🤖 AI Summary
Quantum kernel methods lack systematic performance evaluation, hindering both theoretical understanding and practical deployment. This work presents the largest benchmark study to date, encompassing five data families and 64 datasets, with over 20,000 models trained across classification and regression tasks to systematically compare fidelity-based quantum kernels (FQKs) and projection-based quantum kernels (PQKs). Leveraging Bayesian hyperparameter optimization and correlation analysis, we provide the first empirical evidence linking PQK design degrees of freedom to generalization performance, confirming its robustness advantage in high-dimensional feature mappings. Moving beyond the “single best model” paradigm, we establish a reproducible, interpretable benchmarking framework for quantum kernel methods. This framework yields generalizable insights into kernel mechanisms and informs principled algorithm design, thereby advancing both foundational understanding and practical applicability of quantum machine learning.
📝 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.