Simulating Gaussian boson sampling on graphs in polynomial time

2025-11-20

AI Summary

This work investigates the classical simulability of Gaussian boson sampling (GBS) on graph-structured inputs, addressing whether GBS exhibits exponential quantum speedup for graph-related tasks. Leveraging tools from graph theory, Gaussian state probability analysis, and matrix function theory, we develop a polynomial-time classical sampling algorithm based on Hafnian polynomial approximation and low-rank decomposition. We rigorously prove that the GBS output distribution is efficiently simulable on classical computers for broad graph families—including sparse graphs and small-world graphs. This result refutes the expectation of universal quantum advantage for GBS in typical graph applications. It establishes the first general-purpose classical simulation framework for GBS-derived distributions and reveals the profound sensitivity of quantum sampling advantage to input structure. Our findings advance the fundamental understanding of the quantum-classical boundary in near-term quantum sampling paradigms.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

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.

Problem

• Simulating Gaussian boson sampling on graphs efficiently
• Demonstrating classical polynomial-time sampling for GBS distribution
• Showing quantum advantage absence in graphical GBS applications

Innovation

• Classical simulation of Gaussian boson sampling
• Polynomial time sampling for graph applications
• No quantum speedup in these specific cases