor.array,
+    Id(1).double().to_tensor().eval().array
+)
+```
+
+
+
+
+    True
+
+
+
+Optyx evaluates diagrams via pluggable backends. By default it compiles a diagram to a tensor network, optimizes a contraction path with **cotengra**, and contracts it with **quimb** (CPU/GPU; dense/sparse). For linear-optical circuits, Optyx also exposes a **Perceval** backend using permanent-based algorithms, and a tensor-network-based **DisCoPy** backend; you can choose among these depending on the task.
+
+
+
+```python
+# backends (Perceval, Discopy, Quimb)
+
+from optyx.core.backends import (
+    DiscopyBackend,
+    QuimbBackend
+)
+
+np.allclose(
+    teleportation.eval(DiscopyBackend()).tensor.array,
+    teleportation.eval(QuimbBackend()).tensor.array
+)
+```
+
+
+
+
+    True
+
+
+
+### Verify with PyZX
+
+We can obtain the underlying CPTP map by doubling (CP-construction) an Optyx diagram:
+
+
+```python
+teleportation_monoidal_syntax.double().draw(figsize=(8, 8))
+```
+
+
+    
+![svg](readme_example_files/readme_example_25_0.svg)
+    
+
+
+This way we can use PyZX and its optimisation/simplifications functionalities:
+
+
+```python
+import pyzx
+pyzx_graph = teleportation_monoidal_syntax.double().to_pyzx()
+```
+
+
+```python
+pyzx.full_reduce(pyzx_graph, quiet=True)
+pyzx_graph.normalize()
+pyzx.draw(pyzx_graph)
+```
+
+
+<div style="overflow:auto" id="graph-output-I4zCJPnC"></div>
+<script type="module">
+var d3;
+if (d3 == null) { d3 = await import("https://cdn.skypack.dev/d3@5"); }
+// PyZX - Python library for quantum circuit rewriting 
+//        and optimisation using the ZX-calculus
+// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+
+//    http://www.apache.org/licenses/LICENSE-2.0
+
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// styling functions
+function nodeColor(t) {
+    if (t == 0) return "black";
+    else if (t == 1) return "#ccffcc";
+    else if (t == 2) return "#ff8888";
+    else if (t == 3) return "yellow";
+    else if (t == 4) return "black";
+    else if (t == 5) return "black";
+    else if (t == 6) return "#ccffcc";
+}
+
+function edgeColor(t) {
+    if (t == 1) return "black";
+    else if (t == 2) return "#08f";
+    else if (t == 3) return "gray";
+}
+
+function nodeStyle(selected) {
+    return selected ? "stroke-width: 2px; stroke: #00f" : "stroke-width: 1.5px";
+}
+
+var symbolGround = {
+    draw: function(context, size){
+        let s = size/2;
+
+        context.moveTo(0,-s);
+        context.lineTo(0,0);
+
+        context.moveTo(-s,0);
+        context.lineTo(s,0);
+
+        context.moveTo(-2*s/3,s/3);
+        context.lineTo(2*s/3,s/3);
+
+        context.moveTo(-s/3,2*s/3);
+        context.lineTo(s/3,2*s/3);
+    }
+}
+
+function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {
+    var ntab = {};
+
+    var groundOffset = 2.5 * node_size;
+
+    graph.nodes.forEach(function(d) {
+        ntab[d.name] = d;
+        d.selected = false;
+        d.previouslySelected = false;
+        d.nhd = [];
+    });
+
+    var spiders_and_boundaries = graph.nodes.filter(function(d) {
+        return d.t != 3;
+    });
+
+    graph.links.forEach(function(d) {
+        var s = ntab[d.source];
+        var t = ntab[d.target];
+        d.source = s;
+        d.target = t;
+        s.nhd.push(t);
+        t.nhd.push(s);
+    });
+
+    var shiftKey;
+
+    // SETUP SVG ITEMS
+
+    var svg = d3.select(tag)
+    //.attr("tabindex", 1)
+        .on("keydown.brush", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})
+        .on("keyup.brush", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})
+    //.each(function() { this.focus(); })
+        .append("svg")
+        .attr("style", "max-width: none; max-height: none")
+        .attr("width", width)
+        .attr("height", height);
+
+    var link = svg.append("g")
+        .attr("class", "link")
+        .selectAll("line")
+        .data(graph.links)
+        .enter().append("line")
+        .attr("stroke", function(d) { return edgeColor(d.t); })
+        .attr("style", "stroke-width: 1.5px");
+
+    var brush = svg.append("g")
+        .attr("class", "brush");
+
+    var node = svg.append("g")
+        .attr("class", "node")
+        .selectAll("g")
+        .data(graph.nodes)
+        .enter().append("g")
+        .attr("transform", function(d) {
+            return "translate(" + d.x + "," + d.y +")";
+        });
+
+    // Draw a ground symbol connected to the node.
+    node.filter(function(d) { return d.ground; })
+        .append("path")
+        .attr("stroke", "black")
+        .attr("style", "stroke-width: 1.5px")
+        .attr("fill", "none")
+        .attr("d", "M 0 0 L 0 "+(groundOffset))
+        .attr("class", "selectable");
+    node.filter(function(d) { return d.ground; })
+        .append("path")
+        .attr("stroke", "black")
+        .attr("style", "stroke-width: 1.5px")
+        .attr("fill", "none")
+        .attr("d", d3.symbol().type(symbolGround).size(node_size*1.5))
+        .attr("transform", "translate(0,"+groundOffset+")")
+        .attr("class", "selectable");
+
+    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })
+        .append("circle")
+        .attr("r", function(d) {
+            if (d.t == 0) return 0.5 * node_size;
+            else if (d.t == 4) return 0.25 * node_size;
+            else return node_size;
+        })
+        .attr("fill", function(d) { return nodeColor(d.t); })
+        .attr("stroke", "black")
+        .attr("class", "selectable");
+
+    var hbox = node.filter(function(d) { return d.t == 3; });
+
+    hbox.append("rect")
+        .attr("x", -0.75 * node_size).attr("y", -0.75 * node_size)
+        .attr("width", node_size * 1.5).attr("height", node_size * 1.5)
+        .attr("fill", function(d) { return nodeColor(d.t); })
+        .attr("stroke", "black")
+        .attr("class", "selectable");
+
+    // draw a triangle for d.t == 5
+    node.filter(function(d) { return d.t == 5; })
+        .append("path")
+        .attr("d", "M 0 0 L "+node_size+" "+node_size+" L -"+node_size+" "+node_size+" Z")
+        .attr("fill", function(d) { return nodeColor(d.t); })
+        .attr("stroke", "black")
+        .attr("class", "selectable")
+        .attr("transform", "translate(" + (-node_size/2) + ", 0) rotate(-90)");
+
+    // draw a square for Z box: d.t == 6
+    node.filter(function(d) { return d.t == 6; })
+        .append("rect")
+        .attr("x", -0.75 * node_size).attr("y", -0.75 * node_size)
+        .attr("width", node_size * 1.5).attr("height", node_size * 1.5)
+        .attr("fill", function(d) { return nodeColor(d.t); })
+        .attr("stroke", "black")
+        .attr("class", "selectable");
+
+    node.filter(function(d) { return d.phase != ''; })
+        .append("text")
+        .attr("y", 0.7 * node_size + 14)
+        .text(function (d) { return d.phase })
+        .attr("text-anchor", "middle")
+        .attr("font-size", "12px")
+        .attr("font-family", "monospace")
+        .attr("fill", "#00d")
+        .attr('style', 'pointer-events: none; user-select: none;');
+
+    if (show_labels) {
+        node.append("text")
+            .attr("y", -0.7 * node_size - 8)
+            .text(function (d) { return d.name; })
+            .attr("text-anchor", "middle")
+            .attr("font-size", "10px")
+            .attr("font-family", "monospace")
+            .attr("fill", "#999")
+            .attr('style', 'pointer-events: none; user-select: none;');
+    }
+
+    // Display the chosen data fields over the node.
+    node.filter(d => d.vdata.length > 0)
+        .append("text")
+        .attr("y", d => -0.7 * node_size - 14 - 10 * d.vdata.length)
+        .attr("text-anchor", "middle")
+        .attr("font-size", "8px")
+        .attr("font-family", "monospace")
+        .attr("fill", "#c66")
+        .attr('style', 'pointer-events: none; user-select: none;')
+        .selectAll("tspan")
+        .data(d => d.vdata)
+        .enter()
+        .append("tspan")
+        .attr("x", "0")
+        .attr("dy", "1.2em")
+        .text(x => x.join(": "));
+
+    if (scalar_str != "") {
+        svg.append("text")
+            .text(scalar_str)
+            .attr("x", 60).attr("y", 40)
+            .attr("text-anchor", "middle")
+    }
+
+    function update_hboxes() {
+        if (auto_hbox) {
+            var pos = {};
+            hbox.attr("transform", function(d) {
+                // calculate barycenter of non-hbox neighbours, then nudge a bit
+                // to the NE.
+                var x=0,y=0,sz=0;
+                for (var i = 0; i < d.nhd.length; ++i) {
+                    if (d.nhd[i].t != 3) {
+                        sz++;
+                        x += d.nhd[i].x;
+                        y += d.nhd[i].y;
+                    }
+                }
+
+                offset = 0.25 * scale;
+
+                if (sz != 0) {
+                    x = (x/sz) + offset;
+                    y = (y/sz) - offset;
+
+                    while (pos[[x,y]]) {
+                        x += offset;
+                    }
+                    d.x = x;
+                    d.y = y;
+                    pos[[x,y]] = true;
+                }
+
+                return "translate("+d.x+","+d.y+")";
+            });
+        }
+    }
+
+    update_hboxes();
+
+    link.attr("x1", function(d) { return d.source.x; })
+        .attr("y1", function(d) { return d.source.y; })
+        .attr("x2", function(d) { return d.target.x; })
+        .attr("y2", function(d) { return d.target.y; });
+
+    // EVENTS FOR DRAGGING AND SELECTION
+
+    node.on("mousedown", function(d) {
+        if (shiftKey) {
+            d3.select(this).selectAll(".selectable").attr("style", nodeStyle(d.selected = !d.selected));
+            d3.event.stopImmediatePropagation();
+        } else if (!d.selected) {
+            node.selectAll(".selectable").attr("style", function(p) { return nodeStyle(p.selected = d === p); });
+        }
+    })
+        .call(d3.drag().on("drag", function(d) {
+            var dx = d3.event.dx;
+            var dy = d3.event.dy;
+            // node.filter(function(d) { return d.selected; })
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+            //     .attr("cy", function(d) { return d.y += dy; });
+            node.filter(function(d) { return d.selected; })
+                .attr("transform", function(d) {
+                    d.x += dx;
+                    d.y += dy;
+                    return "translate(" + d.x + "," + d.y +")";
+                });
+
+            update_hboxes();
+
+            link.filter(function(d) { return d.source.selected ||
+                    (auto_hbox && d.source.t == 3); })
+                .attr("x1", function(d) { return d.source.x; })
+                .attr("y1", function(d) { return d.source.y; });
+
+            link.filter(function(d) { return d.target.selected ||
+                    (auto_hbox && d.target.t == 3); })
+                .attr("x2", function(d) { return d.target.x; })
+                .attr("y2", function(d) { return d.target.y; });
+
+            // text.filter(function(d) { return d.selected; })
+            //     .attr("x", function(d) { return d.x; })
+            //     .attr("y", function(d) { return d.y + 0.7 * node_size + 14; });
+        }));
+
+    brush.call(d3.brush().keyModifiers(false)
+        .extent([[0, 0], [width, height]])
+        .on("start", function() {
+            if (d3.event.sourceEvent.type !== "end") {
+                node.selectAll(".selectable").attr("style", function(d) {
+                    return nodeStyle(
+                        d.selected = d.previouslySelected = shiftKey &&
+                        d.selected);
+                });
+            }
+        })
+        .on("brush", function() {
+            if (d3.event.sourceEvent.type !== "end") {
+                var selection = d3.event.selection;
+                node.selectAll(".selectable").attr("style", function(d) {
+                    return nodeStyle(d.selected = d.previouslySelected ^
+                        (selection != null
+                            && selection[0][0] <= d.x && d.x < selection[1][0]
+                            && selection[0][1] <= d.y && d.y < selection[1][1]));
+                });
+            }
+        })
+        .on("end", function() {
+            if (d3.event.selection != null) {
+                d3.select(this).call(d3.event.target.move, null);
+            }
+        }));
+}
+
+
+showGraph('#graph-output-I4zCJPnC',
+  JSON.parse('{"nodes": [{"name": "0", "x": 50, "y": 100, "t": 0, "phase": "", "ground": false, "vdata": []}, {"name": "1", "x": 50, "y": 150, "t": 0, "phase": "", "ground": false, "vdata": []}, {"name": "16", "x": 200, "y": 100, "t": 0, "phase": "", "ground": false, "vdata": []}, {"name": "17", "x": 200, "y": 150, "t": 0, "phase": "", "ground": false, "vdata": []}, {"name": "18", "x": 100, "y": 100, "t": 1, "phase": "", "ground": false, "vdata": []}, {"name": "19", "x": 100, "y": 150, "t": 1, "phase": "", "ground": false, "vdata": []}, {"name": "20", "x": 150, "y": 100, "t": 1, "phase": "", "ground": false, "vdata": []}, {"name": "21", "x": 150, "y": 150, "t": 1, "phase": "", "ground": false, "vdata": []}], "links": [{"source": "0", "target": "18", "t": 2}, {"source": "1", "target": "19", "t": 2}, {"source": "16", "target": "20", "t": 1}, {"source": "17", "target": "21", "t": 1}, {"source": "18", "target": "20", "t": 2}, {"source": "19", "target": "21", "t": 2}]}'), 250, 200, 50,
+  10.0, false, false, '');
+</script>
+
+
+The diagram is a double identity diagram.
+
+## Approximate contraction and photon loss: fusion teleportation
+
+Teleportation with **fusion measurements** uses a Bell pair of dual-rail qubits as the channel: Alice fuses the input with her half using a Type-II fusion, reads the classical outcomes, and Bob applies the corresponding correction. In the **success** branch, the overall map is the **identity** on the teleported qubit up to a known Pauli byproduct, which Bob removes with a conditioned \(X\) correction. In the **failure** branch, the input is effectively measured and the opposite state is prepared at the output. For the standard Type-II scheme this yields identity with probability \(1/2\), and failure otherwise; the paper’s diagrams show both branches explicitly and how the correction restores the state.
+
+
+Ursin, R., Jennewein, T., Aspelmeyer, M. et al. Quantum teleportation across the Danube. Nature 430, 849 (2004). https://doi.org/10.1038/430849a :
+
+<img src="./teleportation_danube.png" alt="Fusion teleportation across the Danube" width="1150px">
+
+Graphically, the fusion measurement we would like to use, takes the following form:
+
+<img src="./fusion_ii.png" alt="Fusion measurement" width="1200px">
+
+
+where $\underline{a}, \underline{b}, \underline{c}, \underline{d}$ are the measurement outcomes as the measured photon numbers. 
+
+$\underline{s} = \underline{a} \oplus \underline{b}$
+
+$\underline{k} = \underline{s} (\underline{b} + \underline{d}) + \neg \underline s (1 - \frac{\underline{a} + \underline{b}}{2})$
+
+### Define the protocol
+
+
+```python
+from optyx.photonic import DualRail
+
+dual_rail_encoded_bell = (
+    bell >>
+    DualRail(1) @ DualRail(1)
+)
+```
+
+
+```python
+from optyx.classical import PostselectBit, BitControlledGate
+from optyx.photonic import Phase
+from optyx.photonic import HadamardBS, qmode
+
+# postselect on fusion success
+fusion_failure_processing = PostselectBit(1)
+
+# apply the box if the control bit is 1, otherwise apply an identity channel
+correction = BitControlledGate(
+    HadamardBS() >>
+    (Phase(0.5) @ qmode) >>
+    HadamardBS()
+)
+```
+
+
+```python
+from optyx.photonic import FusionTypeII
+
+@Channel.from_callable(
+    dom=qubit, cod=qmode @ qmode
+)
+def fusion_teleportation(a):
+    dual_rail_encoded_input = DualRail(1)(a)
+    b, c, d, e = dual_rail_encoded_bell()
+    s, k = FusionTypeII()(*dual_rail_encoded_input, b, c)
+    fusion_failure_processing(s)
+    dr_output_1, dr_output_2 = correction(k, d, e)
+    return dr_output_1, dr_output_2
+```
+
+
+```python
+from optyx.photonic import FusionTypeII
+
+fusion_teleportation_monoidal_syntax = (
+    DualRail(1) @ dual_rail_encoded_bell >>
+    FusionTypeII() @ qmode**2 >>
+    fusion_failure_processing @ correction
+)
+
+fusion_teleportation_monoidal_syntax.foliation().draw(figsize=(8, 8))
+
+```
+
+
+    
+![svg](readme_example_files/readme_example_40_0.svg)
+    
+
+
+### Verify the protocol
+
+
+```python
+import numpy as np
+from optyx.photonic import Id
+
+array_teleportation = fusion_teleportation_monoidal_syntax.eval().tensor.array
+array_dr = (DualRail(1) @ Scalar(0.5**0.5)).double().to_tensor().eval().array
+
+np.allclose(array_teleportation[:, :, :2, :2, :2, :2], array_dr)
+
+```
+
+
+
+
+    True
+
+
+
+### Approximate contraction with Quimb and Cotengra
+
+Approximate contraction in Optyx uses cotengra to plan a low-cost contraction with memory-aware slicing, then executes it in quimb with optional compression of intermediates. Instead of multiplying tensors exactly, large merges are factorized and truncated (e.g., SVD) so only the dominant singular components are kept; you trade speed and memory for a controlled approximation error. Tightening the truncation tolerance (or increasing the allowed bond size) yields higher accuracy at higher cost, while more aggressive truncation/slicing gives faster, lower-memory contractions with small, quantifiable loss in fidelity.
+
+
+```python
+def _flat(x):
+    return np.asarray(x, dtype=complex).ravel()
+
+def cosine_similarity(SU, SV):
+    a, b = _flat(SU), _flat(SV)
+    num = abs(np.vdot(a, b))
+    den = np.linalg.norm(a) * np.linalg.norm(b)
+    if den == 0:
+        return 0.0
+    return float(num / den)
+```
+
+
+```python
+from cotengra import HyperCompressedOptimizer
+
+# cosine similarity between the result of exact contaction and approximate contraction for different chis
+errors = []
+for chi in range(1, 6):
+    optimiser = HyperCompressedOptimizer(
+        chi=chi
+    )
+    error_for_chi = []
+    for _ in range(10):
+         error_for_chi.append(
+             cosine_similarity(
+                 fusion_teleportation.eval(QuimbBackend(optimiser)).tensor.array,
+                 array_teleportation
+             )
+         )
+    errors.append(np.median(error_for_chi))
+
+import matplotlib.pyplot as plt
+plt.plot(range(1, 6), errors, marker='o')
+plt.grid()
+plt.xlabel('Chi')
+plt.ylabel('Average cosine similarity')
+plt.title('Fusion-based Teleportation similarity vs Contraction Chi')
+
+```
+
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+
+
+
+
+
+    Text(0.5, 1.0, 'Fusion-based Teleportation similarity vs Contraction Chi')
+
+
+
+
+    
+![svg](readme_example_files/readme_example_45_2.svg)
+    
+
+
+### Photon loss and channel fidelity
+
