Quantum-inspired classical algorithm for graph problems by Gaussian boson sampling

TL;DR

This paper introduces a classical algorithm inspired by Gaussian boson sampling to solve graph problems, demonstrating comparable performance to quantum samplers and discussing potential advantages of quantum approaches.

Contribution

The paper develops a classical algorithm inspired by Gaussian boson sampling for graph problems, showing it matches quantum sampler performance and analyzing its advantages.

Findings

Classical algorithm performs similarly to quantum samplers in graph problems.

Gaussian boson samplers do not show significant advantage over classical methods.

Potential quantum advantage remains uncertain and warrants further investigation.

Abstract

We present a quantum-inspired classical algorithm that can be used for graph-theoretical problems, such as finding the densest $k$-subgraph and finding the maximum weight clique, which are proposed as applications of a Gaussian boson sampler. The main observation from Gaussian boson samplers is that a given graph's adjacency matrix to be encoded in a Gaussian boson sampler is nonnegative, which does not necessitate quantum interference. We first provide how to program a given graph problem into our efficient classical algorithm. We then numerically compare the performance of ideal and lossy Gaussian boson samplers, our quantum-inspired classical sampler, and the uniform sampler for finding the densest $k$-subgraph and finding the maximum weight clique and show that the advantage from Gaussian boson samplers is not significant in general. We finally discuss the potential advantage of a Gaussian boson sampler over the proposed sampler.