# Computable Model-Independent Bounds for Adversarial Quantum Machine Learning

arXiv: https://arxiv.org/abs/2411.06863 · HTML: https://mlsanity.com/paper/2411.06863/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 86 references that are in the map.
- First posted on arXiv 11 Nov 2024.

## Builds on (most cited first, 30 of 38)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Are adversarial examples inevitable?](https://mlsanity.com/paper/1809.02104/) (2018)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Adversarial vulnerability for any classifier](https://mlsanity.com/paper/1802.08686/) (2018)
- [Quantum Adversarial Machine Learning](https://mlsanity.com/paper/2001.00030/) (2019)
- [Quantum machine learning for image classification](https://mlsanity.com/paper/2304.09224/) (2023)
- [Lower Bounds on Adversarial Robustness from Optimal Transport](https://mlsanity.com/paper/1909.12272/) (2019)
- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [The Curse of Concentration in Robust Learning: Evasion and Poisoning Attacks from Concentration of Measure](https://mlsanity.com/paper/1809.03063/) (2018)
- [Triggering Failures: Out-Of-Distribution detection by learning from local adversarial attacks in Semantic Segmentation](https://mlsanity.com/paper/2108.01634/) (2021)
- [Experimental quantum adversarial learning with programmable superconducting qubits](https://mlsanity.com/paper/2204.01738/) (2022)
- [Benchmarking Adversarially Robust Quantum Machine Learning at Scale](https://mlsanity.com/paper/2211.12681/) (2022)
- [Entangled Datasets for Quantum Machine Learning](https://mlsanity.com/paper/2109.03400/) (2021)

## Abstract (arXiv)

By leveraging the principles of quantum mechanics, QML opens doors to novel approaches in machine learning and offers potential speedup. However, machine learning models are well-documented to be vulnerable to malicious manipulations, and this susceptibility extends to the models of QML. This situation necessitates a thorough understanding of QML's resilience against adversarial attacks, particularly in an era where quantum computing capabilities are expanding. In this regard, this paper examines model-independent bounds on adversarial performance for QML. To the best of our knowledge, we introduce the first computation of an approximate lower bound for adversarial error when evaluating model resilience against sophisticated quantum-based adversarial attacks. Experimental results are compared to the computed bound, demonstrating the potential of QML models to achieve high robustness. In the best case, the experimental error is only 10% above the estimated bound, offering evidence of the inherent robustness of quantum models. This work not only advances our theoretical understanding of quantum model resilience but also provides a precise reference bound for the future development of robust QML algorithms.