+Photon loss is when a photon that should arrive simply doesn’t. In Optyx, you model this by placing a dedicated loss generator exactly where the loss occurs; its single parameter is the photon survival probability. Photon loss is the primary failure mode for photonic qubits. In photonic computing it breaks multi-photon interference and reduces the success of fusion/measurement steps. That’s why if we want to study architectures, thresholds, and mitigation (repeaters, multiplexing, loss-tolerant encodings), we need to be able to model photon loss accurately.
+
+
+```python
+from optyx.photonic import FusionTypeII, PhotonLoss
+
+# photo loss is one of the main error sources in photonic quantum computing
+def fusion_teleportation_with_photon_loss(p):
+    @Channel.from_callable(
+        dom=qubit, cod=qmode**2
+    )
+    def fusion_teleportation(a):
+        dr_input_1, dr_input_2 = DualRail(1)(a)
+        b, c, d, e = dual_rail_encoded_bell()
+        # apply photon loss to all modes here:
+        #-----------------------------------
+        dr_input_1_loss, dr_input_2_loss, b_loss, c_loss, d_loss, e_loss = (
+            PhotonLoss(p)(dr_input_1), PhotonLoss(p)(dr_input_2),
+            PhotonLoss(p)(b), PhotonLoss(p)(c),
+            PhotonLoss(p)(d), PhotonLoss(p)(e)
+        )
+        #-----------------------------------
+        s, k = FusionTypeII()(dr_input_1_loss, dr_input_2_loss, b_loss, c_loss)
+        fusion_failure_processing(s)
+        output_rail_1, output_rail = correction(k, d_loss, e_loss)
+        return output_rail_1, output_rail
+    return fusion_teleportation
+```
+
+
+```python
+from optyx.core.channel import Spider, Diagram
+
+def get_perm(n):
+    return sorted(sorted(list(range(n))), key=lambda i: i % 2)
+
+def channel_fidelity(diagram_1, diagram_2):
+    bell_1 = Channel.tensor(*[Spider(0, 2, ty) for ty in diagram_1.dom])
+    permutation_1 = Diagram.permutation(get_perm(len(bell_1.cod)), bell_1.cod)
+
+    bell_2 = Channel.tensor(*[Spider(0, 2, ty) for ty in diagram_2.dom])
+    permutation_2 = Diagram.permutation(get_perm(len(bell_2.cod)), bell_2.cod)
+
+    choi_1 = bell_1 >> permutation_1 >> (diagram_1 @ diagram_1.dom)
+    choi_2 = bell_2 >> permutation_2 >> (diagram_2 @ diagram_2.dom)
+
+    return (choi_1 >> choi_2.dagger()).eval().tensor.array
+
+```
+
+
+```python
+import numpy as np
+import matplotlib.pyplot as plt
+
+ps = np.linspace(0.0, 1.0, 20)
+
+# compute fidelity for different photon loss probabilities
+F_avg_vals = []
+succ_probs = []
+for p in ps:
+    S_impl = fusion_teleportation_with_photon_loss(p)
+    S_tgt  = fusion_teleportation_monoidal_syntax
+    s = channel_fidelity(S_impl, S_tgt)
+
+    succ_probs.append(s)
+
+plt.figure()
+plt.plot(ps, succ_probs, marker='o')
+plt.grid(True)
+plt.xlabel('Photon Survival Probability (p)')
+plt.ylabel('Fidelity')
+plt.title('Fusion-based Teleportation: Photon Survival Probability vs Fidelity')
+
+```
+
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part
+      return math.isfinite(val)
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part
+      return np.asarray(x, float)
+
+
+
+
+
+    Text(0.5, 1.0, 'Fusion-based Teleportation: Photon Survival Probability vs Fidelity')
+
+
+
+
+    
+![svg](readme_example_files/readme_example_49_2.svg)
+    
+
+
+## Photon distinguishability: distributed entanglement generation
+
+Distributed entanglement generation links two distant quantum nodes (A and B) by creating a shared entangled pair. Each node emits a photon that travels to a shared site, where the photons interfere and a joint (Bell-state) detection flags success — instantly projecting A and B into an entangled state. Because attempts often fail due to loss, the process is repeated-until-success with timing. This is the core primitive behind quantum networks and repeaters, enabling long-distance QKD, teleportation, and multi-node protocols.
+
+Main, D., Drmota, P., Nadlinger, D.P. et al. Distributed quantum computing across an optical network link. Nature 638, 383–388 (2025). https://doi.org/10.1038/s41586-024-08404-x~ :
+
+![Distributed entanglement](./distributed_entanglement.png "An example of distributed entanglement generation")
+
+
+
+### Fusion and photon distinguishability
+
+#### Define the protocol
+
+
+```python
+from optyx.qubits import Z, Scalar, Id, Measure
+from optyx.photonic import DualRail
+from optyx.classical import PostselectBit
+from discopy.drawing import Equation
+
+bell_state = Z(0, 2) @ Scalar(0.5 ** 0.5)
+
+# generators introducing new qubits accepting internal states
+internal_state_1 = [1, 0]
+internal_state_2 = [0, 1]
+dual_rail_encoding = lambda state: DualRail(1, internal_states=[state])
+encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(internal_state_2)
+
+# postselect on fusion success and no errors
+post_select = PostselectBit(1) @ PostselectBit(0)
+
+protocol = (
+    bell_state @ bell_state >>
+    Id(1) @ (encoding_layer >> FusionTypeII() >> post_select) @ Id(1)
+)
+measure = Measure(2)
+
+Equation(protocol >> measure, bell_state >> measure).draw(figsize=(8, 8))
+```
+
+
+    
+![svg](readme_example_files/readme_example_54_0.svg)
+    
+
+
+#### Define a set of internal states with varying degrees of distinguishability
+
+We test how partial photon distinguishability affects a heralded entanglement link. The experiment uses the overlap between two internal two-mode states (`rotated_unit_vectors`), encodes them into dual-rail photons (`dual_rail_encoding`), and performs a Type-II fusion with postselection (`FusionTypeII() >> post_select`). We then project onto the target Bell state (`... >> bell_state.dagger()`) to read off the heralded-state quality, and use a discard step (`... >> Discard(2)`) to extract the success probability. Plotting these versus the state overlap reveals how distinguishability simultaneously degrades fidelity and lowers the entanglement generation rate.
+
+
+
+```python
+import math
+
+# internal states - 2 dimensional - move further and further apart
+def rotated_unit_vectors(n: int = 10):
+    for i in range(n):
+        theta = i * (math.pi / 2) / (n - 1)
+        yield (math.cos(theta), math.sin(theta))
+
+unit_vectors = list(rotated_unit_vectors(15))
+```
+
+#### Run the experiments
+
+
+```python
+from optyx.qubits import Discard
+
+inner_product_states = []
+inner_product_bell_states = []
+
+result_bell = bell_state.eval().tensor.array.flatten()
+result_bell = result_bell / np.linalg.norm(result_bell)
+
+for vector in unit_vectors:
+    encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(vector)
+    experiment = bell_state @ bell_state >> Id(1) @ (encoding_layer >> FusionTypeII()
+                                                                                >> post_select) @ Id(1)
+
+    f = (experiment >> bell_state.dagger()).inflate(2).eval().tensor.array
+    normalisation = (experiment >> Discard(2)).inflate(2).eval().tensor.array
+
+    inner_product_states.append(np.inner(vector, internal_state_1))
+    inner_product_bell_states.append(f/normalisation)
+```
+
+
+```python
+import matplotlib.pyplot as plt
+
+plt.figure(figsize=(6, 4))
+plt.plot(inner_product_states, inner_product_bell_states, marker='o')
+plt.xlabel('<Internal state 1 | Internal state 2>')
+plt.ylabel('<Result | Bell State> (fidelity)')
+plt.title('Fidelity of the resulting state with the perfect Bell state')
+plt.grid(True)
+plt.show()
+```
+
+
+    
+![svg](readme_example_files/readme_example_59_0.svg)
+    
+
+
+## Interfacing with external libraries
+
+### Graphix
+
+Open graphs supported only for now (graph + measurements; desire to implement deterministically - no corrections)
+
+
+```python
+import graphix
+
+circuit = graphix.Circuit(2)
+circuit.cnot(0, 1)
+
+pattern = circuit.transpile().pattern
+
+pattern.draw_graph()
+```
+
+    The pattern is not consistent with flow or gflow structure.
+
+
+
+    
+![svg](readme_example_files/readme_example_62_1.svg)
+    
+
+
+
+```python
+simulator = graphix.simulator.PatternSimulator(pattern, backend="statevector")
+graphix_result = simulator.run().psi.conj()
+```
+
+
+```python
+from optyx import qubits
+
+optyx_zx = qubits.Circuit(pattern)
+
+optyx_res = (
+    qubits.Ket("+")**2 >> optyx_zx
+).eval().amplitudes()
+```
+
+
+```python
+for keys in optyx_res.keys():
+    assert np.isclose(optyx_res[keys], graphix_result[keys], atol=1e-6)
+```
+
+### Perceval circuits and processors
+
+#### Define the protocol in Perceval
+
+
+```python
+import perceval as pcvl
+
+p = pcvl.Processor("SLOS", 6)
+p.add(0, pcvl.catalog["postprocessed cnot"].build_processor())
+
+p.add(0, pcvl.BS.H())
+p.add(0, pcvl.Detector.pnr())
+p.add(1, pcvl.Detector.pnr())
+p.add(2, pcvl.Detector.pnr())
+p.add(3, pcvl.Detector.pnr())
+
+ff_X = pcvl.FFCircuitProvider(
+  2, 0, pcvl.Circuit(2)
+)
+ff_X.add_configuration(
+  [0, 1], pcvl.PERM([1, 0])
+)
+p.add(2, ff_X)
+
+phi = pcvl.P("phi")
+ff_Z = pcvl.FFConfigurator(
+  2, 3,
+  pcvl.PS(phi),
+  {"phi": 0}
+).add_configuration(
+  [0, 1],
+  {"phi": np.pi}
+)
+p.add(0, ff_Z)
+
+pcvl.pdisplay(p, recursive=True)
+```
+
+
+
+
+    
+![svg](readme_example_files/readme_example_68_0.svg)
+    
+
+
+
+
+```python
+from optyx.qubits import Ket
+
+state = Ket("+") >> Z(1, 1, 0.3)
+state_array = state.eval().tensor.array
+state_array = state_array / np.linalg.norm(state_array)
+```
+
+#### Evaluate the protocol in Perceval
+
+
+```python
+to_transmit = (complex(state_array[0])*pcvl.BasicState([1, 0]) +
+               complex(state_array[1])*pcvl.BasicState([0, 1]))
+
+sg = pcvl.StateGenerator(pcvl.Encoding.DUAL_RAIL)
+bell_state = sg.bell_state("phi+")
+
+input_state = to_transmit * bell_state
+p.min_detected_photons_filter(2)
+
+input_state *= pcvl.BasicState([0, 0])
+
+p.with_input(input_state)
+```
+
+
+```python
+result_perceval = p.probs()
+```
+
+#### Convert to Optyx and simulate
+
+
+```python
+from optyx import Channel
+
+optyx_diagram = Channel.from_perceval(p)
+```
+
+
+```python
+from optyx.qubits import Scalar, Ket
+from optyx.photonic import DualRail
+
+bell_state = Z(0, 2) @ Scalar(0.5**0.5)
+transmit = Ket("+") >> Z(1, 1, 0.3)
+
+input_state = transmit @ bell_state
+
+protocol = (
+    input_state >>
+    DualRail(3) >>
+    Channel.from_perceval(p)
+)
+```
+
+
+```python
+result_optyx = protocol.eval().prob_dist()
+```
+
+
+```python
+def check_dict_agreement(d1, d2, rtol=1e-5, atol=1e-8):
+    for key in d1.keys() - d2.keys():
+        assert np.isclose(d1[key], 0, rtol=rtol, atol=atol)
+    for key in d2.keys() - d1.keys():
+        assert np.isclose(d2[key], 0, rtol=rtol, atol=atol)
+    for key in d1.keys() & d2.keys():
+        assert np.isclose(d1[key], d2[key], rtol=rtol, atol=atol)
+```
+
+
+```python
+check_dict_agreement(
+    {tuple(k): v for k, v in dict(result_perceval["results"]).items()},
+    result_optyx
+)
+```
+
+
+```python
+
+```
diff --git a/docs/notebooks/readme_example_files/readme_example_25_0.svg b/docs/notebooks/readme_example_files/readme_example_25_0.svg
new file mode 100644
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index 00000000..d18f33a1
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+<text x="737" y="12" font-size="5" text-anchor="start" font-style="italic">PNR</text>
+<path d="M725,75 L750,75" stroke-width="3" stroke="darkred" stroke-linejoin="miter" fill="none" />
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+<text x="737" y="62" font-size="5" text-anchor="start" font-style="italic">PNR</text>
+<path d="M775,25 L825,25" stroke-width="3" stroke="orange" stroke-linejoin="miter" fill="none" />
+<path d="M775,75 L825,75" stroke-width="3" stroke="orange" stroke-linejoin="miter" fill="none" />
+<path d="M800,90.0 L800,255.0" stroke="white" stroke-width="5" fill="none" />
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+<path d="M800,98.0 L803,95.0" stroke="orange" stroke-width="3" fill="none" />
+<path d="M780,10 L820,10 L820,90 L780,90 Z" stroke="black" fill="lightgreen" stroke-linejoin="miter" />
+<text x="800" y="55.0" font-size="10" text-anchor="middle">FFC</text>
+<path d="M725,275 L775,275" stroke="darkred" stroke-width="3" fill="none" />
+<path d="M730,290 L739,290 L753,260 L744,260 L730,290 L739,290 Z" stroke="black" fill="gray" stroke-linejoin="miter" />
+<text x="747" y="288" font-size="7" text-anchor="start">Φ=phi</text>
+<path d="M725,125.0 L825,125.0" stroke="orange" stroke-width="3" fill="none" />
+<path d="M725,175.0 L825,175.0" stroke="orange" stroke-width="3" fill="none" />
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+<path d="M825,175.0 L840,175.0" stroke-width="3" stroke="orange" stroke-linejoin="miter" fill="none" />
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+<text x="167" y="78" font-size="7" text-anchor="middle">0</text>
+<path d="M157,275 C157,275,157,265,167,265 L175,265 L175,285 L167,285 C157,285,157,275,157,275 L157,275" stroke-width="1" stroke="black" stroke-linejoin="miter" fill="white" />
+<text x="163" y="291" font-size="6" text-anchor="middle" font-style="italic">[herald1]</text>
+<text x="167" y="278" font-size="7" text-anchor="middle">0</text>
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+<path d="M-2,115 L10,115 L10,185 L-2,185 Z" stroke="black" fill="lightgray" stroke-linejoin="miter" />
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+<path d="M840,115 L852,115 L852,185 L840,185 Z" stroke="black" fill="lightgray" stroke-linejoin="miter" />
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+<path d="M283,85 L275,85 L275,65 L283,65 C283,65,293,65,293,75 C293,85,283,85,283,85 L283,85" stroke-width="1" stroke="black" stroke-linejoin="miter" fill="white" />
+<text x="288" y="61" font-size="6" text-anchor="middle" font-style="italic">[herald0]</text>
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+<text x="0" y="228.0" font-size="9" text-anchor="start">4</text>
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+</svg>
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diff --git a/docs/notebooks/readme_example_files/readme_example_6_0.svg b/docs/notebooks/readme_example_files/readme_example_6_0.svg
index 66a402d2..57da6828 100644
--- a/docs/notebooks/readme_example_files/readme_example_6_0.svg
+++ b/docs/notebooks/readme_example_files/readme_example_6_0.svg
@@ -6,7 +6,7 @@
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    <cc:Work>
     <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
-    <dc:date>2025-10-06T10:51:58.741830</dc:date>
+    <dc:date>2025-10-06T13:32:07.037551</dc:date>
     <dc:format>image/svg+xml</dc:format>
     <dc:creator>
      <cc:Agent>
@@ -35,27 +35,27 @@ L 151.2 223.2
 L 151.2 7.2 
 L 7.2 7.2 
 z
-" clip-path="url(#pa6d6a4a1d2)" style="fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter"/>
+" clip-path="url(#pfaef8b967d)" style="fill: #ffffff; stroke: #ffffff; stroke-linejoin: miter"/>
    </g>
    <g id="patch_3">
     <path d="M 43.2 61.2 
 Q 43.2 169.2 43.2 169.2 
-" clip-path="url(#pa6d6a4a1d2)" style="fill: none; stroke: #000000; stroke-linejoin: miter"/>
+" clip-path="url(#pfaef8b967d)" style="fill: none; stroke: #000000; stroke-linejoin: miter"/>
    </g>
    <g id="patch_4">
     <path d="M 115.2 133.2 
 Q 115.2 169.2 115.2 169.2 
-" clip-path="url(#pa6d6a4a1d2)" style="fill: none; stroke: #000000; stroke-linejoin: miter"/>
+" clip-path="url(#pfaef8b967d)" style="fill: none; stroke: #000000; stroke-linejoin: miter"/>
    </g>
    <g id="patch_5">
     <path d="M 43.2 205.2 
 Q 43.2 223.2 43.2 223.2 
-" clip-path="url(#pa6d6a4a1d2)" style="fill: none; stroke: #000000; stroke-linejoin: miter"/>
+" clip-path="url(#pfaef8b967d)" style="fill: none; stroke: #000000; stroke-linejoin: miter"/>
    </g>
    <g id="patch_6">
     <path d="M 115.2 205.2 
 Q 115.2 223.2 115.2 223.2 
-" clip-path="url(#pa6d6a4a1d2)" style="fill: none; stroke: #000000; stroke-linejoin: miter"/>
+" clip-path="url(#pfaef8b967d)" style="fill: none; stroke: #000000; stroke-linejoin: miter"/>
    </g>
    <g id="patch_7">
     <path d="M 25.2 61.2 
@@ -63,7 +63,7 @@ L 25.2 25.2
 L 61.2 25.2 
 L 61.2 61.2 
 z
-" clip-path="url(#pa6d6a4a1d2)" style="fill: #ffffff; stroke: #000000; stroke-linejoin: miter"/>
+" clip-path="url(#pfaef8b967d)" style="fill: #ffffff; stroke: #000000; stroke-linejoin: miter"/>
    </g>
    <g id="patch_8">
     <path d="M 97.2 133.2 
@@ -71,7 +71,7 @@ L 97.2 97.2
 L 133.2 97.2 
 L 133.2 133.2 
 z
-" clip-path="url(#pa6d6a4a1d2)" style="fill: #ffffff; stroke: #000000; stroke-linejoin: miter"/>
+" clip-path="url(#pfaef8b967d)" style="fill: #ffffff; stroke: #000000; stroke-linejoin: miter"/>
    </g>
    <g id="patch_9">
     <path d="M 25.2 205.2 
@@ -79,7 +79,7 @@ L 25.2 169.2
 L 133.2 169.2 
 L 133.2 205.2 
 z
-" clip-path="url(#pa6d6a4a1d2)" style="fill: #ffffff; stroke: #000000; stroke-linejoin: miter"/>
+" clip-path="url(#pfaef8b967d)" style="fill: #ffffff; stroke: #000000; stroke-linejoin: miter"/>
    </g>
    <g id="text_1">
     <!-- qmode -->
@@ -528,7 +528,7 @@ z
   </g>
  </g>
  <defs>
-  <clipPath id="pa6d6a4a1d2">
+  <clipPath id="pfaef8b967d">
    <rect x="7.2" y="7.2" width="144" height="216"/>
   </clipPath>
  </defs>
diff --git a/optyx/core/zx.py b/optyx/core/zx.py
index 71c524a7..d73469b3 100644
--- a/optyx/core/zx.py
+++ b/optyx/core/zx.py
@@ -338,21 +338,21 @@ def to_pyzx(self):
             elif box == H:
                 node, hadamard = scan[offset]
                 scan[offset] = (node, not hadamard)
-            # elif isinstance(box, diagram.Spider):
-            #     node = graph.add_vertex(
-            #         VertexType.Z,
-            #         phase=box.phase * 2 if box.phase else None,
-            #     )
-            #     graph.set_position(node, offset, row + 1)
-            #     for i, _ in enumerate(box.dom):
-            #         source, hadamard = scan[offset + i]
-            #       etype = EdgeType.HADAMARD if hadamard else EdgeType.SIMPLE
-            #         graph.add_edge((source, node), etype)
-            #     scan = (
-            #         scan[:offset]
-            #         + len(box.cod) * [(node, False)]
-            #         + scan[offset + len(box.dom):]
-            #     )
+            elif isinstance(box, diagram.Spider):
+                node = graph.add_vertex(
+                    VertexType.Z,
+                    phase=box.phase * 2 if box.phase else None,
+                )
+                graph.set_position(node, offset, row + 1)
+                for i, _ in enumerate(box.dom):
+                    source, hadamard = scan[offset + i]
+                    etype = EdgeType.HADAMARD if hadamard else EdgeType.SIMPLE
+                    graph.add_edge((source, node), etype)
+                scan = (
+                    scan[:offset]
+                    + len(box.cod) * [(node, False)]
+                    + scan[offset + len(box.dom):]
+                )
             else:
                 raise NotImplementedError
         for i, _ in enumerate(self.cod):

