
Quantum machine learning promises computational advantages for certain tasks, yet rigorous empirical evaluation of quantum clustering algorithms against classical baselines remains limited. This paper presents a comprehensive implementation and comparative analysis of two quantum K-means clustering algorithms—SWAP Test-based and Quantum Fidelity-based—against classical K-means on benchmark datasets. Both quantum approaches employ amplitude encoding to map classical data into quantum state amplitudes and use quantum-native distance metrics derived from inner products in Hilbert space. All three methods are evaluated on the ENB2012 energy efficiency dataset (768 samples, 8 features) and a synthetically expanded high-dimensional dataset (4,998 samples, 16 features), measuring silhouette score, inertia, and wall-clock execution time across cluster counts k ∈ {2, . . . , 7}. The experiments, conducted on Qiskit’s AerSimulator and Statevector backends, show that classical K-means achieves substantially higher silhouette scores (0.391 vs. 0.031 on the original dataset) and orders-of-magnitude faster execution. A rigorous analysis attributes these results to three factors: (i) the information loss inherent in amplitude encoding normalization, (ii) the geometric mismatch between Euclidean and Hilbert-space distance metrics, and (iii) the absence of quantum parallelism in classical simulation. The implications for quantum advantage in unsupervised learning are discussed and concrete requirements for near-term quantum hardware to achieve competitive clustering performance are outlined.
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