# Quantum Expectation-Maximization Algorithm

## TL;DR

This paper introduces a quantum expectation-maximization algorithm for Gaussian mixture models, demonstrating its robustness, quantum speedup, and advantages over k-means in complex clustering scenarios.

## Contribution

It extends quantum clustering methods by developing a quantum EM algorithm for GMMs, showing improved performance and speedup over existing quantum and classical algorithms.

## Key findings

- The quantum EM algorithm is robust and faster than classical methods.
- Numerical results show GMM's advantage over k-means for complex data.
- Quantum speedup is demonstrated for the proposed algorithm.

## Abstract

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.