# Numerical evidence against advantage with quantum fidelity kernels on classical data

arXiv: https://arxiv.org/abs/2211.16551 · HTML: https://mlsanity.com/paper/2211.16551/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 43 references that are in the map.
- First posted on arXiv 29 Nov 2022.

## Builds on (most cited first, 13 of 13)

- [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)
- [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)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)

## Built on by (most cited first, 11 of 11)

- [Quantum Kernel Methods under Scrutiny: A Benchmarking Study](https://mlsanity.com/paper/2409.04406/) (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)
- [Mitigating exponential concentration in covariant quantum kernels for subspace and real-world data](https://mlsanity.com/paper/2412.07915/) (2024)
- [In Search of Quantum Advantage: Estimating the Number of Shots in Quantum Kernel Methods](https://mlsanity.com/paper/2407.15776/) (2024)
- [Exploiting the equivalence between quantum neural networks and perceptrons](https://mlsanity.com/paper/2407.04371/) (2024)
- [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 enhanced stratification of Breast Cancer: exploring quantum expressivity for real omics data](https://mlsanity.com/paper/2409.14089/) (2024)
- [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 machine learning techniques are commonly considered one of the most promising candidates for demonstrating practical quantum advantage. In particular, quantum kernel methods have been demonstrated to be able to learn certain classically intractable functions efficiently if the kernel is well-aligned with the target function. In the more general case, quantum kernels are known to suffer from exponential "flattening" of the spectrum as the number of qubits grows, preventing generalization and necessitating the control of the inductive bias by hyperparameters. We show that the general-purpose hyperparameter tuning techniques proposed to improve the generalization of quantum kernels lead to the kernel becoming well-approximated by a classical kernel, removing the possibility of quantum advantage. We provide extensive numerical evidence for this phenomenon utilizing multiple previously studied quantum feature maps and both synthetic and real data. Our results show that unless novel techniques are developed to control the inductive bias of quantum kernels, they are unlikely to provide a quantum advantage on classical data.