# Importance of Kernel Bandwidth in Quantum Machine Learning

arXiv: https://arxiv.org/abs/2111.05451 · HTML: https://mlsanity.com/paper/2111.05451/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 9 Nov 2021.

## Builds on (most cited first, 9 of 9)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (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)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [To understand deep learning we need to understand kernel learning](https://mlsanity.com/paper/1802.01396/) (2018)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)

## Built on by (most cited first, 30 of 31)

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Bandwidth Enables Generalization in Quantum Kernel Models](https://mlsanity.com/paper/2206.06686/) (2022)
- [QKSAN: A Quantum Kernel Self-Attention Network](https://mlsanity.com/paper/2308.13422/) (2023)
- [Quantum Kernel Methods under Scrutiny: A Benchmarking Study](https://mlsanity.com/paper/2409.04406/) (2024)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [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)
- [Unravelling physics beyond the standard model with classical and quantum anomaly detection](https://mlsanity.com/paper/2301.10787/) (2023)
- [A Hyperparameter Study for Quantum Kernel Methods](https://mlsanity.com/paper/2310.11891/) (2023)
- [A kernel-based quantum random forest for improved classification](https://mlsanity.com/paper/2210.02355/) (2022)
- [Neural auto-designer for enhanced quantum kernels](https://mlsanity.com/paper/2401.11098/) (2024)
- [Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey](https://mlsanity.com/paper/2409.07626/) (2024)
- [Efficient Parameter Optimisation for Quantum Kernel Alignment: A Sub-sampling Approach in Variational Training](https://mlsanity.com/paper/2401.02879/) (2024)
- [QuaCK-TSF: Quantum-Classical Kernelized Time Series Forecasting](https://mlsanity.com/paper/2408.12007/) (2024)
- [Towards Efficient Quantum Anomaly Detection: One-Class SVMs using Variable Subsampling and Randomized Measurements](https://mlsanity.com/paper/2312.09174/) (2023)
- [Benign Overfitting with Quantum Kernels](https://mlsanity.com/paper/2503.17020/) (2025)
- [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)
- [Empowering Credit Scoring Systems with Quantum-Enhanced Machine Learning](https://mlsanity.com/paper/2404.00015/) (2024)
- [Quantum enhanced stratification of Breast Cancer: exploring quantum expressivity for real omics data](https://mlsanity.com/paper/2409.14089/) (2024)
- [Efficient Quantum One-Class Support Vector Machines for Anomaly Detection Using Randomized Measurements and Variable Subsampling](https://mlsanity.com/paper/2407.20753/) (2024)
- [Quantum-Hybrid Support Vector Machines for Anomaly Detection in Industrial Control Systems](https://mlsanity.com/paper/2506.17824/) (2025)
- [Is data-efficient learning feasible with quantum models?](https://mlsanity.com/paper/2508.19437/) (2025)
- [Quantum feature encoding optimization](https://mlsanity.com/paper/2512.02422/) (2025)
- [Maritime object classification with SAR imagery using quantum kernel methods](https://mlsanity.com/paper/2512.11367/) (2025)
- [Geometric and Quantum Kernel Methods for Predicting Skeletal Muscle Outcomes in chronic obstructive pulmonary disease](https://mlsanity.com/paper/2601.00921/) (2026)
- [Quantum Kernels and the Cross-Section of Stock Returns: Anatomy of a Vanishing Advantage](https://mlsanity.com/paper/2607.20168/) (2026)
- [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 considered a promising avenue for applying quantum computers to machine learning problems. Identifying hyperparameters controlling the inductive bias of quantum machine learning models is expected to be crucial given the central role hyperparameters play in determining the performance of classical machine learning methods. In this work we introduce the hyperparameter controlling the bandwidth of a quantum kernel and show that it controls the expressivity of the resulting model. We use extensive numerical experiments with multiple quantum kernels and classical datasets to show consistent change in the model behavior from underfitting (bandwidth too large) to overfitting (bandwidth too small), with optimal generalization in between. We draw a connection between the bandwidth of classical and quantum kernels and show analogous behavior in both cases. Furthermore, we show that optimizing the bandwidth can help mitigate the exponential decay of kernel values with qubit count, which is the cause behind recent observations that the performance of quantum kernel methods decreases with qubit count. We reproduce these negative results and show that if the kernel bandwidth is optimized, the performance instead improves with growing qubit count and becomes competitive with the best classical methods.