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arXiv:2511.16558

Simulating Gaussian boson sampling on graphs in polynomial time

Konrad Anand, Zongchen Chen, Mary Cryan, Graham Freifeld, Leslie Ann Goldberg, Heng Guo, Xinyuan Zhang

quant-phcs.DSSubmitted Nov 20, 2025• Announced Nov 21, 2025• 0 citations• Revised Jun 25, 2026 (v2)
v1 · Nov 20, 2025v2 · Jun 25, 2026
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Abstract

We show that a distribution related to Gaussian Boson Sampling (GBS) on graphs can be sampled classically in polynomial time. Graphical applications of GBS typically sample from this distribution, and thus quantum algorithms do not provide exponential speedup for these applications. We also show that another distribution related to Boson sampling can be sampled classically in polynomial time.

Comments
11 pages, 2 figures

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We show that a distribution related to Gaussian Boson Sampling (GBS) on graphs can be sampled classically in polynomial time. Graphical applications of GBS typically sample from this distribution, and thus quantum algorithms do not provide exponential speedup for these applications. We also show that another distribution related to Boson sampling can be sampled classically in polynomial time.
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Boson sampling devices are a prime candidate for exhibiting quantum supremacy, yet their application for solving problems of practical interest is less well understood. Here we show that Gaussian boson sampling (GBS) can be used for dense subgraph identification. Focusing on the NP-hard densest k-subgraph problem, we find that stochastic algorithms are enhanced through GBS, which selects dense subgraphs with high probability. These findings rely on a link between graph density and the number of perfect matchings-enumerated by the Hafnian-which is the relevant quantity determining sampling probabilities in GBS. We test our findings by constructing GBS-enhanced versions of the random search and simulated annealing algorithms and apply them through numerical simulations of GBS to identify the densest subgraph of a 30 vertex graph.
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