A QUBO Algorithm to Compute Eigenvectors of Symmetric Matrices

TL;DR

This paper introduces a QUBO-based algorithm for accurately computing extremal eigenvalues and eigenvectors of symmetric matrices, applicable to various classes and extendable to generalized eigenproblems, with demonstrated performance on small and large matrices.

Contribution

The paper presents a novel QUBO algorithm for eigenvector computation that is robust, precise, and adaptable to generalized eigenproblems, expanding the toolkit for eigenvalue analysis.

Findings

Effective on small random matrices

Performs well on larger practical matrices

Capable of arbitrary precision eigenpair computation

Abstract

We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of symmetric matrices, can compute the eigenvector/eigenvalue pair to essentially arbitrary precision, and with minor modifications can also solve the generalized eigenvalue problem. Performance is analyzed on small random matrices and selected larger matrices from practical applications.