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

TL;DR

The paper introduces i-QLS, a quantum-assisted iterative algorithm for non-linear regression that improves scalability and precision, enabling near-term quantum hardware to perform complex regression tasks efficiently.

Contribution

It presents a novel iterative quantum-assisted least squares method that extends to non-linear regression, overcoming previous limitations of qubit overhead and fixed discretization.

Findings

Achieves exponential convergence with constant qubits per iteration

Scales efficiently to high-dimensional problems on quantum annealers

Provides competitive accuracy with classical solvers in regression tasks

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.