Quantum Clustering with k-Means: a Hybrid Approach

TL;DR

This paper introduces three hybrid quantum-classical k-Means algorithms that leverage quantum parallelism to accelerate distance computations, potentially improving efficiency for large datasets while maintaining similar clustering quality.

Contribution

The paper presents novel hybrid quantum k-Means algorithms that utilize quantum parallelism to reduce complexity in cluster assignment, a significant advancement over classical methods.

Findings

Quantum algorithms speed up distance calculations.

Hybrid algorithms achieve comparable clustering results.

Efficiency improves with dataset size.

Abstract

Quantum computing is a promising paradigm based on quantum theory for performing fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including machine learning. In this paper, we design, implement, and evaluate three hybrid quantum k-Means algorithms, exploiting different degree of parallelism. Indeed, each algorithm incrementally leverages quantum parallelism to reduce the complexity of the cluster assignment step up to a constant cost. In particular, we exploit quantum phenomena to speed up the computation of distances. The core idea is that the computation of distances between records and centroids can be executed simultaneously, thus saving time, especially for big datasets. We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version, still obtaining comparable clustering results.