From 93e079e4ab0f5406bd6aac4a58be8a056c4b8d27 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Mon, 6 Oct 2025 13:42:17 +0100
Subject: [PATCH 49/59] readme with pyzx

---
 README.md | 454 ++++++++++++++++++++++++++++++++++++++++++++++++++++--
 1 file changed, 442 insertions(+), 12 deletions(-)

diff --git a/README.md b/README.md
index 7c21e36b..d0aac3ad 100644
--- a/README.md
+++ b/README.md
@@ -2,7 +2,7 @@
 
 Optyx is an open-source Python library for designing, simulating, and optimizing networked, hybrid qubit–photon architectures. It offers a compositional, ZX/ZW-based string-diagram front end (built within the DisCoPy ecosystem) that lets you specify experiments mixing qubit registers with discrete-variable photonic modes, lossy channels, heralded measurements, and classical/quantum feedback. Optyx compiles these diagrams to optimized tensor networks and executes them with state-of-the-art contraction backends (Quimb + Cotengra), delivering substantial speedups on low-depth circuits. The result is an end-to-end workflow—from high-level syntax to numerics—well-suited for rapid prototyping of qubit-photon experiments.
 
-## Basic Optyx syntax: the Hong-Ou-Mandel effect
+## Basic Optyx syntax: the Hong-Ou-Mandel effect./docs/notebooks/
 
 We will present the basics of Optyx with a simple example from linear optics.
 
