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

• URL: http://arxiv.org/abs/2302.00536v2
• Date: Sun, 23 Apr 2023 18:22:44 GMT
• Title: Quantum-inspired classical algorithm for graph problems by Gaussian boson sampling
• Authors: Changhun Oh, Bill Fefferman, Liang Jiang, Nicol\'as Quesada
• Abstract summary: We present a quantum-inspired classical algorithm that can be used for graph-theoretical problems. A given graph's adjacency matrix to be encoded in a Gaussian boson sampler is nonnegative, which does not necessitate quantum interference.
• Score: 2.5496329090462626
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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