# A Hyperparameter Study for Quantum Kernel Methods

arXiv: https://arxiv.org/abs/2310.11891 · HTML: https://mlsanity.com/paper/2310.11891/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 18 Oct 2023.

## Builds on (most cited first, 15 of 15)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [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)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [OpenML Benchmarking Suites](https://mlsanity.com/paper/1708.03731/) (2017)
- [Toward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivity](https://mlsanity.com/paper/1602.05897/) (2016)
- [Why does deep and cheap learning work so well?](https://mlsanity.com/paper/1608.08225/) (2016)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [Importance of Kernel Bandwidth in Quantum Machine Learning](https://mlsanity.com/paper/2111.05451/) (2021)
- [Numerical evidence against advantage with quantum fidelity kernels on classical data](https://mlsanity.com/paper/2211.16551/) (2022)
- [Hyperparameter Importance of Quantum Neural Networks Across Small Datasets](https://mlsanity.com/paper/2206.09992/) (2022)

## Built on by (most cited first, 9 of 9)

- [Quantum Kernel Methods under Scrutiny: A Benchmarking Study](https://mlsanity.com/paper/2409.04406/) (2024)
- [Quantum Neural Networks under Depolarization Noise: Exploring White-Box Attacks and Defenses](https://mlsanity.com/paper/2311.17458/) (2023)
- [On the similarity of bandwidth-tuned quantum kernels and classical kernels](https://mlsanity.com/paper/2503.05602/) (2025)
- [Non-variational supervised quantum kernel methods: a review](https://mlsanity.com/paper/2604.07896/) (2026)
- [Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learning](https://mlsanity.com/paper/2602.00048/) (2026)
- [Quantum Kernels for Audio Deepfake Detection Using Spectrogram Patch Features](https://mlsanity.com/paper/2605.06035/) (2026)
- [Is data-efficient learning feasible with quantum models?](https://mlsanity.com/paper/2508.19437/) (2025)
- [Maritime object classification with SAR imagery using quantum kernel methods](https://mlsanity.com/paper/2512.11367/) (2025)
- [Benchmarking Quantum Machine Learning for Power-System Attack Detection: Evaluation Choices Decide the Outcome Before the Models Do](https://mlsanity.com/paper/2608.15617/) (2026)

## Abstract (arXiv)

Quantum kernel methods are a promising method in quantum machine learning thanks to the guarantees connected to them. Their accessibility for analytic considerations also opens up the possibility of prescreening datasets based on their potential for a quantum advantage. To do so, earlier works developed the geometric difference, which can be understood as a closeness measure between two kernel-based machine learning approaches, most importantly between a quantum kernel and a classical kernel. This metric links the quantum and classical model complexities, and it was developed to bound generalization error. Therefore, it raises the question of how this metric behaves in an empirical setting. In this work, we investigate the effects of hyperparameter choice on the model performance and the generalization gap between classical and quantum kernels. The importance of hyperparameters is well known also for classical machine learning. Of special interest are hyperparameters associated with the quantum Hamiltonian evolution feature map, as well as the number of qubits to trace out before computing a projected quantum kernel. We conduct a thorough investigation of the hyperparameters across 11 datasets and we identify certain aspects that can be exploited. Analyzing the effects of certain hyperparameter settings on the empirical performance, as measured by cross validation accuracy, and generalization ability, as measured by geometric difference described above, brings us one step closer to understanding the potential of quantum kernel methods on classical datasets.