@@ -102,6 +102,7 @@ from optyx.qubits import Scalar
 from optyx import Channel
 from optyx.qubits import Z, X, H, Measure, Scalar, qubit, bit
 from optyx.classical import BitControlledGate
+from optyx.core import zx, diagram
 ```
 
 ### Define the protocol
@@ -128,6 +129,23 @@ def cnot(a, b):
 ```python
 bell = Scalar(0.5 ** 0.5) @ Z(0, 2)
 
+controlled_X = Channel(
+  "Controlled-X",
+  zx.X(2, 1) @ diagram.Scalar(2 ** 0.5),
+  dom = bit @ qubit,
+  cod = qubit
+)
+
+controlled_Z = Channel(
+  "Controlled-Z",
+  (
+    zx.H @ diagram.bit >>
+    zx.Z(2, 1) @ diagram.Scalar(2 ** 0.5)
+  ),
+  dom = bit @ qubit,
+  cod = qubit
+)
+
 @Channel.from_callable(
   dom=qubit, cod=qubit
 )
@@ -136,8 +154,8 @@ def teleportation(c):
   cc, aa = cnot(c, a)
   c_ = Measure(1)(H()(cc))
   a_ = Measure(1)(aa)
-  bb = BitControlledGate(X(1, 1, 0.5))(a_, b)
-  return BitControlledGate(Z(1, 1, 0.5))(c_, bb)
+  bb = controlled_X(a_, b)
+  return controlled_Z(c_, bb)
 ```
 
 
@@ -150,8 +168,8 @@ teleportation_monoidal_syntax = (
     cnot @ qubit >>
     H() @ qubit ** 2 >>
     Measure(1) @ Measure(1) @ qubit >>
-    bit @ BitControlledGate(X(1, 1, 0.5)) >>
-    BitControlledGate(Z(1, 1, 0.5))
+    bit @ controlled_X >>
+    controlled_Z
 )
 ```
 
@@ -202,6 +220,374 @@ np.allclose(
 
 
 
+### Verify with PyZX
+
+We can obtain the underlying CPTP map by doubling (CP-construction) an Optyx diagram:
+
+
+```python
+teleportation_monoidal_syntax.double().draw(figsize=(8, 8))
+```
+
+
+
+![svg](./docs/notebooks/readme_example_files/readme_example_25_0.svg)
+
+
+
+This way we can use PyZX and its optimisation/simplifications functionalities:
+
+
+```python
+import pyzx
+pyzx_graph = teleportation_monoidal_syntax.double().to_pyzx()
+```
+
+
+```python
+pyzx.full_reduce(pyzx_graph, quiet=True)
+pyzx_graph.normalize()
+pyzx.draw(pyzx_graph)
+```
+
+
+<div style="overflow:auto" id="graph-output-I4zCJPnC"></div>
+<script type="module">
+var d3;
+if (d3 == null) { d3 = await import("https://cdn.skypack.dev/d3@5"); }
+// PyZX - Python library for quantum circuit rewriting
+//        and optimisation using the ZX-calculus
+// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+
+//    http://www.apache.org/licenses/LICENSE-2.0
+
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// styling functions
+function nodeColor(t) {
+    if (t == 0) return "black";
+    else if (t == 1) return "#ccffcc";
+    else if (t == 2) return "#ff8888";
+    else if (t == 3) return "yellow";
+    else if (t == 4) return "black";
+    else if (t == 5) return "black";
+    else if (t == 6) return "#ccffcc";
+}
+
+function edgeColor(t) {
+    if (t == 1) return "black";
+    else if (t == 2) return "#08f";
+    else if (t == 3) return "gray";
+}
+
+function nodeStyle(selected) {
+    return selected ? "stroke-width: 2px; stroke: #00f" : "stroke-width: 1.5px";
+}
+
+var symbolGround = {
+    draw: function(context, size){
+        let s = size/2;
+
+        context.moveTo(0,-s);
+        context.lineTo(0,0);
+
+        context.moveTo(-s,0);
+        context.lineTo(s,0);
+
+        context.moveTo(-2*s/3,s/3);
+        context.lineTo(2*s/3,s/3);
+
+        context.moveTo(-s/3,2*s/3);
+        context.lineTo(s/3,2*s/3);
+    }
+}
+
+function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {
+    var ntab = {};
+
+    var groundOffset = 2.5 * node_size;
+
+    graph.nodes.forEach(function(d) {
+        ntab[d.name] = d;
+        d.selected = false;
+        d.previouslySelected = false;
+        d.nhd = [];
+    });
+
+    var spiders_and_boundaries = graph.nodes.filter(function(d) {
+        return d.t != 3;
+    });
+
+    graph.links.forEach(function(d) {
+        var s = ntab[d.source];
+        var t = ntab[d.target];
+        d.source = s;
+        d.target = t;
+        s.nhd.push(t);
+        t.nhd.push(s);
+    });
+
+    var shiftKey;
+
+    // SETUP SVG ITEMS
+
+    var svg = d3.select(tag)
+    //.attr("tabindex", 1)
+        .on("keydown.brush", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})
+        .on("keyup.brush", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})
+    //.each(function() { this.focus(); })
+        .append("svg")
+        .attr("style", "max-width: none; max-height: none")
+        .attr("width", width)
+        .attr("height", height);
+
+    var link = svg.append("g")
+        .attr("class", "link")
+        .selectAll("line")
+        .data(graph.links)
+        .enter().append("line")
+        .attr("stroke", function(d) { return edgeColor(d.t); })
+        .attr("style", "stroke-width: 1.5px");
+
+    var brush = svg.append("g")
+        .attr("class", "brush");
+
+    var node = svg.append("g")
+        .attr("class", "node")
+        .selectAll("g")
+        .data(graph.nodes)
+        .enter().append("g")
+        .attr("transform", function(d) {
+            return "translate(" + d.x + "," + d.y +")";
+        });
+
+    // Draw a ground symbol connected to the node.
+    node.filter(function(d) { return d.ground; })
+        .append("path")
+        .attr("stroke", "black")
+        .attr("style", "stroke-width: 1.5px")
+        .attr("fill", "none")
+        .attr("d", "M 0 0 L 0 "+(groundOffset))
+        .attr("class", "selectable");
+    node.filter(function(d) { return d.ground; })
+        .append("path")
+        .attr("stroke", "black")
+        .attr("style", "stroke-width: 1.5px")
+        .attr("fill", "none")
+        .attr("d", d3.symbol().type(symbolGround).size(node_size*1.5))
+        .attr("transform", "translate(0,"+groundOffset+")")
+        .attr("class", "selectable");
+
+    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })
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+        .attr("fill", function(d) { return nodeColor(d.t); })
+        .attr("stroke", "black")
+        .attr("class", "selectable");
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+        .attr("width", node_size * 1.5).attr("height", node_size * 1.5)
+        .attr("fill", function(d) { return nodeColor(d.t); })
+        .attr("stroke", "black")
+        .attr("class", "selectable");
+
+    // draw a triangle for d.t == 5
+    node.filter(function(d) { return d.t == 5; })
+        .append("path")
+        .attr("d", "M 0 0 L "+node_size+" "+node_size+" L -"+node_size+" "+node_size+" Z")
+        .attr("fill", function(d) { return nodeColor(d.t); })
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+        .attr("class", "selectable")
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+    // draw a square for Z box: d.t == 6
+    node.filter(function(d) { return d.t == 6; })
+        .append("rect")
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+        .attr("width", node_size * 1.5).attr("height", node_size * 1.5)
+        .attr("fill", function(d) { return nodeColor(d.t); })
+        .attr("stroke", "black")
+        .attr("class", "selectable");
+
+    node.filter(function(d) { return d.phase != ''; })
+        .append("text")
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+        .text(function (d) { return d.phase })
+        .attr("text-anchor", "middle")
+        .attr("font-size", "12px")
+        .attr("font-family", "monospace")
+        .attr("fill", "#00d")
+        .attr('style', 'pointer-events: none; user-select: none;');
+
+    if (show_labels) {
+        node.append("text")
+            .attr("y", -0.7 * node_size - 8)
+            .text(function (d) { return d.name; })
+            .attr("text-anchor", "middle")
+            .attr("font-size", "10px")
+            .attr("font-family", "monospace")
+            .attr("fill", "#999")
+            .attr('style', 'pointer-events: none; user-select: none;');
+    }
+
+    // Display the chosen data fields over the node.
+    node.filter(d => d.vdata.length > 0)
+        .append("text")
+        .attr("y", d => -0.7 * node_size - 14 - 10 * d.vdata.length)
+        .attr("text-anchor", "middle")
+        .attr("font-size", "8px")
+        .attr("font-family", "monospace")
+        .attr("fill", "#c66")
+        .attr('style', 'pointer-events: none; user-select: none;')
+        .selectAll("tspan")
+        .data(d => d.vdata)
+        .enter()
+        .append("tspan")
+        .attr("x", "0")
+        .attr("dy", "1.2em")
+        .text(x => x.join(": "));
+
+    if (scalar_str != "") {
+        svg.append("text")
+            .text(scalar_str)
+            .attr("x", 60).attr("y", 40)
+            .attr("text-anchor", "middle")
+    }
+
+    function update_hboxes() {
+        if (auto_hbox) {
+            var pos = {};
+            hbox.attr("transform", function(d) {
+                // calculate barycenter of non-hbox neighbours, then nudge a bit
+                // to the NE.
+                var x=0,y=0,sz=0;
+                for (var i = 0; i < d.nhd.length; ++i) {
+                    if (d.nhd[i].t != 3) {
+                        sz++;
+                        x += d.nhd[i].x;
+                        y += d.nhd[i].y;
+                    }
+                }
+
+                offset = 0.25 * scale;
+
+                if (sz != 0) {
+                    x = (x/sz) + offset;
+                    y = (y/sz) - offset;
+
+                    while (pos[[x,y]]) {
+                        x += offset;
+                    }
+                    d.x = x;
+                    d.y = y;
+                    pos[[x,y]] = true;
+                }
+
+                return "translate("+d.x+","+d.y+")";
+            });
+        }
+    }
+
+    update_hboxes();
+
+    link.attr("x1", function(d) { return d.source.x; })
+        .attr("y1", function(d) { return d.source.y; })
+        .attr("x2", function(d) { return d.target.x; })
+        .attr("y2", function(d) { return d.target.y; });
+
+    // EVENTS FOR DRAGGING AND SELECTION
+
+    node.on("mousedown", function(d) {
+        if (shiftKey) {
+            d3.select(this).selectAll(".selectable").attr("style", nodeStyle(d.selected = !d.selected));
+            d3.event.stopImmediatePropagation();
+        } else if (!d.selected) {
+            node.selectAll(".selectable").attr("style", function(p) { return nodeStyle(p.selected = d === p); });
+        }
+    })
+        .call(d3.drag().on("drag", function(d) {
+            var dx = d3.event.dx;
+            var dy = d3.event.dy;
+            // node.filter(function(d) { return d.selected; })
+            //     .attr("cx", function(d) { return d.x += dx; })
+            //     .attr("cy", function(d) { return d.y += dy; });
+            node.filter(function(d) { return d.selected; })
+                .attr("transform", function(d) {
+                    d.x += dx;
+                    d.y += dy;
+                    return "translate(" + d.x + "," + d.y +")";
+                });
+
+            update_hboxes();
+
+            link.filter(function(d) { return d.source.selected ||
+                    (auto_hbox && d.source.t == 3); })
+                .attr("x1", function(d) { return d.source.x; })
+                .attr("y1", function(d) { return d.source.y; });
+
+            link.filter(function(d) { return d.target.selected ||
+                    (auto_hbox && d.target.t == 3); })
+                .attr("x2", function(d) { return d.target.x; })
+                .attr("y2", function(d) { return d.target.y; });
+
+            // text.filter(function(d) { return d.selected; })
+            //     .attr("x", function(d) { return d.x; })
+            //     .attr("y", function(d) { return d.y + 0.7 * node_size + 14; });
+        }));
+
+    brush.call(d3.brush().keyModifiers(false)
+        .extent([[0, 0], [width, height]])
+        .on("start", function() {
+            if (d3.event.sourceEvent.type !== "end") {
+                node.selectAll(".selectable").attr("style", function(d) {
+                    return nodeStyle(
+                        d.selected = d.previouslySelected = shiftKey &&
+                        d.selected);
+                });
+            }
+        })
+        .on("brush", function() {
+            if (d3.event.sourceEvent.type !== "end") {
+                var selection = d3.event.selection;
+                node.selectAll(".selectable").attr("style", function(d) {
+                    return nodeStyle(d.selected = d.previouslySelected ^
+                        (selection != null
+                            && selection[0][0] <= d.x && d.x < selection[1][0]
+                            && selection[0][1] <= d.y && d.y < selection[1][1]));
+                });
+            }
+        })
+        .on("end", function() {
+            if (d3.event.selection != null) {
+                d3.select(this).call(d3.event.target.move, null);
+            }
+        }));
+}
+
+
+showGraph('#graph-output-I4zCJPnC',
+  JSON.parse('{"nodes": [{"name": "0", "x": 50, "y": 100, "t": 0, "phase": "", "ground": false, "vdata": []}, {"name": "1", "x": 50, "y": 150, "t": 0, "phase": "", "ground": false, "vdata": []}, {"name": "16", "x": 200, "y": 100, "t": 0, "phase": "", "ground": false, "vdata": []}, {"name": "17", "x": 200, "y": 150, "t": 0, "phase": "", "ground": false, "vdata": []}, {"name": "18", "x": 100, "y": 100, "t": 1, "phase": "", "ground": false, "vdata": []}, {"name": "19", "x": 100, "y": 150, "t": 1, "phase": "", "ground": false, "vdata": []}, {"name": "20", "x": 150, "y": 100, "t": 1, "phase": "", "ground": false, "vdata": []}, {"name": "21", "x": 150, "y": 150, "t": 1, "phase": "", "ground": false, "vdata": []}], "links": [{"source": "0", "target": "18", "t": 2}, {"source": "1", "target": "19", "t": 2}, {"source": "16", "target": "20", "t": 1}, {"source": "17", "target": "21", "t": 1}, {"source": "18", "target": "20", "t": 2}, {"source": "19", "target": "21", "t": 2}]}'), 250, 200, 50,
+  10.0, false, false, '');
+</script>
+
+
+The diagram is a double identity diagram.
+
 ## Approximate contraction and photon loss: fusion teleportation
 
 Teleportation with **fusion measurements** uses a Bell pair of dual-rail qubits as the channel: Alice fuses the input with her half using a Type-II fusion, reads the classical outcomes, and Bob applies the corresponding correction. In the **success** branch, the overall map is the **identity** on the teleported qubit up to a known Pauli byproduct, which Bob removes with a conditioned \(X\) correction. In the **failure** branch, the input is effectively measured and the opposite state is prepared at the output. For the standard Type-II scheme this yields identity with probability \(1/2\), and failure otherwise; the paper’s diagrams show both branches explicitly and how the correction restores the state.
@@ -283,7 +669,7 @@ fusion_teleportation_monoidal_syntax.foliation().draw(figsize=(8, 8))
 
 
 
-![svg](./docs/notebooks/readme_example_files/readme_example_33_0.svg)
+![svg](./docs/notebooks/readme_example_files/readme_example_40_0.svg)
 
 
 
@@ -354,7 +740,35 @@ plt.ylabel('Average cosine similarity')
 plt.title('Fusion-based Teleportation similarity vs Contraction Chi')
 
 ```
-![svg](./docs/notebooks/readme_example_files/readme_example_38_2.svg)
+
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
+      warnings.warn(
+
+
+
+
+
+    Text(0.5, 1.0, 'Fusion-based Teleportation similarity vs Contraction Chi')
+
+
+
+
+
+![svg](./docs/notebooks/readme_example_files/readme_example_45_2.svg)
 
 
 
@@ -435,7 +849,23 @@ plt.ylabel('Fidelity')
 plt.title('Fusion-based Teleportation: Photon Survival Probability vs Fidelity')
 
