# Granular-Ball Quantum Clustering for Resource-Efficient and Robust Learning

arXiv: https://arxiv.org/abs/2609.06016 · HTML: https://mlsanity.com/paper/2609.06016/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 41 references that are in the map.
- First posted on arXiv 5 Sep 2026.

## Builds on (most cited first, 2 of 2)

- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [GBC: An Efficient and Adaptive Clustering Algorithm Based on Granular-Ball](https://mlsanity.com/paper/2205.14592/) (2022)

## Abstract (arXiv)

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.