On the application of matrix congruence to QUBO formulations for systems of linear equations

TL;DR

This paper introduces a novel approach to simplify QUBO formulations for solving linear systems by leveraging matrix congruence, demonstrating potential computational advantages over classical methods.

Contribution

The paper presents a new method using matrix congruence to diagonalize symmetric matrices in QUBO formulations, improving efficiency for quantum annealing solutions.

Findings

QUBO formulations can be simplified via matrix congruence.

Proposed models outperform classical algorithms like QR and SVD.

Method enhances quantum annealing efficiency for linear systems.

Abstract

Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively parallelize quadratic unconstrained binary optimization (QUBO) formulations of systems of linear equations. In this paper, we simplify these formulations by exploiting congruence of real symmetric matrices to diagonal matrices. We further exhibit computational merits of the proposed QUBO models, which can outperform classical algorithms such as QR and SVD decomposition.