Equivariant Quantum Clustering with Differential Privacy: Parameter-Efficient Privacy-Preserving Analysis Across Heterogeneous Sensitive Datasets

Privacy-preserving clustering is critical for analyzing sensitive data in healthcare, cybersecurity, and enterprise applications, where maintaining data confidentiality must be balanced with analytical performance. This paper presents Equivariant Quantum Clustering (EQC), a parameter-efficient framework that integrates symmetry-aware quantum circuits with differential privacy to improve the privacy-utility tradeoff. EQC employs p4m equivariant parameter sharing to reduce circuit complexity while preserving informative feature representations. The framework is evaluated on three privacy-sensitive datasets: NSL-KDD, CERT Insider Threat v6.2, and a synthetic MIMIC-III clinical dataset. On the NSL-KDD benchmark, EQC achieves 79.3% clustering accuracy while reducing membership inference attack success to 38.3% under a privacy budget of ε = 1.0 and δ = 10^-5, outperforming representative classical and quantum baselines. Ablation studies indicate that the performance gains primarily arise from parameter-efficient circuit design combined with differential privacy. The results demonstrate that EQC provides a practical quantum-ready framework for secure and privacy-preserving clustering across heterogeneous sensitive datasets.