# The interplay of robustness and generalization in quantum machine learning

arXiv: https://arxiv.org/abs/2506.08455 · HTML: https://mlsanity.com/paper/2506.08455/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 54 references that are in the map.
- First posted on arXiv 10 Jun 2025.

## Builds on (most cited first, 30 of 32)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (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)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks](https://mlsanity.com/paper/1802.04034/) (2018)
- [Training robust neural networks using Lipschitz bounds](https://mlsanity.com/paper/2005.02929/) (2020)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [Quantum noise protects quantum classifiers against adversaries](https://mlsanity.com/paper/2003.09416/) (2020)
- [Quantum Adversarial Machine Learning](https://mlsanity.com/paper/2001.00030/) (2019)
- [Stochastic gradient descent for hybrid quantum-classical optimization](https://mlsanity.com/paper/1910.01155/) (2019)
- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [Shadows of quantum machine learning](https://mlsanity.com/paper/2306.00061/) (2023)
- [Benchmarking Adversarially Robust Quantum Machine Learning at Scale](https://mlsanity.com/paper/2211.12681/) (2022)
- [Towards quantum enhanced adversarial robustness in machine learning](https://mlsanity.com/paper/2306.12688/) (2023)
- [Optimal Provable Robustness of Quantum Classification via Quantum Hypothesis Testing](https://mlsanity.com/paper/2009.10064/) (2020)
- [Universal Adversarial Examples and Perturbations for Quantum Classifiers](https://mlsanity.com/paper/2102.07788/) (2021)
- [Let Quantum Neural Networks Choose Their Own Frequencies](https://mlsanity.com/paper/2309.03279/) (2023)
- [Training robust and generalizable quantum models](https://mlsanity.com/paper/2311.11871/) (2023)
- [Robustness Verification of Quantum Classifiers](https://mlsanity.com/paper/2008.07230/) (2020)
- [A Comparative Analysis of Adversarial Robustness for Quantum and Classical Machine Learning Models](https://mlsanity.com/paper/2404.16154/) (2024)
- [Double descent in quantum kernel methods](https://mlsanity.com/paper/2501.10077/) (2025)
- [Robustness of quantum algorithms against coherent control errors](https://mlsanity.com/paper/2303.00618/) (2023)
- [Robustness and Generalization in Quantum Reinforcement Learning via Lipschitz Regularization](https://mlsanity.com/paper/2410.21117/) (2024)

## Abstract (arXiv)

While adversarial robustness and generalization have individually received substantial attention in the recent literature on quantum machine learning, their interplay is much less explored. In this chapter, we address this interplay for variational quantum models, which were recently proposed as function approximators in supervised learning. We discuss recent results quantifying both robustness and generalization via Lipschitz bounds, which explicitly depend on model parameters. Thus, they give rise to a regularization-based training approach for robust and generalizable quantum models, highlighting the importance of trainable data encoding strategies. The practical implications of the theoretical results are demonstrated with an application to time series analysis.