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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.
Highlights
Within the rapidly evolving field of quantum machine learning (QML) (Biamonte et al 2017; Cerezo et al 2022), quantum kernel methods (QKMs) (Schuld and Killoran 2019; Havlícek et al 2019; Peters et al 2021; Tomono and Natsubori 2022; Hubregtsen et al 2022; Jerbi et al 2023; Gan et al 2023) have emerged as a interesting and promising branch of research
Results for each QKM and dataset within the respective dataset family are aggregated across the data encoding circuits with corresponding obtained optimal n∗layers, yielding the best mean squared error (MSE) or ROC-AUC score, respectively
Another remarkable observation significantly extends the findings of Bowles et al (2024) and generally reveals that circuits without entanglement perform on par with or better than those with entangling gates. We show this across various encoding circuits, using both fidelity quantum kernels (FQKs) and projected quantum kernels (PQKs) within quantum support vector machines (QSVMs) and quantum kernel ridge regression (QKRR) approaches and addressing both regression and classification problems
Summary
Within the rapidly evolving field of quantum machine learning (QML) (Biamonte et al 2017; Cerezo et al 2022), quantum kernel methods (QKMs) (Schuld and Killoran 2019; Havlícek et al 2019; Peters et al 2021; Tomono and Natsubori 2022; Hubregtsen et al 2022; Jerbi et al 2023; Gan et al 2023) have emerged as a interesting and promising branch of research. Quantum kernel methods leverage the principles of quantum mechanics to perform these mappings into the exponentially large Hilbert space of quantum states. This is realized by parameterized quantum circuits (PQCs) (Schuld and Killoran 2019; Lloyd et al 2020; Schuld et al 2021; Jerbi et al 2023), which in the context of quantum kernels are referred to as data encoding circuits.
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