Biclustering is a problem in machine learning and data mining that seeks to
group together rows and columns of a dataset according to certain criteria. In
this work, we highlight the natural relation that quantum computing models like
boson and Gaussian boson sampling (GBS) have to this problem. We first explore
the use of boson sampling to identify biclusters based on matrix permanents. We
then propose a heuristic that finds clusters in a dataset using Gaussian boson
sampling by (i) converting the dataset into a bipartite graph and then (ii)
running GBS to find the densest sub-graph(s) within the larger bipartite graph.
Our simulations for the above proposed heuristics show promising results for
future exploration in this area.

使用玻色子抽样方法实现基于矩阵永久性的双聚类识别，并提出一种使用高斯玻色子抽样方法在数据集中找到最密集子图的启发式方法，通过将数据集转换为二部图并运行高斯玻色子抽样来实现。

应用光子量子计算对数据集进行双聚类分析

Biclustering a dataset using photonic quantum computing

Gaussian boson sampling exploits squeezed states to provide a highly
efficient way to demonstrate quantum computational advantage. We perform
experiments with 50 input single-mode squeezed states with high
indistinguishability and squeezing parameters, which are fed into a 100-mode
ultralow-loss interferometer with full connectivity and random transformation,
and sampled using 100 high-efficiency single-photon detectors. The whole
optical set-up is phase-locked to maintain a high coherence between the
superposition of all photon number states. We observe up to 76 output
photon-clicks, which yield an output state space dimension of $10^{30}$ and a
sampling rate that is $10^{14}$ faster than using the state-of-the-art
simulation strategy and supercomputers. The obtained samples are validated
against various hypotheses including using thermal states, distinguishable
photons, and uniform distribution.

使用高度相似和压缩参数的 50 个输入单模压缩态，通过 100 模超低损耗干涉仪进行随机变换和采样，以及 100 个高效单光子探测器进行采样，实现了一个 $10^{30}$ 维的输出状态空间，采样速率比使用先进模拟策略和超级计算机快了 $10^{14}$，并通过多种假设进行了验证。