Q-means using variational quantum feature embedding

TL;DR

This paper introduces a hybrid quantum-classical algorithm that learns a quantum feature map to effectively separate non-linearly separable data using variational circuits and quantum k-means clustering, enhancing unsupervised learning.

Contribution

It presents a novel variational quantum feature embedding method combined with quantum k-means for improved unsupervised clustering of complex data.

Findings

Successfully separates non-linearly separable data in quantum feature space

Demonstrates the effectiveness of quantum feature maps in clustering tasks

Provides a framework for optimizing quantum circuits for data separation

Abstract

This paper proposes a hybrid quantum-classical algorithm that learns a suitable quantum feature map that separates unlabelled data that is originally non linearly separable in the classical space using a Variational quantum feature map and q-means as a subroutine for unsupervised learning. The objective of the Variational circuit is to maximally separate the clusters in the quantum feature Hilbert space. First part of the circuit embeds the classical data into quantum states. Second part performs unsupervised learning on the quantum states in the quantum feature Hilbert space using the q-means quantum circuit. The output of the quantum circuit are characteristic cluster quantum states that represent a superposition of all quantum states belonging to a particular cluster. The final part of the quantum circuit performs measurements on the characteristic cluster quantum states to output the inter-cluster overlap based on fidelity. The output of the complete quantum circuit is used to compute the value of the cost function that is based on the Hilbert-Schmidt distance between the density matrices of the characteristic cluster quantum states. The gradient of the expectation value is used to optimize the parameters of the variational circuit to learn a better quantum feature map.