Solving the Graph Isomorphism Problem with a Quantum Annealer

TL;DR

This paper introduces a quantum annealing approach to solve the Graph Isomorphism problem, demonstrating its potential on highly symmetric graphs and current quantum hardware like D-Wave One.

Contribution

The paper presents a novel quantum annealing method for graph isomorphism, extending quantum computing applications to this complex combinatorial problem.

Findings

Effective analysis of strongly regular graphs

Method applicable to existing quantum hardware

Potential for quantum advantage in graph isomorphism

Abstract

We propose a novel method using a quantum annealer -- an analog quantum computer based on the principles of quantum adiabatic evolution -- to solve the Graph Isomorphism problem, in which one has to determine whether two graphs are isomorphic (i.e., can be transformed into each other simply by a relabeling of the vertices). We demonstrate the capabilities of the method by analyzing several types of graph families, focusing on graphs with particularly high symmetry called strongly regular graphs (SRG's). We also show that our method is applicable, within certain limitations, to currently available quantum hardware such as "D-Wave One".