# Quantum Expectation-Maximization Algorithm

arXiv: https://arxiv.org/abs/1908.06655 · HTML: https://mlsanity.com/paper/1908.06655/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2019.

## Built on by (most cited first, 3 of 3)

- [Quantum Capsule Networks](https://mlsanity.com/paper/2201.01778/) (2022)
- [Quantum Advantage in Variational Bayes Inference](https://mlsanity.com/paper/2207.03104/) (2022)
- [Density Operator Expectation Maximization](https://mlsanity.com/paper/2507.22786/) (2025)

## Abstract (arXiv)

Clustering algorithms are a cornerstone of machine learning applications. Recently, a quantum algorithm for clustering based on the k-means algorithm has been proposed by Kerenidis, Landman, Luongo and Prakash. Based on their work, we propose a quantum expectation-maximization (EM) algorithm for Gaussian mixture models (GMMs). The robustness and quantum speedup of the algorithm is demonstrated. We also show numerically the advantage of GMM over k-means for non-trivial cluster data.