Analyzing the Quantum Annealing Approach for Solving Linear Least Squares Problems

TL;DR

This paper explores the potential of quantum annealing to solve linear least squares problems, proposing a new variable representation and analyzing conditions for quantum advantage over classical methods.

Contribution

It introduces a compact variable encoding using two's and one's complement on quantum annealers and provides a theoretical analysis of when this approach may outperform classical solutions.

Findings

Proposes a new variable representation for quantum annealing.

Provides conditions under which quantum annealing can outperform classical methods.

Discusses promising future research directions in quantum optimization.

Abstract

With the advent of quantum computers, researchers are exploring if quantum mechanics can be leveraged to solve important problems in ways that may provide advantages not possible with conventional or classical methods. A previous work by O'Malley and Vesselinov in 2016 briefly explored using a quantum annealing machine for solving linear least squares problems for real numbers. They suggested that it is best suited for binary and sparse versions of the problem. In our work, we propose a more compact way to represent variables using two's and one's complement on a quantum annealer. We then do an in-depth theoretical analysis of this approach, showing the conditions for which this method may be able to outperform the traditional classical methods for solving general linear least squares problems. Finally, based on our analysis and observations, we discuss potentially promising areas of further research where quantum annealing can be especially beneficial.