# Bandwidth Enables Generalization in Quantum Kernel Models

arXiv: https://arxiv.org/abs/2206.06686 · HTML: https://mlsanity.com/paper/2206.06686/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 48 references that are in the map.
- First posted on arXiv 14 Jun 2022.

## Builds on (most cited first, 16 of 16)

- [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)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (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)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks](https://mlsanity.com/paper/2002.02561/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [Towards understanding the power of quantum kernels in the NISQ era](https://mlsanity.com/paper/2103.16774/) (2021)
- [Importance of Kernel Bandwidth in Quantum Machine Learning](https://mlsanity.com/paper/2111.05451/) (2021)
- [Sublinear quantum algorithms for training linear and kernel-based classifiers](https://mlsanity.com/paper/1904.02276/) (2019)
- [Statistical mechanics of complex neural systems and high dimensional data](https://mlsanity.com/paper/1301.7115/) (2013)

## Built on by (most cited first, 30 of 32)

- [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)
- [Quantum Kernel Methods under Scrutiny: A Benchmarking Study](https://mlsanity.com/paper/2409.04406/) (2024)
- [A Unified Framework for Trace-induced Quantum Kernels](https://mlsanity.com/paper/2311.13552/) (2023)
- ['Eliv'agar: Efficient Quantum Circuit Search for Classification](https://mlsanity.com/paper/2401.09393/) (2024)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [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)
- [Statistical Complexity of Quantum Learning](https://mlsanity.com/paper/2309.11617/) (2023)
- [Automatic and effective discovery of quantum kernels](https://mlsanity.com/paper/2209.11144/) (2022)
- [Benchmarking quantum machine learning kernel training for classification tasks](https://mlsanity.com/paper/2408.10274/) (2024)
- [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)
- [Exploiting the equivalence between quantum neural networks and perceptrons](https://mlsanity.com/paper/2407.04371/) (2024)
- [Provable Quantum Algorithm Advantage for Gaussian Process Quadrature](https://mlsanity.com/paper/2502.14467/) (2025)
- [On the similarity of bandwidth-tuned quantum kernels and classical kernels](https://mlsanity.com/paper/2503.05602/) (2025)
- [Quantum AI for Alzheimer's disease early screening](https://mlsanity.com/paper/2405.00755/) (2024)
- [Benign Overfitting with Quantum Kernels](https://mlsanity.com/paper/2503.17020/) (2025)
- [Kernel-based optimization of measurement operators for quantum reservoir computers](https://mlsanity.com/paper/2602.14677/) (2026)
- [Quantum enhanced stratification of Breast Cancer: exploring quantum expressivity for real omics data](https://mlsanity.com/paper/2409.14089/) (2024)
- [Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise](https://mlsanity.com/paper/2412.11451/) (2024)
- [Position: Quantum Kernel Machines Should Move Beyond Scalar-Valued Kernels to Realize Their Potential](https://mlsanity.com/paper/2506.03779/) (2025)
- [Theory and interpretability of Quantum Extreme Learning Machines: a Pauli-transfer matrix approach](https://mlsanity.com/paper/2602.18377/) (2026)
- [Is data-efficient learning feasible with quantum models?](https://mlsanity.com/paper/2508.19437/) (2025)
- [Aligning Inductive Bias for Data-Efficient Generalization in State Space Models](https://mlsanity.com/paper/2509.20789/) (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)
- [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)

## Abstract (arXiv)

Quantum computers are known to provide speedups over classical state-of-the-art machine learning methods in some specialized settings. For example, quantum kernel methods have been shown to provide an exponential speedup on a learning version of the discrete logarithm problem. Understanding the generalization of quantum models is essential to realizing similar speedups on problems of practical interest. Recent results demonstrate that generalization is hindered by the exponential size of the quantum feature space. Although these results suggest that quantum models cannot generalize when the number of qubits is large, in this paper we show that these results rely on overly restrictive assumptions. We consider a wider class of models by varying a hyperparameter that we call quantum kernel bandwidth. We analyze the large-qubit limit and provide explicit formulas for the generalization of a quantum model that can be solved in closed form. Specifically, we show that changing the value of the bandwidth can take a model from provably not being able to generalize to any target function to good generalization for well-aligned targets. Our analysis shows how the bandwidth controls the spectrum of the kernel integral operator and thereby the inductive bias of the model. We demonstrate empirically that our theory correctly predicts how varying the bandwidth affects generalization of quantum models on challenging datasets, including those far outside our theoretical assumptions. We discuss the implications of our results for quantum advantage in machine learning.