Clustering Within Quantum Mechanical Framework

Antonin Lefevre

Suzhen Yuan, Qilin Xie, Lifeng Shen +3 more

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.

Jincheng Zhang

This paper explores the application of quantum computing to enhance the process of topological data analysis, specifically focusing on the identification of underlying patterns and relationships within complex topological data structures. We propose an adaptive clustering algorithm that leverages quantum properties, aiming to surpass classical clustering methods in terms of speed and accuracy. The core mechanism centers around quantum entanglement to facilitate the exploration of intricate correlations within the data, leading to a more nuanced understanding of the underlying structure. The paper details the theoretical framework, the implementation of the quantum algorithm, and initial results demonstrating improvements over traditional clustering techniques.

Péter Wittek

Davide Pastorello

Walid El Maouaki, Nouhaila Innan, Alberto Marchisio +3 more

In this study, we develop a novel quantum machine learning (QML) framework to analyze cybersecurity vulnerabilities using data from the 2022 CISA Known Exploited Vulnerabilities catalog, which includes detailed information on vulnerability types, severity levels, common vulnerability scoring system (CVSS) scores, and product specifics. Our framework preprocesses this data into a quantum-compatible format, enabling clustering analysis through our advanced quantum techniques, QCSWAPK-means and QkerneIK-means. These quantum algorithms demonstrate superior performance compared to state-of-the-art classical clustering techniques like k-means and spectral clustering, achieving Silhouette scores of 0.491, Davies-Bouldin indices below 0.745, and Calinski-Harabasz scores exceeding 884, indicating more distinct and well-separated clusters. Our frame-work categorizes vulnerabilities into distinct groups, reflecting varying levels of risk severity: Cluster0, primarily consisting of critical Microsoft-related vulnerabilities; Cluster 1, featuring medium severity vulnerabilities from various enterprise software vendors and network solutions; Cluster 2, with high severity vulnerabilities from Adobe, Cisco, and Google; and Cluster 3, encompassing vulnerabilities from Microsoft and Oracle with high to medium severity. These findings highlight the potential of QML to enhance the precision of vulnerability assessments and prioritization, advancing cybersecurity practices by enabling more strategic and proactive defense mechanisms.