# Stability and Generalization of Quantum Neural Networks

arXiv: https://arxiv.org/abs/2501.12737 · HTML: https://mlsanity.com/paper/2501.12737/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 61 references that are in the map.
- First posted on arXiv 22 Jan 2025.

## Builds on (most cited first, 30 of 31)

- [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)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Stability of Stochastic Gradient Descent on Nonsmooth Convex Losses](https://mlsanity.com/paper/2006.06914/) (2020)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Fine-Grained Analysis of Stability and Generalization for Stochastic Gradient Descent](https://mlsanity.com/paper/2006.08157/) (2020)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Quantum machine learning: a classical perspective](https://mlsanity.com/paper/1707.08561/) (2017)
- [Sharper bounds for uniformly stable algorithms](https://mlsanity.com/paper/1910.07833/) (2019)
- [Data-Dependent Stability of Stochastic Gradient Descent](https://mlsanity.com/paper/1703.01678/) (2017)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Stability and Generalization of Graph Convolutional Neural Networks](https://mlsanity.com/paper/1905.01004/) (2019)
- [Generalization Bounds for Uniformly Stable Algorithms](https://mlsanity.com/paper/1812.09859/) (2018)
- [Trainability of Dissipative Perceptron-Based Quantum Neural Networks](https://mlsanity.com/paper/2005.12458/) (2020)
- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [Toward Better Generalization Bounds with Locally Elastic Stability](https://mlsanity.com/paper/2010.13988/) (2020)
- [Stability and Generalization of Stochastic Gradient Methods for Minimax Problems](https://mlsanity.com/paper/2105.03793/) (2021)
- [Pseudo-dimension of quantum circuits](https://mlsanity.com/paper/2002.01490/) (2020)
- [Stability & Generalisation of Gradient Descent for Shallow Neural Networks without the Neural Tangent Kernel](https://mlsanity.com/paper/2107.12723/) (2021)
- [On the statistical complexity of quantum circuits](https://mlsanity.com/paper/2101.06154/) (2021)
- [Structural risk minimization for quantum linear classifiers](https://mlsanity.com/paper/2105.05566/) (2021)
- [Stability and Generalization Analysis of Gradient Methods for Shallow Neural Networks](https://mlsanity.com/paper/2209.09298/) (2022)
- [Simple Stochastic and Online Gradient Descent Algorithms for Pairwise Learning](https://mlsanity.com/paper/2111.12050/) (2021)
- [Learning with Gradient Descent and Weakly Convex Losses](https://mlsanity.com/paper/2101.04968/) (2021)
- [Effects of quantum resources on the statistical complexity of quantum circuits](https://mlsanity.com/paper/2102.03282/) (2021)
- [Method for noise-induced regularization in quantum neural networks](https://mlsanity.com/paper/2410.19921/) (2024)
- [Deeper Insights into Deep Graph Convolutional Networks: Stability and Generalization](https://mlsanity.com/paper/2410.08473/) (2024)

## Built on by (most cited first, 3 of 3)

- [When Federated Learning Meets Quantum Computing: Survey and Research Opportunities](https://mlsanity.com/paper/2504.08814/) (2025)
- [On the Generalization of Adversarially Trained Quantum Classifiers](https://mlsanity.com/paper/2504.17690/) (2025)
- [New Insights on Unfolding and Fine-tuning Quantum Federated Learning](https://mlsanity.com/paper/2506.20016/) (2025)

## Abstract (arXiv)

Quantum neural networks (QNNs) play an important role as an emerging technology in the rapidly growing field of quantum machine learning. While their empirical success is evident, the theoretical explorations of QNNs, particularly their generalization properties, are less developed and primarily focus on the uniform convergence approach. In this paper, we exploit an advanced tool in classical learning theory, i.e., algorithmic stability, to study the generalization of QNNs. We first establish high-probability generalization bounds for QNNs via uniform stability. Our bounds shed light on the key factors influencing the generalization performance of QNNs and provide practical insights into both the design and training processes. We next explore the generalization of QNNs on near-term noisy intermediate-scale quantum (NISQ) devices, highlighting the potential benefits of quantum noise. Moreover, we argue that our previous analysis characterizes worst-case generalization guarantees, and we establish a refined optimization-dependent generalization bound for QNNs via on-average stability. Numerical experiments on various real-world datasets support our theoretical findings.