Hybrid Quantum--Classical k-Means Clustering via Quantum Feature Maps

TL;DR

This paper introduces a quantum-enhanced k-means clustering algorithm that uses quantum kernels for similarity measurement, demonstrating improved stability and accuracy on classical datasets with shallow quantum circuits.

Contribution

It proposes a novel quantum kernel-based approach for k-means clustering, replacing classical distances with quantum inner products to better capture data structure.

Findings

Achieved 88.6% accuracy on Iris dataset with quantum feature maps.

Achieved 91.0% accuracy on breast cancer dataset using quantum kernels.

Demonstrated improved clustering stability over classical k-means.

Abstract

Clustering is one of the most fundamental tasks in machine learning, and the k-means clustering algorithm is perhaps one of the most widely used clustering algorithms. However, it suffers from several limitations, such as sensitivity to centroid initialization, difficulty capturing non-linear structure, and poor performance in high-dimensional spaces. Recent work has proposed improved initialization strategies and quantum-assisted distance computation, but the similarity metric itself has largely remained classical. In this study, we propose a quantum-enhanced variant of k-means that replaces the Euclidean distance with a quantum kernel derived from the inner product between feature-mapped quantum states. Using the Iris dataset, we use multiple quantum feature maps, including entangled SU2 and ZZ circuits, to embed classical data into a higher-dimensional Hilbert space where cluster structures become more separable. We will also be testing using another dataset, namely the breast cancer dataset. Similarity between data points is computed through the inner product between two states. Our results show that this approach achieves improved clustering stability and competitive accuracy compared to the classical algorithm, with the SU2 feature map yielding an accuracy of 88.6 % on the Iris dataset and 91.0 % on the breast cancer dataset, despite operating on NISQ-feasible shallow circuits. These findings suggest that quantum kernels provide a richer similarity landscape than traditional distance metrics, offering a promising path toward more robust unsupervised learning in the NISQ era.