A Quantum Photonic Approach to Graph Coloring

TL;DR

This paper explores using Gaussian Boson Sampling, a quantum photonic technique, to solve graph coloring problems by reformulating them as integer programs and identifying cliques via quantum sampling.

Contribution

It introduces a novel quantum approach to graph coloring by leveraging GBS to find independent sets, demonstrating potential advantages over classical methods.

Findings

GBS can identify large independent sets in graphs.

Quantum approach shows competitive results against classical heuristics.

Potential for quantum-enhanced heuristics in combinatorial optimization.

Abstract

Gaussian Boson Sampling (GBS) is a quantum computational model that leverages linear optics to solve sampling problems believed to be classically intractable. Recent experimental breakthroughs have demonstrated quantum advantage using GBS, motivating its application to real-world combinatorial optimization problems. In this work, we reformulate the graph coloring problem as an integer programming problem using the independent set formulation. This enables the use of GBS to identify cliques in the complement graph, which correspond to independent sets in the original graph. Our method is benchmarked against classical heuristics and exact algorithms on two sets of instances: Erd\H{o}s-R\'enyi random graphs and graphs derived from a smart-charging use case. The results demonstrate that GBS can provide competitive solutions, highlighting its potential as a quantum-enhanced heuristic for graph-based optimization.