 ```
-![svg](./docs/notebooks/readme_example_files/readme_example_42_2.svg)
+
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part
+      return math.isfinite(val)
+    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part
+      return np.asarray(x, float)
+
+
+
+
+
+    Text(0.5, 1.0, 'Fusion-based Teleportation: Photon Survival Probability vs Fidelity')
+
+
+
+
+
+![svg](./docs/notebooks/readme_example_files/readme_example_49_2.svg)
 
 
 
@@ -482,7 +912,7 @@ Equation(protocol >> measure, bell_state >> measure).draw(figsize=(8, 8))
 
 
 
-![svg](./docs/notebooks/readme_example_files/readme_example_47_0.svg)
+![svg](./docs/notebooks/readme_example_files/readme_example_54_0.svg)
 
 
 
@@ -543,7 +973,7 @@ plt.show()
 
 
 
-![svg](./docs/notebooks/readme_example_files/readme_example_52_0.svg)
+![svg](./docs/notebooks/readme_example_files/readme_example_59_0.svg)
 
 
 
@@ -570,7 +1000,7 @@ pattern.draw_graph()
 
 
 
-![svg](./docs/notebooks/readme_example_files/readme_example_55_1.svg)
+![svg](./docs/notebooks/readme_example_files/readme_example_62_1.svg)
 
 
 
@@ -640,7 +1070,7 @@ pcvl.pdisplay(p, recursive=True)
 
 
 
-![svg](./docs/notebooks/readme_example_files/readme_example_61_0.svg)
+![svg](./docs/notebooks/readme_example_files/readme_example_68_0.svg)
 
 
 

From 6fcdf227cb26cfed4b6d156523c3f6bd50be802b Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Mon, 6 Oct 2025 13:45:47 +0100
Subject: [PATCH 50/59] pyzx graph in readme

---
 README.md                                     | 337 +-----------------
 .../readme_example_files/pyzx_identity.png    | Bin 0 -> 2352 bytes
 2 files changed, 2 insertions(+), 335 deletions(-)
 create mode 100644 docs/notebooks/readme_example_files/pyzx_identity.png

diff --git a/README.md b/README.md
index d0aac3ad..135f5e79 100644
--- a/README.md
+++ b/README.md
@@ -2,7 +2,7 @@
 
 Optyx is an open-source Python library for designing, simulating, and optimizing networked, hybrid qubit–photon architectures. It offers a compositional, ZX/ZW-based string-diagram front end (built within the DisCoPy ecosystem) that lets you specify experiments mixing qubit registers with discrete-variable photonic modes, lossy channels, heralded measurements, and classical/quantum feedback. Optyx compiles these diagrams to optimized tensor networks and executes them with state-of-the-art contraction backends (Quimb + Cotengra), delivering substantial speedups on low-depth circuits. The result is an end-to-end workflow—from high-level syntax to numerics—well-suited for rapid prototyping of qubit-photon experiments.
 
-## Basic Optyx syntax: the Hong-Ou-Mandel effect./docs/notebooks/
+## Basic Optyx syntax: the Hong-Ou-Mandel effect
 
 We will present the basics of Optyx with a simple example from linear optics.
 
@@ -250,340 +250,7 @@ pyzx_graph.normalize()
 pyzx.draw(pyzx_graph)
 ```
 
-
-<div style="overflow:auto" id="graph-output-I4zCJPnC"></div>
-<script type="module">
-var d3;
-if (d3 == null) { d3 = await import("https://cdn.skypack.dev/d3@5"); }
-// PyZX - Python library for quantum circuit rewriting
-//        and optimisation using the ZX-calculus
-// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering
-
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-
-//    http://www.apache.org/licenses/LICENSE-2.0
-
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-// styling functions
-function nodeColor(t) {
-    if (t == 0) return "black";
-    else if (t == 1) return "#ccffcc";
-    else if (t == 2) return "#ff8888";
-    else if (t == 3) return "yellow";
-    else if (t == 4) return "black";
-    else if (t == 5) return "black";
-    else if (t == 6) return "#ccffcc";
-}
-
-function edgeColor(t) {
-    if (t == 1) return "black";
-    else if (t == 2) return "#08f";
-    else if (t == 3) return "gray";
-}
-
-function nodeStyle(selected) {
-    return selected ? "stroke-width: 2px; stroke: #00f" : "stroke-width: 1.5px";
-}
-
-var symbolGround = {
-    draw: function(context, size){
-        let s = size/2;
-
-        context.moveTo(0,-s);
-        context.lineTo(0,0);
-
-        context.moveTo(-s,0);
-        context.lineTo(s,0);
-
-        context.moveTo(-2*s/3,s/3);
-        context.lineTo(2*s/3,s/3);
-
-        context.moveTo(-s/3,2*s/3);
-        context.lineTo(s/3,2*s/3);
-    }
-}
-
-function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {
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-
-    var groundOffset = 2.5 * node_size;
-
-    graph.nodes.forEach(function(d) {
-        ntab[d.name] = d;
-        d.selected = false;
-        d.previouslySelected = false;
-        d.nhd = [];
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-    var spiders_and_boundaries = graph.nodes.filter(function(d) {
-        return d.t != 3;
-    });
-
-    graph.links.forEach(function(d) {
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-        d.source = s;
-        d.target = t;
-        s.nhd.push(t);
-        t.nhd.push(s);
-    });
-
-    var shiftKey;
-
-    // SETUP SVG ITEMS
-
-    var svg = d3.select(tag)
-    //.attr("tabindex", 1)
-        .on("keydown.brush", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})
-        .on("keyup.brush", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})
-    //.each(function() { this.focus(); })
-        .append("svg")
-        .attr("style", "max-width: none; max-height: none")
-        .attr("width", width)
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-
-    var link = svg.append("g")
-        .attr("class", "link")
-        .selectAll("line")
-        .data(graph.links)
-        .enter().append("line")
-        .attr("stroke", function(d) { return edgeColor(d.t); })
-        .attr("style", "stroke-width: 1.5px");
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-    var brush = svg.append("g")
-        .attr("class", "brush");
-
-    var node = svg.append("g")
-        .attr("class", "node")
-        .selectAll("g")
-        .data(graph.nodes)
-        .enter().append("g")
-        .attr("transform", function(d) {
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-        });
-
-    // Draw a ground symbol connected to the node.
-    node.filter(function(d) { return d.ground; })
-        .append("path")
-        .attr("stroke", "black")
-        .attr("style", "stroke-width: 1.5px")
-        .attr("fill", "none")
-        .attr("d", "M 0 0 L 0 "+(groundOffset))
-        .attr("class", "selectable");
-    node.filter(function(d) { return d.ground; })
-        .append("path")
-        .attr("stroke", "black")
-        .attr("style", "stroke-width: 1.5px")
-        .attr("fill", "none")
-        .attr("d", d3.symbol().type(symbolGround).size(node_size*1.5))
-        .attr("transform", "translate(0,"+groundOffset+")")
-        .attr("class", "selectable");
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-        .attr("r", function(d) {
-            if (d.t == 0) return 0.5 * node_size;
-            else if (d.t == 4) return 0.25 * node_size;
-            else return node_size;
-        })
-        .attr("fill", function(d) { return nodeColor(d.t); })
-        .attr("stroke", "black")
-        .attr("class", "selectable");
-
-    var hbox = node.filter(function(d) { return d.t == 3; });
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-        .attr("x", -0.75 * node_size).attr("y", -0.75 * node_size)
-        .attr("width", node_size * 1.5).attr("height", node_size * 1.5)
-        .attr("fill", function(d) { return nodeColor(d.t); })
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From 5a9497b5eb6adb8be8086790aa7e8ead3467c37c Mon Sep 17 00:00:00 2001
From: Mateusz Kupper <mateusz.kupper@gmail.com>
Date: Mon, 6 Oct 2025 14:01:14 +0100
Subject: [PATCH 51/59] Clean up user warning messages in README

Removed multiple user warnings related to HyperOptimizer and matplotlib from README.
---
 README.md | 42 ------------------------------------------
 1 file changed, 42 deletions(-)

diff --git a/README.md b/README.md
index 135f5e79..f82a2690 100644
--- a/README.md
+++ b/README.md
@@ -408,33 +408,6 @@ plt.title('Fusion-based Teleportation similarity vs Contraction Chi')
 
 ```
 
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/cotengra/hyperoptimizers/hyper.py:329: UserWarning: Trial error: not enough values to unpack (expected 2, got 1). Set `HyperOptimizer` kwarg `on_trial_error='raise'` to raise this error, or `on_trial_error='ignore'` to silence.
-      warnings.warn(
-
-
-
-
-
-    Text(0.5, 1.0, 'Fusion-based Teleportation similarity vs Contraction Chi')
-
-
-
-
-
 ![svg](./docs/notebooks/readme_example_files/readme_example_45_2.svg)
 
 
@@ -517,21 +490,6 @@ plt.title('Fusion-based Teleportation: Photon Survival Probability vs Fidelity')
 
 ```
 
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part
-      return math.isfinite(val)
-    /home/mateuszkupper/Documents/optyx/.venv/lib/python3.12/site-packages/matplotlib/cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part
-      return np.asarray(x, float)
-
-
-
-
-
-    Text(0.5, 1.0, 'Fusion-based Teleportation: Photon Survival Probability vs Fidelity')
-
-
-
-
-
 ![svg](./docs/notebooks/readme_example_files/readme_example_49_2.svg)
 
 

From 2838a9fbf1550370a6fcd6c8e676d6033a6f24ba Mon Sep 17 00:00:00 2001
From: Mateusz Kupper <mateusz.kupper@gmail.com>
Date: Mon, 6 Oct 2025 17:16:42 +0100
Subject: [PATCH 52/59] Remove duplicate content in README.md

Removed duplicate paragraph about teleportation with fusion measurements.
---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index f82a2690..6c3809bf 100644
--- a/README.md
+++ b/README.md
@@ -257,7 +257,7 @@ The diagram is a double identity diagram.
 
 ## Approximate contraction and photon loss: fusion teleportation
 
-Teleportation with **fusion measurements** uses a Bell pair of dual-rail qubits as the channel: Alice fuses the input with her half using a Type-II fusion, reads the classical outcomes, and Bob applies the corresponding correction. In the **success** branch, the overall map is the **identity** on the teleported qubit up to a known Pauli byproduct, which Bob removes with a conditioned \(X\) correction. In the **failure** branch, the input is effectively measured and the opposite state is prepared at the output. For the standard Type-II scheme this yields identity with probability \(1/2\), and failure otherwise; the paper’s diagrams show both branches explicitly and how the correction restores the state.
+Teleportation with **fusion measurements** uses a Bell pair of dual-rail qubits as the channel: Alice fuses the input with her half using a Type-II fusion, reads the classical outcomes, and Bob applies the corresponding correction. In the **success** branch, the overall map is the **identity** on the teleported qubit up to a known Pauli byproduct, which Bob removes with a conditioned \(X\) correction. In the **failure** branch, the input is effectively measured and the opposite state is prepared at the output. For the standard Type-II scheme this yields identity with probability \(1/2\), and failure otherwise; the diagrams show both branches explicitly and how the correction restores the state.
 
 
 Ursin, R., Jennewein, T., Aspelmeyer, M. et al. Quantum teleportation across the Danube. Nature 430, 849 (2004). https://doi.org/10.1038/430849a :

From 2d9686b476b1b7498d391c31943015fcfec75c59 Mon Sep 17 00:00:00 2001
From: giodefelice <giodefelice@protonmail.com>
Date: Mon, 6 Oct 2025 19:47:38 +0100
Subject: [PATCH 53/59] edit README, add CtrlX and CtrlZ to classical

---
 README.md          | 539 ++++++++-------------------------------------
 optyx/classical.py |  16 ++
 2 files changed, 107 insertions(+), 448 deletions(-)

diff --git a/README.md b/README.md
index 6c3809bf..e89b0db2 100644
--- a/README.md
+++ b/README.md
@@ -1,151 +1,59 @@
 # Optyx: A ZX-based Python library for networked quantum architectures
 
-Optyx is an open-source Python library for designing, simulating, and optimizing networked, hybrid qubit–photon architectures. It offers a compositional, ZX/ZW-based string-diagram front end (built within the DisCoPy ecosystem) that lets you specify experiments mixing qubit registers with discrete-variable photonic modes, lossy channels, heralded measurements, and classical/quantum feedback. Optyx compiles these diagrams to optimized tensor networks and executes them with state-of-the-art contraction backends (Quimb + Cotengra), delivering substantial speedups on low-depth circuits. The result is an end-to-end workflow—from high-level syntax to numerics—well-suited for rapid prototyping of qubit-photon experiments.
+Optyx is an open-source Python library for designing, simulating, and optimizing networked, hybrid qubit–photon architectures. It offers a compositional, ZX/ZW-based, string-diagram front end (built within the [DisCoPy](https://github.com/discopy/discopy) ecosystem) that lets you specify experiments mixing qubit registers with discrete-variable photonic modes, lossy channels, heralded measurements, and classical/quantum feedback. Optyx compiles these diagrams to optimized tensor networks and executes them with state-of-the-art contraction backends ([Quimb](https://github.com/jcmgray/quimb) and [Cotengra](https://github.com/jcmgray/cotengra)), delivering substantial speedups on hybrid circuits. The result is an end-to-end workflow—from high-level syntax to numerics—well-suited for rapid prototyping of qubit-photon experiments.
 
-## Basic Optyx syntax: the Hong-Ou-Mandel effect
+## Basic syntax: the CNOT gate
 
-We will present the basics of Optyx with a simple example from linear optics.
+Circuits in Optyx are **diagrams** made of **wires** and **boxes**. Wires represent different types of data such as quantum `qubit` and `qmode` or classical `bit` and `mode`. Boxes are basic processes with input and output wires that can be composed, in sequence or in parallel, to form diagrams.
 
-The Hong–Ou–Mandel (HOM) effect is a two-photon interference phenomenon where indistinguishable photons entering a 50:50 beamsplitter “bunch” and exit together through the same output register. When their temporal, spectral, polarization, and spatial modes overlap perfectly, destructive interference suppresses the outcome with one photon in each output. This effect is a standard benchmark for photon indistinguishability in photonic experiments.
-
-### Experiment definition
-
-Circuits in Optyx are diagrams made of typed wires (qubits, photonic modes, classical bits) and generators (gates, sources, optics, measurements). You build them by connecting outputs to inputs (sequence) and placing blocks side-by-side (parallel); types must match at every connection. Generators carry parameters and labels; measurements produce classical wires you can route into later blocks. A circuit is just the set of generators plus the wiring between their ports.
-
-Let us build a diagram to study the HOM effect.
+### Monoidal syntax
 
+In monoidal syntax, `>>` denotes sequential composition and `@` denotes parallel composition (also known as tensor product).
+For example, you can build the CNOT gate from the **Z** and **X** generators of the **ZX caluclus** (don't forget the scalar!).
 
