Covariant quantum kernels for data with group structure

TL;DR

This paper introduces covariant quantum kernels tailored for data with group structures, leveraging unitary representations and kernel alignment, and demonstrates their application on a 27-qubit superconducting quantum processor.

Contribution

The paper proposes a new class of quantum kernels based on group representations, optimized via kernel alignment, for improved learning on structured data.

Findings

Successfully implemented on 27 qubits

Applied to coset-space learning problem

Demonstrated potential advantage over classical methods

Abstract

The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to computational hardness assumptions, cannot be computed classically. It is an important challenge to find quantum kernels that provide an advantage in the classification of real-world data. We introduce a class of quantum kernels that can be used for data with a group structure. The kernel is defined in terms of a unitary representation of the group and a fiducial state that can be optimized using a technique called kernel alignment. We apply this method to a learning problem on a coset-space that embodies the structure of many essential learning problems on groups. We implement the learning algorithm with $27$ qubits on a superconducting processor.