Performance of Gaussian Boson Sampling on Planted Bipartite Clique Detection

2025-10-14

AI Summary

This study investigates quantum advantage of Gaussian boson sampling (GBS) for solving the planted biclique problem, focusing on small planted sizes where classical algorithms struggle. Methodologically, we first rigorously characterize the probability distribution of node weights induced by GBS output, revealing a fundamental limitation: the bias signal introduced by the planted structure is overwhelmed by intrinsic quantum fluctuations within the classically hard parameter regime. We then develop a detection framework based on node-weight statistics, integrating probabilistic analysis with graph-theoretic tools to systematically evaluate GBS’s capability in identifying hidden dense subgraphs. Our results show that, within the classically hard regime, simple thresholding or sorting strategies fail to achieve reliable detection. Crucially, overcoming this bottleneck necessitates moving beyond standard GBS sampling paradigms—requiring instead novel quantum algorithms endowed with structural awareness and tailored inference mechanisms.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

We investigate whether Gaussian Boson Sampling (GBS) can provide a computational advantage for solving the planted biclique problem, which is a graph problem widely believed to be classically hard when the planted structure is small. Although GBS has been heuristically and experimentally observed to favor sampling dense subgraphs, its theoretical performance on this classically hard problem remains largely unexplored. We focus on a natural statistic derived from GBS output: the frequency with which a node appears in GBS samples, referred to as the node weight. We rigorously analyze whether this signal is strong enough to distinguish planted biclique nodes from background nodes. Our analysis characterizes the distribution of node weights under GBS and quantifies the bias introduced by the planted structure. The results reveal a sharp limitation: when the planted biclique size falls within the conjectured hard regime, the natural fluctuations in node weights dominate the bias signal, making detection unreliable using simple ranking strategies. These findings provide the first rigorous evidence that planted biclique detection may remain computationally hard even under GBS-based quantum computing, and they motivate further investigation into more advanced GBS-based algorithms or other quantum approaches for this problem.

Problem

• GBS addresses planted bipartite clique detection problem
• It analyzes node weight distribution from GBS samples
• It determines detection limitations in quantum computing regime

Innovation

• GBS analyzes node weight distribution for detection
• Rigorous analysis of bias signal from planted structure
• Reveals detection limitation in hard regime fluctuations