Quantum Kernel Methods under Scrutiny: A Benchmarking Study

TL;DR

This comprehensive benchmarking study evaluates quantum kernel methods across diverse datasets and design choices, revealing insights into their performance, hyperparameter importance, and underlying principles for effective quantum machine learning.

Contribution

It provides the first large-scale systematic comparison of fidelity and projected quantum kernels, analyzing their performance and design principles across multiple tasks and datasets.

Findings

Hyperparameters significantly influence model performance.

No single best model; universal patterns in quantum kernel effectiveness.

Design choices impact the learning mechanisms of quantum kernels.

Abstract

Since the entry of kernel theory in the field of quantum machine learning, quantum kernel methods (QKMs) have gained increasing attention with regard to both probing promising applications and delivering intriguing research insights. Benchmarking these methods is crucial to gain robust insights and to understand their practical utility. In this work, we present a comprehensive large-scale study examining QKMs based on fidelity quantum kernels (FQKs) and projected quantum kernels (PQKs) across a manifold of design choices. Our investigation encompasses both classification and regression tasks for five dataset families and 64 datasets, systematically comparing the use of FQKs and PQKs quantum support vector machines and kernel ridge regression. This resulted in over 20,000 models that were trained and optimized using a state-of-the-art hyperparameter search to ensure robust and comprehensive insights. We delve into the importance of hyperparameters on model performance scores and support our findings through rigorous correlation analyses. Additionally, we provide an in-depth analysis addressing the design freedom of PQKs and explore the underlying principles responsible for learning. Our goal is not to identify the best-performing model for a specific task but to uncover the mechanisms that lead to effective QKMs and reveal universal patterns.