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

• URL: http://arxiv.org/abs/2505.02788v1
• Date: Mon, 05 May 2025 17:02:35 GMT
• Title: i-QLS: Quantum-supported Algorithm for Least Squares Optimization in Non-Linear Regression
• Authors: Supreeth Mysore Venkatesh, Antonio Macaluso, Diego Arenas, Matthias Klusch, Andreas Dengel,
• Abstract summary: We propose an iterative quantum-assisted least squares (i-QLS) optimization method.<n>We overcome the scalability and precision limitations of prior quantum least squares approaches.<n> Experiments confirm that i-QLS enables near-term quantum hardware to perform regression tasks with improved precision and scalability.
• Score: 4.737806718785056
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose an iterative quantum-assisted least squares (i-QLS) optimization method that leverages quantum annealing to overcome the scalability and precision limitations of prior quantum least squares approaches. Unlike traditional QUBO-based formulations, which suffer from a qubit overhead due to fixed discretization, our approach refines the solution space iteratively, enabling exponential convergence while maintaining a constant qubit requirement per iteration. This iterative refinement transforms the problem into an anytime algorithm, allowing for flexible computational trade-offs. Furthermore, we extend our framework beyond linear regression to non-linear function approximation via spline-based modeling, demonstrating its adaptability to complex regression tasks. We empirically validate i-QLS on the D-Wave quantum annealer, showing that our method efficiently scales to high-dimensional problems, achieving competitive accuracy with classical solvers while outperforming prior quantum approaches. Experiments confirm that i-QLS enables near-term quantum hardware to perform regression tasks with improved precision and scalability, paving the way for practical quantum-assisted machine learning applications.

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