Here we present a quantum algorithm for clustering data based on a variational quantum circuit. The algorithm allows to classify data into many clusters, and can easily be implemented in few-qubit Noisy Intermediate-Scale Quantum (NISQ) devices. The idea of the algorithm relies on reducing the clustering problem to an optimization, and then solving it via a Variational Quantum Eigensolver (VQE) combined with non-orthogonal qubit states. In practice, the method uses maximally-orthogonal states of the target Hilbert space instead of the usual computational basis, allowing for a large number of clusters to be considered even with few qubits. We benchmark the algorithm with numerical simulations using real datasets, showing excellent performance even with one single qubit. Moreover, a tensor network simulation of the algorithm implements, by construction, a quantum-inspired clustering algorithm that can run on current classical hardware.

翻译：本文提出了一种基于变分量子电路的量子数据聚类算法。该算法能够将数据分类至多个聚类中，且易于在少量子比特的中等规模含噪量子（NISQ）设备上实现。其核心思想是将聚类问题转化为优化问题，并通过结合非正交量子比特态的变分量子本征求解器（VQE）进行求解。实际应用中，该方法采用目标希尔伯特空间的最大正交态替代传统的计算基态，从而在少量量子比特下也能处理大量聚类。我们利用真实数据集进行数值模拟验证，结果表明即使仅使用单量子比特也能获得优异性能。此外，该算法的张量网络模拟天然实现了可在当前经典硬件上运行的量子启发聚类算法。