A practical heuristic for finding graph minors

TL;DR

This paper introduces a practical heuristic algorithm for efficiently identifying graph minors in large sparse graphs, which is useful for mapping complex optimization problems onto quantum annealers.

Contribution

The paper presents a new heuristic method tailored for sparse graphs to find minors, addressing a practical challenge in quantum optimization problem mapping.

Findings

Effective for graphs with hundreds of vertices

Applicable to sparse graph structures

Facilitates mapping quadratic pseudo-boolean problems onto quantum annealers

Abstract

We present a heuristic algorithm for finding a graph $H$ as a minor of a graph $G$ that is practical for sparse $G$ and $H$ with hundreds of vertices. We also explain the practical importance of finding graph minors in mapping quadratic pseudo-boolean optimization problems onto an adiabatic quantum annealer.