On the application of Sylvester's law of inertia to QUBO formulations for systems of linear equations

TL;DR

This paper enhances QUBO formulations for linear systems by applying Sylvester's law of inertia, aiming to improve quantum algorithms for solving higher-dimensional equations, with experimental comparisons to classical methods.

Contribution

It introduces a novel QUBO formulation using Sylvester's law of inertia for systems of linear equations, facilitating higher-dimensional quantum computations.

Findings

Effective QUBO models for linear systems developed

Experimental results compare quantum and classical algorithms

Potential for improved quantum solutions of large systems

Abstract

Previous research on quantum annealing methods focused on effectively modeling systems of linear equations by utilizing quadratic unconstrained binary optimization (QUBO) formulations. These studies take part in enhancing quantum computing algorithms, which extract properties of quantum computers suitable for improving classical computational models. In this paper, we further develop the QUBO formulations of systems of linear equations by applying Sylvester's law of inertia, which explores matrix congruence of any real symmetric matrix to a diagonal matrix. We expect that the proposed algorithm can effectively implement higher dimensional systems of linear equations on a quantum computer. Further experimental verification of the proposed QUBO models as well as their comparisons to classical algorithms are also made.