Clustering by Contour Coreset and Variational Quantum Eigensolver

Recent work has proposed solving the k-means clustering problem on quantum computers via the Quantum Approximate Optimization Algorithm (QAOA) and coreset techniques. Although the current method demonstrates the possibility of quantum k-means clustering, it does not ensure high accuracy and consistency across a wide range of datasets. The existing coreset techniques are designed for classical algorithms, and there is no quantum-tailored coreset technique designed to boost the accuracy of quantum algorithms. This study proposes solving the k-means clustering problem with the variational quantum eigensolver (VQE) and a customized coreset method, the Contour coreset, which is formulated with a specific focus on quantum algorithms. Extensive simulations with synthetic and real-life data demonstrated that the VQE+Contour Coreset approach outperforms existing QAOA+Coreset k-means clustering approaches with higher accuracy and lower standard deviation. This research demonstrates that quantum-tailored coreset techniques can remarkably boost the performance of quantum algorithms compared to generic off-the-shelf coreset techniques.