# Quantum Kernel Methods under Scrutiny: A Benchmarking Study

arXiv: https://arxiv.org/abs/2409.04406 · HTML: https://mlsanity.com/paper/2409.04406/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 71 references that are in the map.
- First posted on arXiv 6 Sep 2024.

## Builds on (most cited first, 29 of 29)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performance](https://mlsanity.com/paper/2304.11127/) (2023)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [How Complex is your classification problem? A survey on measuring classification complexity](https://mlsanity.com/paper/1808.03591/) (2018)
- [Deep Networks and the Multiple Manifold Problem](https://mlsanity.com/paper/2008.11245/) (2020)
- [Bandwidth Enables Generalization in Quantum Kernel Models](https://mlsanity.com/paper/2206.06686/) (2022)
- [Importance of Kernel Bandwidth in Quantum Machine Learning](https://mlsanity.com/paper/2111.05451/) (2021)
- [Quantum machine learning of large datasets using randomized measurements](https://mlsanity.com/paper/2108.01039/) (2021)
- [Automatic design of quantum feature maps](https://mlsanity.com/paper/2105.12626/) (2021)
- [Reduction of finite sampling noise in quantum neural networks](https://mlsanity.com/paper/2306.01639/) (2023)
- [A Unified Framework for Trace-induced Quantum Kernels](https://mlsanity.com/paper/2311.13552/) (2023)
- [Quantum Advantage Seeker with Kernels (QuASK): a software framework to speed up the research in quantum machine learning](https://mlsanity.com/paper/2206.15284/) (2022)
- [Numerical evidence against advantage with quantum fidelity kernels on classical data](https://mlsanity.com/paper/2211.16551/) (2022)
- [The role of entanglement for enhancing the efficiency of quantum kernels towards classification](https://mlsanity.com/paper/2209.05142/) (2022)
- [Benchmarking quantum machine learning kernel training for classification tasks](https://mlsanity.com/paper/2408.10274/) (2024)
- [A Hyperparameter Study for Quantum Kernel Methods](https://mlsanity.com/paper/2310.11891/) (2023)
- [Reinforcement learning-based architecture search for quantum machine learning](https://mlsanity.com/paper/2406.02717/) (2024)

## Built on by (most cited first, 22 of 22)

- [On the similarity of bandwidth-tuned quantum kernels and classical kernels](https://mlsanity.com/paper/2503.05602/) (2025)
- [Evaluating Angle and Amplitude Encoding Strategies for Variational Quantum Machine Learning: their impact on model's accuracy](https://mlsanity.com/paper/2508.00768/) (2025)
- [AQKA: Active Quantum Kernel Acquisition Under a Shot Budget](https://mlsanity.com/paper/2605.14672/) (2026)
- [Non-variational supervised quantum kernel methods: a review](https://mlsanity.com/paper/2604.07896/) (2026)
- [Benchmarking Quantum Kernel Support Vector Machines Against Classical Baselines on Tabular Data: A Rigorous Empirical Study with Hardware Validation](https://mlsanity.com/paper/2604.18837/) (2026)
- [Quantum Machine Learning in Multi-Qubit Phase-Space Part I: Foundations](https://mlsanity.com/paper/2507.12117/) (2025)
- [Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learning](https://mlsanity.com/paper/2602.00048/) (2026)
- [Theory and interpretability of Quantum Extreme Learning Machines: a Pauli-transfer matrix approach](https://mlsanity.com/paper/2602.18377/) (2026)
- [Quantum Kernels for Audio Deepfake Detection Using Spectrogram Patch Features](https://mlsanity.com/paper/2605.06035/) (2026)
- [AutoQML: A Framework for Automated Quantum Machine Learning](https://mlsanity.com/paper/2502.21025/) (2025)
- [Predicting fermionic densities using a Projected Quantum Kernel method](https://mlsanity.com/paper/2504.14002/) (2025)
- [Supervised Quantum Machine Learning: A Future Outlook from Qubits to Enterprise Applications](https://mlsanity.com/paper/2505.24765/) (2025)
- [Quantum Kernel Methods: Convergence Theory, Separation Bounds and Applications to Marketing Analytics](https://mlsanity.com/paper/2510.11744/) (2025)
- [Maritime object classification with SAR imagery using quantum kernel methods](https://mlsanity.com/paper/2512.11367/) (2025)
- [HyQuRP: Hybrid quantum-classical neural network with rotational and permutational equivariance](https://mlsanity.com/paper/2602.06381/) (2026)
- [Spectral Phase Encoding for Quantum Kernel Methods](https://mlsanity.com/paper/2602.19644/) (2026)
- [Hybrid Classical-Quantum (HCQ) Alzheimer's Classification via Supervised β-VAE and Quantum Kernels](https://mlsanity.com/paper/2606.14194/) (2026)
- [Implementations of Quantum and Classical Topology-Aligned Architectures for Molecular Property Prediction](https://mlsanity.com/paper/2607.13737/) (2026)
- [Statevector-to-Hardware Reconstruction of a Four-Qubit ZZ Quantum Kernel: A Single-Backend Case Study of Three Execution Jobs](https://mlsanity.com/paper/2607.20377/) (2026)
- [Investigating Quantum-Embedded Transformers on Classical Datasets for Cross-Modality Classification](https://mlsanity.com/paper/2608.06846/) (2026)
- [Fractal dimension predicts quantum kernel collapse in angle-encoded data](https://mlsanity.com/paper/2609.00475/) (2026)
- [Candidate Comparability Before Promotion: Conditional Validation in Adaptive Network Intrusion Detection](https://mlsanity.com/paper/2609.04388/) (2026)

## Abstract (arXiv)

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.