An adaptive quantum-classical approach for scalable clustering and analytical decision-making

Clustering remains a cornerstone of unsupervised learning, yet classical algorithms often struggle with the inherent complexities of modern datasets, such as high dimensionality, non-linear separability, and significant noise. This paper introduces the Hybrid Quantum-Classical Clustering Algorithm (HQCA), a novel framework that leverages the power of quantum computation and the robustness of classical machine learning to overcome these limitations. HQCA integrates a quantum kernel estimation phase, utilizing a parameterized quantum circuit to project data into a high-dimensional Hilbert space, thereby enhancing cluster separability where classical kernels fail. Furthermore, it employs a quantum-enhanced optimization routine, based on the Quantum Approximate Optimization Algorithm (QAOA), to determine optimal cluster centroids, thereby mitigating the common pitfall of local minima encountered by algorithms like K-Means. The algorithm also incorporates a quantum-inspired gap statistic to autonomously determine the optimal number of clusters. We rigorously evaluate HQCA against state-of-the-art classical clustering methods, including K-Means, DBSCAN, and Spectral Clustering, on multiple real-world benchmark datasets from the UCI repository, such as Iris, Wine, and a high-dimensional image dataset (Fashion-MNIST). Our results demonstrate that HQCA consistently achieves superior performance across multiple evaluation metrics, including Purity, Silhouette Score, and Adjusted Rand Index (ARI), particularly excelling in scenarios involving complex, non-linear data manifolds. The proposed hybrid paradigm not only signifies a substantial leap in clustering accuracy and robustness but also provides a scalable pathway for leveraging current Noisy Intermediate-Scale Quantum (NISQ) devices in practical data analytics workflows, marking a critical step toward potential quantum advantage in unsupervised learning. We emphasize that the demonstrated advantage is algorithmic and representational, not an asymptotic runtime advantage.