 ```python
-from optyx.photonic import BBS
+from optyx import qubit
+from optyx.qubits import Z, X, Scalar
 
-# diagram generators:
-# beam-splitter
-beam_splitter = BBS(0)
-beam_splitter.draw()
+cnot = Z(1, 2) @ qubit >> qubit @ X(2, 1) @ Scalar(2 ** 0.5)
+cnot.draw()
 ```
 
+### Function syntax
 
-
-![svg](./docs/notebooks/readme_example_files/readme_example_5_0.svg)
-
-
-
+Alternatively, you can treat each generator as a **function** acting on **labelled wires** and **call the generators** 
+directly on the labels. This makes complex diagrams easier to read and write, and mirrors the style used in [Guppy](https://github.com/CQCL/guppylang).
 
 ```python
-from optyx.photonic import Create
-
-# diagram composition with monoidal syntax
-# create two single-photon states and send them to a beam-splitter
-hong_ou_mandel = (
-    Create(1) @ Create(1) >>
-    beam_splitter
+@Channel.from_callable(
+  dom=qubit @ qubit, cod=qubit @ qubit
 )
-
-hong_ou_mandel.draw()
-```
-
-
-
-![svg](./docs/notebooks/readme_example_files/readme_example_6_0.svg)
-
-
-
-The result of this experiment should be a zero probability of having single photons in two output modes:
-
- ![HOM](./docs/notebooks/hom.png "Hong-Ou-Mandel Effect")
-
-### Diagram evaluation
-
-Call `diagram.eval()` to evaluate a diagram (Quimb backend by default). It returns an evaluated object; use `.tensor.array` to extract the numeric tensor/array, or `.prob_dist()` to get an outcome distribution. You can chain it inline, e.g., `(...).eval().tensor.array`.
-
-
-```python
-# an amplitude (raw result of tensor contraction)
-from optyx.classical import Select
-(
-    hong_ou_mandel >> Select(1, 1)
-).eval().tensor.array
-```
-
-
-
-
-    array(-0.+0.j)
-
-
-
-
-```python
-hong_ou_mandel.eval().prob_dist()
+def cnot(a, b):
+  c, d = Z(1, 2)(a)
+  e = X(2, 1)(d, b)
+  Scalar(2 ** 0.5)()
+  return c, e
 ```
 
+## Qubit example: teleportation protocol
 
-
-
-    {(0, 2): 0.5, (1, 1): 4.9303806576313227e-32, (2, 0): 0.5}
-
-
-
-## Function syntax and backends: qubit teleportation
-
-Quantum teleportation transfers an unknown qubit state from sender (Alice) to receiver (Bob) using shared entanglement and two classical bits. Alice performs a joint Bell-state measurement on the unknown qubit and her half of an entangled pair, which projects Bob’s distant qubit into a state related to the original. She sends the two-bit outcome to Bob, who applies a corresponding Pauli correction (I, X, Z, or XZ) to recover the exact state. No information travels faster than light and the original is destroyed by measurement, so the state is relocated—not copied.
+Quantum teleportation transfers an unknown qubit state from sender (Alice) to receiver (Bob) using shared entanglement and feedforward of two classical bits. Alice performs a joint Bell-state measurement on the unknown qubit and her half of an entangled pair, and sends the two-bit outcome to Bob, who applies a corresponding Pauli correction (I, X, Z, or XZ) to recover the exact state.
 
 https://en.wikipedia.org/wiki/Quantum_teleportation#/media/File:Quantum_teleportation_circuit.svg :
 
 <img src="./docs/notebooks/teleport.svg" alt="Teleportation Protocol" width="800" style="max-width:100%;">
 
-
-```python
-from optyx import qubit, bit
-from optyx.qubits import Scalar
-
-from optyx import Channel
-from optyx.qubits import Z, X, H, Measure, Scalar, qubit, bit
-from optyx.classical import BitControlledGate
-from optyx.core import zx, diagram
-```
-
 ### Define the protocol
 
-
-Instead of wiring generators together with sequential (`>>`) and parallel (`@`) composition (which we call the monoidal syntax), you can treat each generator as a **function on its domain wires**. You **label the wires** and then **call generators with those labels**, which lets you feed specific wires directly into the right box without inserting explicit `Swap`s to reorder them. This makes complex diagrams easier to read and write, and mirrors the style used in **Guppy**; it’s an alternative surface syntax that’s equivalent to the usual `>>`/`@` composition.
-
-
+Write the protocol using function syntax:
 
 ```python
-# function syntax
-# CNOT from ZX generators
+from optyx import bit
+from optyx.qubits import Measure
+from optyx.classical import CtrlX, CtrlZ
 
-@Channel.from_callable(
-  dom=qubit @ qubit, cod=qubit @ qubit
-)
-def cnot(a, b):
-  c, d = Z(1, 2)(a)
-  Scalar(2 ** 0.5)()
-  return c, X(2, 1)(d, b)
-```
-
-
-```python
 bell = Scalar(0.5 ** 0.5) @ Z(0, 2)
 
-controlled_X = Channel(
-  "Controlled-X",
-  zx.X(2, 1) @ diagram.Scalar(2 ** 0.5),
-  dom = bit @ qubit,
-  cod = qubit
-)
-
-controlled_Z = Channel(
-  "Controlled-Z",
-  (
-    zx.H @ diagram.bit >>
-    zx.Z(2, 1) @ diagram.Scalar(2 ** 0.5)
-  ),
-  dom = bit @ qubit,
-  cod = qubit
-)
-
 @Channel.from_callable(
   dom=qubit, cod=qubit
 )
@@ -154,33 +62,30 @@ def teleportation(c):
   cc, aa = cnot(c, a)
   c_ = Measure(1)(H()(cc))
   a_ = Measure(1)(aa)
-  bb = controlled_X(a_, b)
-  return controlled_Z(c_, bb)
+  bb = CtrlX(a_, b)
+  return CtrlZ(c_, bb)
 ```
 
+Or using monoidal syntax:
 
 ```python
-# function syntax avoids explicit swaps and identity wires
-# this is the equivalent monoidal syntax:
-
 teleportation_monoidal_syntax = (
     qubit @ bell >>
     cnot @ qubit >>
     H() @ qubit ** 2 >>
     Measure(1) @ Measure(1) @ qubit >>
-    bit @ controlled_X >>
-    controlled_Z
+    bit @ CtrlX >>
+    CtrlZ
 )
 ```
 
-### Verify the protocol
+### Simulate using backends
 
 
 ```python
 import numpy as np
 from optyx.qubits import Id
 
-# both implementations are equivalent
 np.allclose(
     teleportation.eval().tensor.array,
     teleportation_monoidal_syntax.eval().tensor.array,
@@ -188,20 +93,9 @@ np.allclose(
 )
 ```
 
-
-
-
-    True
-
-
-
 Optyx evaluates diagrams via pluggable backends. By default it compiles a diagram to a tensor network, optimizes a contraction path with **cotengra**, and contracts it with **quimb** (CPU/GPU; dense/sparse). For linear-optical circuits, Optyx also exposes a **Perceval** backend using permanent-based algorithms, and a tensor-network-based **DisCoPy** backend; you can choose among these depending on the task.
 
-
-
 ```python
-# backends (Perceval, Discopy, Quimb)
-
 from optyx.core.backends import (
     DiscopyBackend,
     QuimbBackend
@@ -214,12 +108,6 @@ np.allclose(
 ```
 
 
-
-
-    True
-
-
-
 ### Verify with PyZX
 
 We can obtain the underlying CPTP map by doubling (CP-construction) an Optyx diagram:
@@ -235,16 +123,12 @@ teleportation_monoidal_syntax.double().draw(figsize=(8, 8))
 
 
 
-This way we can use PyZX and its optimisation/simplifications functionalities:
+This way we can use [PyZX](https://github.com/zxcalc/pyzx) and its optimisation/simplifications functionalities:
 
 
 ```python
 import pyzx
 pyzx_graph = teleportation_monoidal_syntax.double().to_pyzx()
-```
-
-
-```python
 pyzx.full_reduce(pyzx_graph, quiet=True)
 pyzx_graph.normalize()
 pyzx.draw(pyzx_graph)
@@ -252,261 +136,89 @@ pyzx.draw(pyzx_graph)
 
 ![png](./docs/notebooks/readme_example_files/pyzx_identity.png)
 
+The diagram (a doubled identity) is the identity CPTP map as expected.
 
-The diagram is a double identity diagram.
 
-## Approximate contraction and photon loss: fusion teleportation
+## Photonic example: the Hong-Ou-Mandel effect
 
-Teleportation with **fusion measurements** uses a Bell pair of dual-rail qubits as the channel: Alice fuses the input with her half using a Type-II fusion, reads the classical outcomes, and Bob applies the corresponding correction. In the **success** branch, the overall map is the **identity** on the teleported qubit up to a known Pauli byproduct, which Bob removes with a conditioned \(X\) correction. In the **failure** branch, the input is effectively measured and the opposite state is prepared at the output. For the standard Type-II scheme this yields identity with probability \(1/2\), and failure otherwise; the diagrams show both branches explicitly and how the correction restores the state.
-
-
-Ursin, R., Jennewein, T., Aspelmeyer, M. et al. Quantum teleportation across the Danube. Nature 430, 849 (2004). https://doi.org/10.1038/430849a :
-
-<img src="./docs/notebooks/teleportation_danube.png" alt="Fusion teleportation across the Danube" width="1150px">
-
-Graphically, the fusion measurement we would like to use, takes the following form:
-
-<img src="./docs/notebooks/fusion_ii.png" alt="Fusion measurement" width="1200px">
-
-
-where $\underline{a}, \underline{b}, \underline{c}, \underline{d}$ are the measurement outcomes as the measured photon numbers.
-
-$\underline{s} = \underline{a} \oplus \underline{b}$
-
-$\underline{k} = \underline{s} (\underline{b} + \underline{d}) + \neg \underline s (1 - \frac{\underline{a} + \underline{b}}{2})$
-
-### Define the protocol
-
-
-```python
-from optyx.photonic import DualRail
-
-dual_rail_encoded_bell = (
-    bell >>
-    DualRail(1) @ DualRail(1)
-)
-```
-
-
-```python
-from optyx.classical import PostselectBit, BitControlledGate
-from optyx.photonic import Phase
-from optyx.photonic import HadamardBS, qmode
-
-# postselect on fusion success
-fusion_failure_processing = PostselectBit(1)
-
-# apply the box if the control bit is 1, otherwise apply an identity channel
-correction = BitControlledGate(
-    HadamardBS() >>
-    (Phase(0.5) @ qmode) >>
-    HadamardBS()
-)
-```
+he Hong–Ou–Mandel (HOM) effect is a two-photon interference phenomenon where indistinguishable photons entering a 50:50 beamsplitter “bunch” and exit together through the same output register. This effect is a standard benchmark for photon indistinguishability in photonic experiments. We show via simulation how both distinguishability and photon loss affect the effect.
 
+### Noiseless setting
 
 ```python
-from optyx.photonic import FusionTypeII
-
-@Channel.from_callable(
-    dom=qubit, cod=qmode @ qmode
-)
-def fusion_teleportation(a):
-    dual_rail_encoded_input = DualRail(1)(a)
-    b, c, d, e = dual_rail_encoded_bell()
-    s, k = FusionTypeII()(*dual_rail_encoded_input, b, c)
-    fusion_failure_processing(s)
-    dr_output_1, dr_output_2 = correction(k, d, e)
-    return dr_output_1, dr_output_2
-```
-
+from optyx.photonic import BS, Create
 
-```python
-from optyx.photonic import FusionTypeII
+beam_splitter = BS
+beam_splitter.draw()
 
-fusion_teleportation_monoidal_syntax = (
-    DualRail(1) @ dual_rail_encoded_bell >>
-    FusionTypeII() @ qmode**2 >>
-    fusion_failure_processing @ correction
+HOM = (
+    Create(1) @ Create(1) >>
+    beam_splitter
 )
 
-fusion_teleportation_monoidal_syntax.foliation().draw(figsize=(8, 8))
-
+HOM.eval().prob_dist()
 ```
 
 
 
-![svg](./docs/notebooks/readme_example_files/readme_example_40_0.svg)
 
+    {(0, 2): 0.5, (1, 1): 0, (2, 0): 0.5}
 
 
-### Verify the protocol
+### Photon loss
 
+We model photon loss in optyx using the `PhotonLoss` generator. We can check that the HOM circuit gives a non-zero probability of detecting one photon, in the presence of loss.
 
 ```python
-import numpy as np
-from optyx.photonic import Id
-
-array_teleportation = fusion_teleportation_monoidal_syntax.eval().tensor.array
-array_dr = (DualRail(1) @ Scalar(0.5**0.5)).double().to_tensor().eval().array
-
-np.allclose(array_teleportation[:, :, :2, :2, :2, :2], array_dr)
+from optyx.photonic import Id, PhotonLoss, NumberResolvingMeasurement
+from optyx.classical import AddN
 
+lossy_HOM = Create(1, 1) >> PhotonLoss(0.8) @ Id(1) >> BS 
+lossy_HOM = lossy_HOM >> NumberResolvingMeasurement(2) >> AddN(2)
+assert np.isclose(lossy_HOM.eval().prob_dist()[(1,)], 0.2)
 ```
 
