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

2025-05-05

AI Summary

To address the poor scalability and limited accuracy of existing quantum least squares (QLS) methods in nonlinear regression, this paper proposes i-QLS—an iterative quantum-assisted least squares optimization framework. i-QLS is the first to integrate quantum annealing (D-Wave) into nonlinear regression, combining spline basis function modeling with iterative QUBO reformulation to construct a scalable nonlinear function approximation scheme. Its key contributions are: (1) a novel iterative solution-space refinement mechanism that achieves exponential convergence while maintaining constant qubit overhead per iteration; and (2) an extension of quantum least squares into an anytime algorithm with adaptive precision control. Experimental evaluation on D-Wave hardware demonstrates that i-QLS matches classical solvers in accuracy for high-dimensional regression tasks and significantly outperforms prior quantum approaches, thereby advancing practical quantum-enhanced machine learning.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

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.

Problem

• Overcoming scalability limits in quantum least squares optimization
• Reducing qubit overhead via iterative refinement in QUBO
• Extending quantum-assisted regression to non-linear function approximation

Innovation

• Quantum annealing for scalable least squares optimization
• Iterative refinement with constant qubit usage
• Spline-based modeling for non-linear regression