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 has been no quantum-tailored coreset technique which is designed to boost the accuracy of quantum algorithms. In this work, we propose solving the k-means clustering problem with the variational quantum eigensolver (VQE) and a customised coreset method, the Contour coreset, which has been formulated with specific focus on quantum algorithms. Extensive simulations with synthetic and real-life data demonstrated that our VQE+Contour Coreset approach outperforms existing QAOA+Coreset k-means clustering approaches with higher accuracy and lower standard deviation. Our work has shown that quantum tailored coreset techniques has the potential to significantly boost the performance of quantum algorithms when compared to using generic off-the-shelf coreset techniques.

翻译：近期研究提出了通过量子近似优化算法（QAOA）与核心集技术在量子计算机上求解k-means聚类问题的方法。尽管现有方法展示了量子k-means聚类实现的可行性，但其在大范围数据集上难以保证高精度与一致性。现有核心集技术主要针对经典算法设计，尚未出现专为量子算法定制的、旨在提升量子算法准确性的核心集方法。本研究提出采用变分量子本征求解器（VQE）结合定制化核心集方法——轮廓核心集（Contour coreset）来解决k-means聚类问题，该方法特为量子算法进行设计。基于合成数据与真实数据的广泛仿真结果表明，相较于现有QAOA+核心集k-means聚类方法，我们提出的VQE+轮廓核心集方法在更高精度与更低标准差方面表现更优。本工作表明，相较于使用通用型核心集技术，量子定制化核心集方法具有显著提升量子算法性能的潜力。