发表机构
Chongqing University of Posts and Telecommunications; University of Otago（重庆邮电大学; 奥塔哥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出粒球量子聚类框架，通过PCA引导的粒球压缩减少80%量子核评估，并利用量子内聚机制过滤噪声，在多种数据集上实现更优的聚类准确性和鲁棒性。
AI 中文摘要
量子聚类旨在利用量子特征表示来揭示超越传统欧几里得几何的复杂数据结构。然而，这种样本级核构建需要对n个数据点执行O(n^2)次量子电路，在近期量子资源约束下造成了主要瓶颈。先前的解决方案未能解决这一效率-准确性困境：经典粒球聚类降低了样本复杂度，但依赖无法捕捉量子相关性的欧几里得度量，而现有的量子压缩方案优先考虑效率而非结构保持，导致在非凸或噪声数据上性能下降。在此，我们提出粒球量子聚类（GBQC），一个将粒球结构抽象与量子特征学习紧密耦合的框架。GBQC首先通过PCA引导的分裂策略将原始数据压缩为紧凑、有代表性的粒球，与全样本方法相比，核评估减少了80%。随后，一种量子内聚机制在希尔伯特空间中过滤噪声粒球，以提高聚类鲁棒性。在合成、噪声、重叠和真实世界数据集上的大量实验表明，与代表性的经典和量子聚类方法相比，GBQC始终实现更优的聚类准确性和鲁棒性。同时，所提出的粒球压缩显著减少了量子核评估和计算开销，使得在参数化量子学习框架内对更大数据集进行量子聚类实验成为可能。这些结果表明，粒球表示不仅作为一种压缩机制来降低量子计算成本，而且作为一种有效的结构抽象机制，通过消除冗余和结构模糊的学习单元来提高聚类质量。
英文摘要
Quantum clustering aims to exploit quantum feature representations to uncover complex data structures beyond conventional Euclidean geometry. Yet this sample-level kernel construction requires O(n^2) quantum circuit executions for n data points, creating a major bottleneck under near-term quantum resource constraints. Prior solutions fail to resolve this efficiency-accuracy dilemma: classical granular-ball clustering reduces sample complexity but relies on Euclidean metrics that cannot capture quantum correlations, while existing quantum compression schemes prioritize efficiency over structural preservation, degrading performance on non-convex or noisy data. Here we propose Granular-Ball Quantum Clustering (GBQC), a framework that tightly couples granular-ball structural abstraction with quantum feature learning. GBQC first compresses raw data into compact, representative granular balls via a PCA-guided splitting strategy, reducing kernel evaluations by 80% compared to full-sample methods. A quantum cohesion mechanism then filters noisy granules in Hilbert space to improve clustering robustness. Extensive experiments on synthetic, noisy, overlapping, and real-world datasets demonstrate that GBQC consistently achieves superior clustering accuracy and robustness compared with representative classical and quantum clustering methods. Meanwhile, the proposed granular-ball compression significantly reduces quantum kernel evaluations and computational overhead, enabling quantum clustering experiments on larger datasets within parameterized quantum learning frameworks. These results suggest that granular-ball representations serve not only as a compression mechanism to reduce quantum computational costs but also as an effective structural abstraction mechanism that improves clustering quality by eliminating redundant and structurally ambiguous learning units.
