QUBO transformation using Eigenvalue Decomposition

TL;DR

This paper introduces a novel QUBO transformation method using eigenvalue decomposition to enhance the search process in combinatorial optimization, leading to improved performance on benchmark problems.

Contribution

It presents a new approach that leverages eigenvalue decomposition of the Q matrix to guide the search more effectively in QUBO problems.

Findings

Significant performance improvements on benchmark datasets.

Effective utilization of dominant eigenvalues for search guidance.

Enhanced solution quality in combinatorial optimization.

Abstract

Quadratic Unconstrained Binary Optimization (QUBO) is a general-purpose modeling framework for combinatorial optimization problems and is a requirement for quantum annealers. This paper utilizes the eigenvalue decomposition of the underlying Q matrix to alter and improve the search process by extracting the information from dominant eigenvalues and eigenvectors to implicitly guide the search towards promising areas of the solution landscape. Computational results on benchmark datasets illustrate the efficacy of our routine demonstrating significant performance improvements on problems with dominant eigenvalues.