# Clustering by Contour coreset and variational quantum eigensolver

arXiv: https://arxiv.org/abs/2312.03516 · HTML: https://mlsanity.com/paper/2312.03516/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 6 Dec 2023.

## Builds on (most cited first, 7 of 7)

- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Practical Coreset Constructions for Machine Learning](https://mlsanity.com/paper/1703.06476/) (2017)
- [One-Shot Coresets: The Case of k-Clustering](https://mlsanity.com/paper/1711.09649/) (2017)
- [Strong Coresets for Hard and Soft Bregman Clustering with Applications to Exponential Family Mixtures](https://mlsanity.com/paper/1508.05243/) (2015)
- [Coreset Clustering on Small Quantum Computers](https://mlsanity.com/paper/2004.14970/) (2020)
- [Performance analysis of coreset selection for quantum implementation of K-Means clustering algorithm](https://mlsanity.com/paper/2206.07852/) (2022)
- [Adiabatic Quantum Computing for Binary Clustering](https://mlsanity.com/paper/1706.05528/) (2017)

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

- [Quantum Kernel Learning for Small Dataset Modeling in Semiconductor Fabrication: Application to Ohmic Contact](https://mlsanity.com/paper/2409.10803/) (2024)
- [PASS: Certified Subset Repair for Classical and Quantum Pairwise Constrained Clustering](https://mlsanity.com/paper/2601.20157/) (2026)

## Abstract (arXiv)

Recent work has proposed solving the k-means clustering problem on quantum computers via the Quantum Approximate Optimization Algorithm (QAOA) and coreset techniques. Although the current method demonstrates the possibility of quantum k-means clustering, it does not ensure high accuracy and consistency across a wide range of datasets. The existing coreset techniques are designed for classical algorithms and there has been no quantum-tailored coreset technique which is designed to boost the accuracy of quantum algorithms. In this work, we propose solving the k-means clustering problem with the variational quantum eigensolver (VQE) and a customised coreset method, the Contour coreset, which has been formulated with specific focus on quantum algorithms. Extensive simulations with synthetic and real-life data demonstrated that our VQE+Contour Coreset approach outperforms existing QAOA+Coreset k-means clustering approaches with higher accuracy and lower standard deviation. Our work has shown that quantum tailored coreset techniques has the potential to significantly boost the performance of quantum algorithms when compared to using generic off-the-shelf coreset techniques.