iso_peps_to_circuit

This directory contains the code that converts an iso-PEPS tensor network on a lattice into a quantum circuit, and then simulates / analyzes that circuit in Qiskit.

Directory structure

• circuit_optimize/: Code for optimizing unitary gate decompositions
• circuit_simulation/: Code for simulating and analyzing circuits
• gates/: Gates and decomposed circuits
• samples/: Sampled images

Basic workflow

1. Convert iso-PEPS tensors to unitary gates:

   cd circuit_optimize
   python3 iso_to_uni.py          # writes tensors to ../gates/unitary_gates/

2. Optimize per-gate U3+MS decompositions:

   cd circuit_optimize
   python3 optimize_unitary_gates.py   # writes ../gates/decomposed_gates/gate_index{i}/

3. Simulate the decomposed circuit, compute the nll and sample:

   cd circuit_simulation
   python3 nll_circuit.py
   # prints NLL and saves images to ../samples/

4. Build the optimized circuit and merge consecutive U3 gates:

   cd circuit_optimize
   python3 build_entire_circuit.py
   # builds circuit from decomposed gates, merges U3 gates, saves to ../gates/final_circuit/

5. Simulate the final optimized circuit:

   cd circuit_simulation
   python3 circuit_simulation.py      # no noise
   python3 noisy_circuit_simulation.py # with noise

Gate set

The circuit uses:

• U3 gates: Universal single-qubit gates with 3 parameters (theta, phi, lam)
• MS gates: Mølmer-Sørensen two-qubit gates, defined as MS(θ) = exp(-i * θ/4 * (X⊗X + Y⊗Y))

Dependencies

• Python 3.8+
• PyTorch
• NumPy, SciPy
• Matplotlib
• Qiskit (core) and qiskit-aer
• Pyomo + SCIP (only required for optimize_circuit_layout.py)