i-QLS: Quantum-supported Algorithm for Least Squares Optimization in Non-Linear Regression

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🔍 Iterative Quantum-Assisted Least Squares (i-QLS)

This repository contains the official implementation of our paper:

i-QLS: Quantum-supported Algorithm for Least Squares Optimization in Non-Linear Regression
🏛️ Accepted at 25th International Conference on Computational Science (Main Track – Quantum Computing)

Preprint available on arXiv:2505.02788

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🌟 Overview

Least squares optimization is at the heart of many machine learning and scientific computing tasks. But solving it with quantum hardware has traditionally been limited by the trade-off between precision and hardware constraints.

This project introduces i-QLS, an iterative quantum-classical hybrid method that reformulates the least squares objective into a series of QUBO problems — solvable by quantum annealers — and refines the solution across iterations to achieve higher accuracy with fewer qubits.

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⚙️ How It Works

At a high level:

1. Discretize the continuous weight space into binary representations (using m bits per weight).
2. Formulate the least squares loss as a QUBO (Quadratic Unconstrained Binary Optimization) problem.
3. Solve the QUBO using a quantum annealer (e.g., D-Wave Advantage).
4. Shrink the search interval based on the best solution found.
5. Repeat the process iteratively — each round zooms in on the optimal solution.

This process makes our algorithm an anytime method: you can stop after any iteration and still get a meaningful solution.

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✨ Features

• ✅ Scalable to 175+ features on real quantum hardware
• ✅ Demonstrated on both linear and non-linear regression (via splines)
• 🔁 Iterative and qubit-efficient
• 🧠 Extensible to non-linear function approximation
• 🧪 Includes experiments on real-world D-Wave annealers

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📈 Why It Matters

Traditional quantum approaches to least squares solve a single massive QUBO — requiring many qubits and offering limited flexibility. Our iterative refinement strategy breaks the problem into smaller, manageable QUBOs and converges exponentially to the true solution.

This makes i-QLS:

• 💡 Scalable: Works with today's limited quantum hardware
• 🔬 Precise: Achieves high accuracy through iteration
• 🔗 Hybrid: Bridges quantum optimization with classical preprocessing

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🧪 Experiments & Reproducibility

You’ll find:

• 📊 MSE plots showing convergence across iterations
• 🧬 Code for reproducing quantum runs on D-Wave (requires D-Wave API token)

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Citing this Work

If you find this code useful in your research, please cite the following paper:

@InProceedings{iqls,
      author="Venkatesh, Supreeth Mysore
      and Macaluso, Antonio
      and Arenas, Diego
      and Klusch, Matthias
      and Dengel, Andreas",
      editor="Lees, Michael H.
      and Cai, Wentong
      and Cheong, Siew Ann
      and Su, Yi
      and Abramson, David
      and Dongarra, Jack J.
      and Sloot, Peter M. A.",
      title="i-QLS: Quantum-Supported Algorithm for Least Squares Optimization in Non-linear Regression",
      booktitle="Computational Science -- ICCS 2025",
      year="2025",
      publisher="Springer Nature Switzerland",
      address="Cham",
      pages="19--34",
      isbn="978-3-031-97629-2",
      doi="10.1007/978-3-031-97629-2_2"
      }

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💬 Questions or Feedback?

Open an issue or drop us a message. We welcome collaborations, ideas, and contributions!

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Contact

Supreeth Mysore Venkatesh

For any inquiries, please reach out to:

• Email: contact@supreethmv.com
• LinkedIn: Supreeth Mysore Venkatesh
• Website: www.supreethmv.com

Contributors