# Balanced k-Means Clustering on an Adiabatic Quantum Computer

arXiv: https://arxiv.org/abs/2008.04419 · HTML: https://mlsanity.com/paper/2008.04419/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2020.

## Built on by (most cited first, 9 of 9)

- [Quantum Vision Clustering](https://mlsanity.com/paper/2309.09907/) (2023)
- [A Hybrid Quantum-Classical Neural Network Architecture for Binary Classification](https://mlsanity.com/paper/2201.01820/) (2022)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [Probabilistic Sampling of Balanced K-Means using Adiabatic Quantum Computing](https://mlsanity.com/paper/2310.12153/) (2023)
- [Discriminating Quantum States with Quantum Machine Learning](https://mlsanity.com/paper/2112.00313/) (2021)
- [Convex Non-negative Matrix Factorization Through Quantum Annealing](https://mlsanity.com/paper/2203.15634/) (2022)
- [Efficient correlation-based discretization of continuous variables for annealing machines](https://mlsanity.com/paper/2301.07244/) (2023)
- [Adiabatic Quantum Support Vector Machines](https://mlsanity.com/paper/2401.12485/) (2024)
- [Discovering the influence of personal features in psychological processes using Artificial Intelligence techniques: the case of COVID19 lockdown in Spain](https://mlsanity.com/paper/2503.05729/) (2025)

## Abstract (arXiv)

Adiabatic quantum computers are a promising platform for approximately solving challenging optimization problems. We present a quantum approach to solving the balanced k-means clustering training problem on the D-Wave 2000Q adiabatic quantum computer. Existing classical approaches scale poorly for large datasets and only guarantee a locally optimal solution. We show that our quantum approach better targets the global solution of the training problem, while achieving better theoretic scalability on large datasets. We test our quantum approach on a number of small problems, and observe clustering performance similar to the best classical algorithms.