Variational Quantum and Quantum-Inspired Clustering

TL;DR

This paper introduces a variational quantum clustering algorithm suitable for NISQ devices, capable of classifying data into many clusters using few qubits, and also presents a classical tensor network simulation for quantum-inspired clustering.

Contribution

The paper proposes a novel variational quantum clustering method that leverages non-orthogonal states and tensor networks, enabling efficient clustering with limited quantum hardware.

Findings

Excellent performance with single-qubit simulations

Effective clustering on real datasets

Quantum-inspired classical implementation demonstrated

Abstract

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.