A Unified Framework for Trace-induced Quantum Kernels

TL;DR

This paper introduces a unified framework for trace-induced quantum kernels, combining various types into a common structure, and demonstrates how to systematically enhance their complexity and efficiency for improved quantum machine learning models.

Contribution

It unifies different trace-induced quantum kernels into a single framework and proposes a systematic method to increase their complexity and resource efficiency.

Findings

Local projected kernels achieve comparable performance to global fidelity kernels.

The framework relates kernel expressiveness to the number of Lego kernels used.

Fewer quantum resources are needed for certain local kernels without sacrificing accuracy.

Abstract

Quantum kernel methods are promising candidates for achieving a practical quantum advantage for certain machine learning tasks. Similar to classical machine learning, an exact form of a quantum kernel is expected to have a great impact on the model performance. In this work we combine all trace-induced quantum kernels, including the commonly-used global fidelity and local projected quantum kernels, into a common framework. We show how generalized trace-induced quantum kernels can be constructed as combinations of the fundamental building blocks we coin "Lego" kernels, which impose an inductive bias on the resulting quantum models. We relate the expressive power and generalization ability to the number of non-zero weight Lego kernels and propose a systematic approach to increase the complexity of a quantum kernel model, leading to a new form of the local projected kernels that require fewer quantum resources in terms of the number of quantum gates and measurement shots. We show numerically that models based on local projected kernels can achieve comparable performance to the global fidelity quantum kernel. Our work unifies existing quantum kernels and provides a systematic framework to compare their properties.