Variational Quantum and Quantum-Inspired Clustering
This work addresses clustering for data analysis, offering a quantum and quantum-inspired approach that is incremental by building on existing variational methods.
The authors tackled the problem of clustering data by developing a variational quantum algorithm that reduces clustering to optimization and solves it using a Variational Quantum Eigensolver with non-orthogonal qubit states, achieving excellent performance in numerical simulations with real datasets even with a single qubit.
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.