Distance estimation for quantum prototypes based clustering

Abstract

Quantum machine learning is a new area of research with the recent work on quantum versions of supervised and unsupervised algorithms. In recent years, many quantum machine learning algorithms have been proposed providing a speed-up over the classical algorithms. In this paper, we propose an analysis and a comparison of three quantum distances for protoptypes-based clustering techniques. As an application of this work, we present a quantum K-means version which gives a good classification just like its classical version, the difference resides in the complexity: while the classical version of K-means takes polynomial time, the quantum version takes only logarithmic time especially in large datasets. Finally, we validate the benefits of the proposed approach by performing a series of empirical evaluations regarding the quantum distance estimation and its behavior versus the stability of finding the nearest centers in the right order.