Learning Equivariant Maps with Variational Quantum Circuits

TL;DR

This paper introduces a method for learning equivariant maps using variational quantum circuits, enabling symmetric data embedding and covariant quantum channel learning, which advances quantum machine learning by leveraging data symmetries.

Contribution

It presents a novel approach to learn equivariant maps with variational quantum circuits, facilitating symmetric embeddings and covariant quantum channels in quantum machine learning.

Findings

Feasibility of learning equivariant maps demonstrated

Examples illustrating symmetric embedding procedures provided

Potential for improved quantum machine learning models shown

Abstract

Geometric quantum machine learning uses the symmetries inherent in data to design tailored machine learning tasks with reduced search space dimension. The field has been well-studied recently in an effort to avoid barren plateau issues while improving the accuracy of quantum machine learning models. This work explores the related problem of learning an equivariant map given two unitary representations of a finite group, which in turn allows the symmetric embedding of the data to be learned rather than simply required. Moreover, this procedure allows the learning of covariant quantum channels, which are an essential tool in quantum information theory. We demonstrate the feasibility of this task and give examples to illustrate the procedure.