 
+### Distinguishability
 
-
-    True
-
-
-
-### Approximate contraction with Quimb and Cotengra
-
-Approximate contraction in Optyx uses cotengra to plan a low-cost contraction with memory-aware slicing, then executes it in quimb with optional compression of intermediates. Instead of multiplying tensors exactly, large merges are factorized and truncated (e.g., SVD) so only the dominant singular components are kept; you trade speed and memory for a controlled approximation error. Tightening the truncation tolerance (or increasing the allowed bond size) yields higher accuracy at higher cost, while more aggressive truncation/slicing gives faster, lower-memory contractions with small, quantifiable loss in fidelity.
-
-
-```python
-def _flat(x):
-    return np.asarray(x, dtype=complex).ravel()
-
-def cosine_similarity(SU, SV):
-    a, b = _flat(SU), _flat(SV)
-    num = abs(np.vdot(a, b))
-    den = np.linalg.norm(a) * np.linalg.norm(b)
-    if den == 0:
-        return 0.0
-    return float(num / den)
-```
-
-
-```python
-from cotengra import HyperCompressedOptimizer
-
-# cosine similarity between the result of exact contaction and approximate contraction for different chis
-errors = []
-for chi in range(1, 6):
-    optimiser = HyperCompressedOptimizer(
-        chi=chi
-    )
-    error_for_chi = []
-    for _ in range(10):
-         error_for_chi.append(
-             cosine_similarity(
-                 fusion_teleportation.eval(QuimbBackend(optimiser)).tensor.array,
-                 array_teleportation
-             )
-         )
-    errors.append(np.median(error_for_chi))
-
-import matplotlib.pyplot as plt
-plt.plot(range(1, 6), errors, marker='o')
-plt.grid()
-plt.xlabel('Chi')
-plt.ylabel('Average cosine similarity')
-plt.title('Fusion-based Teleportation similarity vs Contraction Chi')
-
-```
-
-![svg](./docs/notebooks/readme_example_files/readme_example_45_2.svg)
-
-
-
-### Photon loss and channel fidelity
-
-Photon loss is when a photon that should arrive simply doesn’t. In Optyx, you model this by placing a dedicated loss generator exactly where the loss occurs; its single parameter is the photon survival probability. Photon loss is the primary failure mode for photonic qubits. In photonic computing it breaks multi-photon interference and reduces the success of fusion/measurement steps. That’s why if we want to study architectures, thresholds, and mitigation (repeaters, multiplexing, loss-tolerant encodings), we need to be able to model photon loss accurately.
-
-
-```python
-from optyx.photonic import FusionTypeII, PhotonLoss
-
-# photo loss is one of the main error sources in photonic quantum computing
-def fusion_teleportation_with_photon_loss(p):
-    @Channel.from_callable(
-        dom=qubit, cod=qmode**2
-    )
-    def fusion_teleportation(a):
-        dr_input_1, dr_input_2 = DualRail(1)(a)
-        b, c, d, e = dual_rail_encoded_bell()
-        # apply photon loss to all modes here:
-        #-----------------------------------
-        dr_input_1_loss, dr_input_2_loss, b_loss, c_loss, d_loss, e_loss = (
-            PhotonLoss(p)(dr_input_1), PhotonLoss(p)(dr_input_2),
-            PhotonLoss(p)(b), PhotonLoss(p)(c),
-            PhotonLoss(p)(d), PhotonLoss(p)(e)
-        )
-        #-----------------------------------
-        s, k = FusionTypeII()(dr_input_1_loss, dr_input_2_loss, b_loss, c_loss)
-        fusion_failure_processing(s)
-        output_rail_1, output_rail = correction(k, d_loss, e_loss)
-        return output_rail_1, output_rail
-    return fusion_teleportation
-```
-
-
-```python
-from optyx.core.channel import Spider, Diagram
-
-def get_perm(n):
-    return sorted(sorted(list(range(n))), key=lambda i: i % 2)
-
-def channel_fidelity(diagram_1, diagram_2):
-    bell_1 = Channel.tensor(*[Spider(0, 2, ty) for ty in diagram_1.dom])
-    permutation_1 = Diagram.permutation(get_perm(len(bell_1.cod)), bell_1.cod)
-
-    bell_2 = Channel.tensor(*[Spider(0, 2, ty) for ty in diagram_2.dom])
-    permutation_2 = Diagram.permutation(get_perm(len(bell_2.cod)), bell_2.cod)
-
-    choi_1 = bell_1 >> permutation_1 >> (diagram_1 @ diagram_1.dom)
-    choi_2 = bell_2 >> permutation_2 >> (diagram_2 @ diagram_2.dom)
-
-    return (choi_1 >> choi_2.dagger()).eval().tensor.array
-
-```
-
+We model distinshability in optyx by assigning **internal states** to photons in the circuit.
+The overlap between internal states defines the pairwise distinguishability of the corresponding photons.
 
 ```python
 import numpy as np
-import matplotlib.pyplot as plt
+from optyx.photonic import BS
 
-ps = np.linspace(0.0, 1.0, 20)
+internal_state_1 = [1, 0]
+internal_state_2 = [np.sqrt(0.9), np.sqrt(0.1)]
 
-# compute fidelity for different photon loss probabilities
-F_avg_vals = []
-succ_probs = []
-for p in ps:
-    S_impl = fusion_teleportation_with_photon_loss(p)
-    S_tgt  = fusion_teleportation_monoidal_syntax
-    s = channel_fidelity(S_impl, S_tgt)
+create = Create(1, 1, internal_states=(
+    internal_state_1, internal_state_2))
 
-    succ_probs.append(s)
-
-plt.figure()
-plt.plot(ps, succ_probs, marker='o')
-plt.grid(True)
-plt.xlabel('Photon Survival Probability (p)')
-plt.ylabel('Fidelity')
-plt.title('Fusion-based Teleportation: Photon Survival Probability vs Fidelity')
+distinguishable_HOM = create >> BS >> NumberResolvingMeasurement(2)
+result = distinguishable_HOM.inflate(
+    len(internal_state_1)).eval().prob_dist()
 
+theoretical_result = 0.5 - 0.5 * np.abs(
+    np.array(internal_state_1).dot(
+        np.array(internal_state_2).conjugate()))**2
+assert np.isclose(result[(1, 1)], theoretical_result, 3)
 ```
 
-![svg](./docs/notebooks/readme_example_files/readme_example_49_2.svg)
-
-
+ 
+## Hybrid example: distributed entanglement generation
 
-## Photon distinguishability: distributed entanglement generation
-
-Distributed entanglement generation links two distant quantum nodes (A and B) by creating a shared entangled pair. Each node emits a photon that travels to a shared site, where the photons interfere and a joint (Bell-state) detection flags success — instantly projecting A and B into an entangled state. Because attempts often fail due to loss, the process is repeated-until-success with timing. This is the core primitive behind quantum networks and repeaters, enabling long-distance QKD, teleportation, and multi-node protocols.
+Distributed entanglement generation links two distant quantum nodes (A and B) by creating a shared entangled pair. Each node emits a photon that travels to a shared site, where the photons interfere and a joint Bell measurement flags success — instantly projecting A and B into an entangled state. Because attempts often fail due to loss, the process is repeated-until-success with timing. This is the core primitive behind quantum networks and repeaters, enabling long-distance QKD, teleportation, and multi-node protocols.
 
 Main, D., Drmota, P., Nadlinger, D.P. et al. Distributed quantum computing across an optical network link. Nature 638, 383–388 (2025). https://doi.org/10.1038/s41586-024-08404-x~ :
 
 ![Distributed entanglement](./docs/notebooks/distributed_entanglement.png "An example of distributed entanglement generation")
 
 
+### Define the protocol
 
-### Fusion and photon distinguishability
-
-#### Define the protocol
+Bell measurements on photonic qubits can be performed probabilistically using a circuit known as Type II fusion.
+Since the photons are emitted from distinct processors, they will be partially distinguishable. 
+This is modeled in optyx by assigning internal states to the `DualRail` boxes that encode a qubit into two photonic modes.
 
 
 ```python
@@ -517,13 +229,12 @@ from discopy.drawing import Equation
 
 bell_state = Z(0, 2) @ Scalar(0.5 ** 0.5)
 
-# generators introducing new qubits accepting internal states
 internal_state_1 = [1, 0]
 internal_state_2 = [0, 1]
 dual_rail_encoding = lambda state: DualRail(1, internal_states=[state])
 encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(internal_state_2)
 
-# postselect on fusion success and no errors
+# postselect on fusion success and no Pauli byproducts
 post_select = PostselectBit(1) @ PostselectBit(0)
 
 protocol = (
@@ -535,54 +246,40 @@ measure = Measure(2)
 Equation(protocol >> measure, bell_state >> measure).draw(figsize=(8, 8))
 ```
 
-
-
 ![svg](./docs/notebooks/readme_example_files/readme_example_54_0.svg)
 
 
+#### Test the protocol for different internal states
 
-#### Define a set of internal states with varying degrees of distinguishability
-
-We test how partial photon distinguishability affects a heralded entanglement link. The experiment uses the overlap between two internal two-mode states (`rotated_unit_vectors`), encodes them into dual-rail photons (`dual_rail_encoding`), and performs a Type-II fusion with postselection (`FusionTypeII() >> post_select`). We then project onto the target Bell state (`... >> bell_state.dagger()`) to read off the heralded-state quality, and use a discard step (`... >> Discard(2)`) to extract the success probability. Plotting these versus the state overlap reveals how distinguishability simultaneously degrades fidelity and lowers the entanglement generation rate.
-
-
+We test how partial photon distinguishability affects the heralded entanglement link. We compute the **process fidelity** of the protocol(overlap between the noisy and ideal states).
 
 ```python
 import math
+from optyx.qubits import Discard
 
-# internal states - 2 dimensional - move further and further apart
 def rotated_unit_vectors(n: int = 10):
     for i in range(n):
         theta = i * (math.pi / 2) / (n - 1)
         yield (math.cos(theta), math.sin(theta))
 
 unit_vectors = list(rotated_unit_vectors(15))
-```
-
-#### Run the experiments
-
-
-```python
-from optyx.qubits import Discard
 
 inner_product_states = []
 inner_product_bell_states = []
 
-result_bell = bell_state.eval().tensor.array.flatten()
-result_bell = result_bell / np.linalg.norm(result_bell)
-
 for vector in unit_vectors:
     encoding_layer =  dual_rail_encoding(internal_state_1) @ dual_rail_encoding(vector)
     experiment = bell_state @ bell_state >> Id(1) @ (encoding_layer >> FusionTypeII()
                                                                                 >> post_select) @ Id(1)
 
-    f = (experiment >> bell_state.dagger()).inflate(2).eval().tensor.array
+    process_fidelity = (experiment >> bell_state.dagger()).inflate(2).eval().tensor.array
     normalisation = (experiment >> Discard(2)).inflate(2).eval().tensor.array
 
     inner_product_states.append(np.inner(vector, internal_state_1))
-    inner_product_bell_states.append(f/normalisation)
+    inner_product_bell_states.append(process_fidelity/normalisation)
 ```
 
+The simulation data reveals how distinguishability affects the fidelity of the entanglement generation protocol.
 
 ```python
 import matplotlib.pyplot as plt
@@ -596,17 +293,14 @@ plt.grid(True)
 plt.show()
 ```
 
-
-
 ![svg](./docs/notebooks/readme_example_files/readme_example_59_0.svg)
 
 
+## Interfaces with external libraries
 
-## Interfacing with external libraries
-
-### Graphix
+### Graphix interface
 
-Open graphs supported only for now (graph + measurements; desire to implement deterministically - no corrections)
+Import an `OpenGraph` from [graphix](https://github.com/TeamGraphix/graphix).
 
 
 ```python
@@ -617,44 +311,27 @@ circuit.cnot(0, 1)
 
 pattern = circuit.transpile().pattern
 
-pattern.draw_graph()
-```
-
-    The pattern is not consistent with flow or gflow structure.
-
-
-
-
-![svg](./docs/notebooks/readme_example_files/readme_example_62_1.svg)
-
-
-
-
-```python
 simulator = graphix.simulator.PatternSimulator(pattern, backend="statevector")
 graphix_result = simulator.run().psi.conj()
 ```
 
 
 ```python
-from optyx import qubits
+from optyx.qubits import Circuit, Ket
 
-optyx_zx = qubits.Circuit(pattern)
+optyx_zx = Circuit(pattern)
 
 optyx_res = (
     qubits.Ket("+")**2 >> optyx_zx
 ).eval().amplitudes()
-```
 
-
-```python
 for keys in optyx_res.keys():
     assert np.isclose(optyx_res[keys], graphix_result[keys], atol=1e-6)
 ```
 
 ### Perceval circuits and processors
 
-#### Define the protocol in Perceval
+Interface with both processors and circuits in [Perceval](https://github.com/Quandela/Perceval).
 
 
 ```python
@@ -694,25 +371,16 @@ pcvl.pdisplay(p, recursive=True)
 
 
 
-
 ![svg](./docs/notebooks/readme_example_files/readme_example_68_0.svg)
 
 
 
 
 
-```python
-from optyx.qubits import Ket
-
-state = Ket("+") >> Z(1, 1, 0.3)
-state_array = state.eval().tensor.array
-state_array = state_array / np.linalg.norm(state_array)
-```
-
-#### Evaluate the protocol in Perceval
-
+Evaluate the protocol in Perceval.
 
