# Variational Quantum and Quantum-Inspired Clustering

arXiv: https://arxiv.org/abs/2206.09893 · HTML: https://mlsanity.com/paper/2206.09893/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 20 references that are in the map.
- First posted on arXiv 20 Jun 2022.

## Builds on (most cited first, 1 of 1)

- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)

## Built on by (most cited first, 2 of 2)

- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Financial Risk Management on a Neutral Atom Quantum Processor](https://mlsanity.com/paper/2212.03223/) (2022)

## Abstract (arXiv)

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.