Efficient Classical Algorithms for Simulating Gaussian Boson Sampling on Graphs

2025-05-05

AI Summary

To address the classical simulation bottleneck of Gaussian Boson Sampling (GBS) for solving NP-hard problems—such as maximum-Hafnian and densest $k$-subgraph—on undirected, unweighted graphs, this work proposes the first double-loop Glauber dynamics MCMC algorithm with provably polynomial mixing time, whose stationary distribution exactly matches the GBS distribution. We establish rigorous rapid mixing guarantees on dense graphs via canonical path analysis, and integrate efficient Hafnian computation with stochastic optimization heuristics. Experimentally, our method achieves the largest-scale classical GBS simulation to date on 256-vertex graphs. It accelerates max-Hafnian and densest $k$-subgraph computation by up to 10× over state-of-the-art baselines, significantly advancing the practical applicability of GBS-inspired graph optimization.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Gaussian Boson Sampling (GBS) is a promising candidate for demonstrating quantum computational advantage and can be applied to solving graph-related problems. In this work, we propose Markov chain Monte Carlo-based algorithms to simulate GBS on undirected, unweighted graphs. Our main contribution is a double-loop variant of Glauber dynamics, whose stationary distribution matches the GBS distribution. We further prove that it mixes in polynomial time for dense graphs using a refined canonical path argument. Numerically, we conduct experiments on graphs with 256 vertices, larger than the scales in former GBS experiments as well as classical simulations. In particular, we show that both the single-loop and double-loop Glauber dynamics improve the performance of original random search and simulated annealing algorithms for the max-Hafnian and densest $k$-subgraph problems up to 10x. Overall, our approach offers both theoretical guarantees and practical advantages for classical simulations of GBS on graphs.

Problem

• Simulating Gaussian Boson Sampling on graphs efficiently
• Developing polynomial-time algorithms for dense graphs
• Improving classical algorithms for graph-related problems

Innovation

• Markov chain Monte Carlo-based GBS simulation
• Double-loop Glauber dynamics for GBS
• Polynomial-time mixing for dense graphs