 ```python
+
 to_transmit = (complex(state_array[0])*pcvl.BasicState([1, 0]) +
                complex(state_array[1])*pcvl.BasicState([0, 1]))
 
@@ -725,26 +393,15 @@ p.min_detected_photons_filter(2)
 input_state *= pcvl.BasicState([0, 0])
 
 p.with_input(input_state)
-```
-
 
-```python
 result_perceval = p.probs()
 ```
 
-#### Convert to Optyx and simulate
+Convert to optyx and check that the results agree.
 
 
 ```python
-from optyx import Channel
-
 optyx_diagram = Channel.from_perceval(p)
-```
-
-
-```python
-from optyx.qubits import Scalar, Ket
-from optyx.photonic import DualRail
 
 bell_state = Z(0, 2) @ Scalar(0.5**0.5)
 transmit = Ket("+") >> Z(1, 1, 0.3)
@@ -756,15 +413,9 @@ protocol = (
     DualRail(3) >>
     Channel.from_perceval(p)
 )
-```
 
-
-```python
 result_optyx = protocol.eval().prob_dist()
-```
-
 
-```python
 def check_dict_agreement(d1, d2, rtol=1e-5, atol=1e-8):
     for key in d1.keys() - d2.keys():
         assert np.isclose(d1[key], 0, rtol=rtol, atol=atol)
@@ -772,17 +423,9 @@ def check_dict_agreement(d1, d2, rtol=1e-5, atol=1e-8):
         assert np.isclose(d2[key], 0, rtol=rtol, atol=atol)
     for key in d1.keys() & d2.keys():
         assert np.isclose(d1[key], d2[key], rtol=rtol, atol=atol)
-```
-
 
-```python
 check_dict_agreement(
     {tuple(k): v for k, v in dict(result_perceval["results"]).items()},
     result_optyx
 )
-```
-
-
-```python
-
-```
+```
\ No newline at end of file
diff --git a/optyx/classical.py b/optyx/classical.py
index b6e0c5eb..e113a83f 100644
--- a/optyx/classical.py
+++ b/optyx/classical.py
@@ -693,6 +693,22 @@ def __init__(self, *photons: int):
 
 Bit = lambda *bits: PostselectBit(*bits).dagger()  # noqa: E731
 
+CtrlX = Channel(
+  "Controlled-X",
+  zx.X(2, 1) @ diagram.Scalar(2 ** 0.5),
+  dom = bit @ qubit,
+  cod = qubit
+)
+
+CtrlZ = Channel(
+  "Controlled-Z",
+  (
+    zx.H @ diagram.bit >>
+    zx.Z(2, 1) @ diagram.Scalar(2 ** 0.5)
+  ),
+  dom = bit @ qubit,
+  cod = qubit
+)
 
 def Id(n):
     """

From 7be3c1dbaa04d72864e04a4b88a5e1547b2c3fbe Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Tue, 7 Oct 2025 16:38:29 +0100
Subject: [PATCH 54/59] flake8ing

---
 optyx/classical.py    | 9 +++++----
 optyx/core/channel.py | 4 +---
 2 files changed, 6 insertions(+), 7 deletions(-)

diff --git a/optyx/classical.py b/optyx/classical.py
index e113a83f..920f1021 100644
--- a/optyx/classical.py
+++ b/optyx/classical.py
@@ -696,8 +696,8 @@ def __init__(self, *photons: int):
 CtrlX = Channel(
   "Controlled-X",
   zx.X(2, 1) @ diagram.Scalar(2 ** 0.5),
-  dom = bit @ qubit,
-  cod = qubit
+  dom=bit @ qubit,
+  cod=qubit
 )
 
 CtrlZ = Channel(
@@ -706,10 +706,11 @@ def __init__(self, *photons: int):
     zx.H @ diagram.bit >>
     zx.Z(2, 1) @ diagram.Scalar(2 ** 0.5)
   ),
-  dom = bit @ qubit,
-  cod = qubit
+  dom=bit @ qubit,
+  cod=qubit
 )
 
+
 def Id(n):
     """
     Classical identity wire.
diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index 577d6e21..5e1d69ae 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -153,9 +153,7 @@
 from discopy.cat import factory
 from pytket.extensions.pyzx import pyzx_to_tk
 from pyzx import extract_circuit
-from optyx.core import zx, diagram
-from optyx.utils.utils import explode_channel
-from optyx.core.path import Matrix
+from optyx.core import diagram
 
 
 class Ob(frobenius.Ob):

From ea41d059b69e6a6cea31fe8e267c2349975b5e81 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Tue, 7 Oct 2025 16:49:13 +0100
Subject: [PATCH 55/59] removed tests -- decomp and to_path moved from zx to
 qubits

---
 optyx/core/zx.py | 74 ------------------------------------------------
 1 file changed, 74 deletions(-)

diff --git a/optyx/core/zx.py b/optyx/core/zx.py
index d73469b3..4834aeda 100644
--- a/optyx/core/zx.py
+++ b/optyx/core/zx.py
@@ -35,83 +35,9 @@
 Examples of usage
 ------------------
 
-We can map ZX diagrams to :class:`path` diagrams using
-dual-rail encoding. For example, we can create a GHZ state:
-
->>> from discopy.drawing import Equation
->>> from optyx.core.diagram import dual_rail, embedding_tensor
->>> ghz = Z(0, 3)
->>> ghz_decom = decomp(ghz)
->>> ghz_path = zx_to_path(ghz_decom)
->>> Equation(ghz >> dual_rail(3), ghz_path, \\
-... symbol="$\\mapsto$").draw(figsize=(10, 10), \\
-... path="docs/_static/ghz_dr.svg")
-
-.. image:: /_static/ghz_dr.svg
-    :align: center
-
-We can also create a graph state as follows
-(where we omit the labels):
-
->>> graph = (Z(0, 2) >> Id(1) @ H >> Id(1) @ Z(1, 2) >> \\
-... Id(2) @ H >> Id(2) @ Z(1, 2))
->>> graph_decom = decomp(graph)
->>> graph_path = zx_to_path(graph_decom)
->>> Equation(graph >> dual_rail(4), graph_path, \\
-... symbol="$\\mapsto$").draw(figsize=(10, 14), \\
-... path="docs/_static/graph_dr.svg", draw_type_labels=False, \\
-... draw_box_labels=False)
-
-.. image:: /_static/graph_dr.svg
-    :align: center
-
-We can check that both diagrams produce the same tensors (we need to
-ensure the tensor dimensions match):
-
->>> assert np.allclose(graph_path.to_tensor().eval().array, \\
-... ((graph >> dual_rail(4)).to_tensor() >> \\
-... (tensor.Id(Dim(*[2]*7)) @ embedding_tensor(1, 4))).eval().array)
-
-As shown in the example above, we need to decompose a ZX diagram
-into more elementary spiders before mapping it to a path diagram.
-More explicitely:
-
->>> dgr = Z(2, 1, 0.25) >> X(1, 1, 0.35)
->>> print(decomp(dgr))
-Z(2, 1) >> Z(1, 1, 0.25) >> H >> Z(1, 1, 0.35) >> H
->>> print(zx2path(decomp(dgr))[:2])
-mode @ W[::-1] @ mode >> mode @ Select(1) @ mode
->>> assert zx2path(decomp(dgr)) == zx_to_path(dgr)
-
 Evaluating ZX diagrams using PyZX or via the dual rail
 encoding is equivalent.
 
->>> ket = lambda *xs: Id(diagram.Bit(0)).tensor(\\
-...         *[X(0, 1, 0.5 if x == 1 else 0) for x in xs])
->>> cnot = Z(1, 2) @ Id(1) >> Id(1) @ X(2, 1)
->>> control = lambda x: ket(x) @ Id(1) >> cnot >> ket(x).dagger() @ Id(1)
->>> assert np.allclose(zx_to_path(control(0)).to_path().eval(1).array, \\
-...                    control(0).to_pyzx().to_tensor())
->>> assert np.allclose(zx_to_path(control(1)).to_path().eval(1).array, \\
-...                    control(1).to_pyzx().to_tensor())
->>> cz = lambda phi: cnot >> Z(1, 1, phi) @ H
->>> amplitude = ket(1, 1) >> cz(0.7) >> ket(1, 1).dagger()
->>> assert np.allclose(zx_to_path(amplitude).to_path().eval().array, \\
-...                    amplitude.to_pyzx().to_tensor())
-
-Corner case where :code:`to_pyzx` and
-:code:`zx_to_path` agree only up to global
-phase.
-
->>> diagram = X(0, 2) @ Z(0, 1, 0.25) @ scalar(1/2)\\
-...     >> Id(1) @ Z(2, 1) >> X(2, 0, 0.35)
->>> print(decomp(diagram)[:3])
-X(0, 1) >> H >> Z(1, 2)
->>> print(zx_to_path(diagram)[:2])
-Create(1) >> mode @ Create((0,))
->>> pyzx_ampl = diagram.to_pyzx().to_tensor()
->>> assert np.allclose(pyzx_ampl, zx_to_path(diagram).to_path().eval().array)
-
 The array properties of Z and X spiders agree with PyZX.
 
 >>> z = Z(n_legs_in = 2, n_legs_out = 2, phase = 0.5)

From 83a7cb4d5bc28df46f17b276d6ab276848b32c57 Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Tue, 7 Oct 2025 17:11:21 +0100
Subject: [PATCH 56/59] Adding tests to qubits

---
 optyx/core/channel.py |  2 +-
 optyx/core/diagram.py |  7 ++++++-
 optyx/qubits.py       | 31 +++++++++++++++++++++++++++++++
 3 files changed, 38 insertions(+), 2 deletions(-)

diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index 5e1d69ae..7a8ff032 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -392,7 +392,7 @@ def to_dual_rail(self):
             cod=frobenius.Category(Ty, Diagram),
         )(self.decomp())
 
-    def to_tket(self):
+    def to_tket(self): # pragma: no cover
         """
         Convert to tket circuit. The circuit must be a pure circuit.
         """
diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index e1ea90ab..fbce5ccd 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -375,7 +375,12 @@ def to_tensor(
         return diagram
 
     @classmethod
-    def from_bosonic_operator(cls, n_modes, operators, scalar=1):
+    def from_bosonic_operator(
+        cls,
+        n_modes,
+        operators,
+        scalar=1
+    ): # pragma: no cover
         """Create a :class:`zw` diagram from a bosonic operator."""
         # pylint: disable=import-outside-toplevel
         from optyx.core import zw
diff --git a/optyx/qubits.py b/optyx/qubits.py
index 647ed2d3..137cc038 100644
--- a/optyx/qubits.py
+++ b/optyx/qubits.py
@@ -263,6 +263,37 @@
 .. image:: /_static/graph_dr_qubit.svg
     :align: center
 
+We can map ZX diagrams to dual-rail encoding.
+For example, we can create a GHZ state:
+
+>>> from discopy.drawing import Equation
+>>> from optyx.photonic import DualRail
+>>> from optyx.core.diagram import embedding_tensor
+>>> ghz = Z(0, 3)
+>>> ghz_decom = ghz.decomp()
+>>> ghz_path = ghz_decom.to_dual_rail()
+>>> Equation(ghz >> DualRail(3), ghz_path, \\
+... symbol="$\\mapsto$").draw(figsize=(10, 10), \\
+... path="docs/_static/ghz_dr.svg")
+
+.. image:: /_static/ghz_dr.svg
+    :align: center
+
+We can also create a graph state as follows
+(where we omit the labels):
+
+>>> graph = (Z(0, 2) >> Id(1) @ H() >> Id(1) @ Z(1, 2) >> \\
+... Id(2) @ H() >> Id(2) @ Z(1, 2))
+>>> graph_decom = graph.decomp()
+>>> graph_path = graph_decom.to_dual_rail()
+>>> Equation(graph >> DualRail(4), graph_path, \\
+... symbol="$\\mapsto$").draw(figsize=(10, 14), \\
+... path="docs/_static/graph_dr.svg", draw_type_labels=False, \\
+... draw_box_labels=False)
+
+.. image:: /_static/graph_dr.svg
+    :align: center
+
 """  # noqa E501
 
 from typing import Literal

From 8adc08fa1fd385ae55078fd86384b7554f3619fb Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Tue, 7 Oct 2025 18:10:26 +0100
Subject: [PATCH 57/59] linting and adding tests

---
 optyx/core/channel.py | 2 +-
 optyx/core/diagram.py | 2 +-
 optyx/qubits.py       | 4 ++--
 3 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/optyx/core/channel.py b/optyx/core/channel.py
index 7a8ff032..0d3b2a1c 100644
--- a/optyx/core/channel.py
+++ b/optyx/core/channel.py
@@ -392,7 +392,7 @@ def to_dual_rail(self):
             cod=frobenius.Category(Ty, Diagram),
         )(self.decomp())
 
-    def to_tket(self): # pragma: no cover
+    def to_tket(self):  # pragma: no cover
         """
         Convert to tket circuit. The circuit must be a pure circuit.
         """
diff --git a/optyx/core/diagram.py b/optyx/core/diagram.py
index fbce5ccd..51f9627e 100644
--- a/optyx/core/diagram.py
+++ b/optyx/core/diagram.py
@@ -380,7 +380,7 @@ def from_bosonic_operator(
         n_modes,
         operators,
         scalar=1
-    ): # pragma: no cover
+    ):  # pragma: no cover
         """Create a :class:`zw` diagram from a bosonic operator."""
         # pylint: disable=import-outside-toplevel
         from optyx.core import zw
diff --git a/optyx/qubits.py b/optyx/qubits.py
index 137cc038..1700f68e 100644
--- a/optyx/qubits.py
+++ b/optyx/qubits.py
@@ -282,7 +282,7 @@
 We can also create a graph state as follows
 (where we omit the labels):
 
->>> graph = (Z(0, 2) >> Id(1) @ H() >> Id(1) @ Z(1, 2) >> \\
+>>> graph = (Z(0, 2) >> Id(1) @ H() >> Id(1) @ X(1, 2, 0.5) >> \\
 ... Id(2) @ H() >> Id(2) @ Z(1, 2))
 >>> graph_decom = graph.decomp()
 >>> graph_path = graph_decom.to_dual_rail()
@@ -765,7 +765,7 @@ def _decomp(self):
         )
         return box.decomp()
 
-    def _to_dual_rail(self):
+    def _to_dual_rail(self):  # pragma: no cover
         """Convert to dual-rail encoding."""
         from optyx import (
             photonic,

From c507136ac17ad46d86a2eb4f58f7f0a9c0fecda4 Mon Sep 17 00:00:00 2001
From: giodefelice <giodefelice@protonmail.com>
Date: Tue, 7 Oct 2025 18:51:09 +0100
Subject: [PATCH 58/59] minor edit docs

---
 optyx/core/backends.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/optyx/core/backends.py b/optyx/core/backends.py
index 5b8b2441..552933fb 100644
--- a/optyx/core/backends.py
+++ b/optyx/core/backends.py
@@ -420,7 +420,7 @@ def eval(
 
     def _process_term(self, term: Diagram) -> np.ndarray:
         """
-        Process a term in a diagram with multiple terms.
+        Process a term in a sum of diagrams.
 
         Args:
             term (Diagram): The term to process.

From 5c0a1afa5e74816363b4c9d618f8d90895e0e33a Mon Sep 17 00:00:00 2001
From: mateuszkupper <mateusz.kupper@gmail.com>
Date: Wed, 8 Oct 2025 10:48:06 +0100
Subject: [PATCH 59/59] Removed compile_to_semm from docs

---
 docs/notebooks.rst | 1 -
 1 file changed, 1 deletion(-)

diff --git a/docs/notebooks.rst b/docs/notebooks.rst
index a7b78f4a..2b6e74e8 100644
--- a/docs/notebooks.rst
+++ b/docs/notebooks.rst
@@ -11,5 +11,4 @@ Here we give examples of using ``optyx``:
     notebooks/optyx-compilation.ipynb
     notebooks/optyx-vqe-experiment.ipynb
     notebooks/bosonic-vqe.ipynb
-    notebooks/compile_to_semm.ipynb
     notebooks/photon_distinguishability.ipynb