Evolutionary Approaches to Optimization Problems in Chimera Topologies

TL;DR

This paper explores the application of evolutionary algorithms to Ising spin glass problems on Chimera graphs, aiming to understand how topology influences optimization success and to benchmark quantum and classical methods.

Contribution

It is the first study to evaluate EAs on Chimera topology Ising instances, analyzing the impact of graph structure on algorithm performance.

Findings

EAs can effectively solve Chimera-based Ising problems.

Topology information can improve EA performance.

Characteristics of instances affect success rates.

Abstract

Chimera graphs define the topology of one of the first commercially available quantum computers. A variety of optimization problems have been mapped to this topology to evaluate the behavior of quantum enhanced optimization heuristics in relation to other optimizers, being able to efficiently solve problems classically to use them as benchmarks for quantum machines. In this paper we investigate for the first time the use of Evolutionary Algorithms (EAs) on Ising spin glass instances defined on the Chimera topology. Three genetic algorithms (GAs) and three estimation of distribution algorithms (EDAs) are evaluated over $1000$ hard instances of the Ising spin glass constructed from Sidon sets. We focus on determining whether the information about the topology of the graph can be used to improve the results of EAs and on identifying the characteristics of the Ising instances that influence the success rate of GAs and EDAs.