Vol. 2, Issue 1, Part A (2025)

Quantum computing has emerged as a revolutionary paradigm capable of solving computationally intensive problems that remain intractable for classical systems. This study presents a comprehensive analysis of efficient quantum algorithms for data clustering applications, focusing on the design, implementation, and evaluation of two hybrid quantum-classical models: Quantum K-Means (Q-KMeans) and Variational Quantum Embedding Clustering (VQE-Cluster). Leveraging quantum principles such as superposition, entanglement, amplitude encoding, and quantum phase estimation, the research investigates how quantum subroutines can accelerate key clustering operations, including distance computation and centroid optimization. Benchmark datasets—comprising Iris, MNIST subsets, and synthetic Gaussian mixtures—were used to assess clustering performance, runtime scalability, and fidelity across multiple simulation trials. The results indicate that quantum-enhanced methods achieve significantly improved silhouette scores and reduced inertia compared with classical K-Means and DBSCAN, particularly in high-dimensional and nonlinear data contexts. Furthermore, runtime analyses demonstrated polynomial-to-exponential speedups as dataset size increased, confirming the theoretical advantages of quantum linear-algebraic computations. Variational quantum embeddings maintained high fidelity (≈0.93-0.95) even at moderate circuit depths, underscoring the feasibility of deploying such models on near-term NISQ hardware. Statistical analyses further validated the robustness and reproducibility of results, while ablation experiments revealed an optimal trade-off between circuit depth and clustering quality. The study concludes that carefully optimized hybrid quantum-clustering algorithms can effectively bridge the gap between theoretical quantum advantage and practical data science needs. Practical recommendations emphasize the importance of shallow circuit architectures, hybrid workflow integration, error mitigation, and the strategic use of quantum simulation platforms to maximize performance within current hardware constraints. Overall, this work contributes to advancing quantum machine learning by providing a scalable, hardware-efficient pathway for clustering complex datasets, thereby laying a foundation for future real-world quantum data analytics systems.