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.

翻译：本研究探讨了高斯玻色子采样（GBS）能否为解决植入二分团问题提供计算优势，该图论问题在植入结构较小时被广泛认为在经典计算中具有困难性。尽管启发式观察和实验结果表明GBS倾向于采样稠密子图，但其在此类经典困难问题上的理论性能尚未得到充分探索。我们聚焦于从GBS输出中提取的自然统计量：节点在GBS样本中出现的频率（称为节点权重）。我们严格分析了该信号是否足够强以区分植入二分团节点与背景节点。通过解析GBS下节点权重的分布特征，并量化植入结构引入的偏差，研究结果揭示了一个显著局限：当植入二分团尺寸处于推测的困难区间时，节点权重的自然波动将主导偏差信号，导致基于简单排序策略的检测方法不可靠。这些发现首次提供了严格证据，表明即使在基于GBS的量子计算框架下，植入二分团检测可能仍保持计算困难性，从而推动了对更先进的GBS算法或其他量子方法解决该问题的进一步研究。