Covariant quantum kernels for data with group structure

Jennifer R. Glick; Tanvi P. Gujarati; Antonio D. Corcoles; Youngseok Kim; Abhinav Kandala; Jay M. Gambetta; Kristan Temme

doi:10.48550/arxiv.2105.03406

Papers

qcr:2606.04960.1

Covariant quantum kernels for data with group structure

arXiv

Jennifer R. Glick, Tanvi P. Gujarati, Antonio D. Corcoles, +4 more

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 qubits on a superconducting processor.

10.48550/arxiv.2105.03406

Published 2021

Uploaded 4 days ago

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