# Defence against adversarial attacks using classical and quantum-enhanced Boltzmann machines

arXiv: https://arxiv.org/abs/2012.11619 · HTML: https://mlsanity.com/paper/2012.11619/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2020.

## Built on by (most cited first, 5 of 5)

- [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)
- [Adversarial Robustness Guarantees for Quantum Classifiers](https://mlsanity.com/paper/2405.10360/) (2024)
- [Accelerating the training of single-layer binary neural networks using the HHL quantum algorithm](https://mlsanity.com/paper/2210.12707/) (2022)
- [Tensorization of neural networks for improved privacy and interpretability](https://mlsanity.com/paper/2501.06300/) (2025)

## Abstract (arXiv)

We provide a robust defence to adversarial attacks on discriminative algorithms. Neural networks are naturally vulnerable to small, tailored perturbations in the input data that lead to wrong predictions. On the contrary, generative models attempt to learn the distribution underlying a dataset, making them inherently more robust to small perturbations. We use Boltzmann machines for discrimination purposes as attack-resistant classifiers, and compare them against standard state-of-the-art adversarial defences. We find improvements ranging from 5% to 72% against attacks with Boltzmann machines on the MNIST dataset. We furthermore complement the training with quantum-enhanced sampling from the D-Wave 2000Q annealer, finding results comparable with classical techniques and with marginal improvements in some cases. These results underline the relevance of probabilistic methods in constructing neural networks and highlight a novel scenario of practical relevance where quantum computers, even with limited hardware capabilites, could provide advantages over classical computers. This work is dedicated to the memory of Peter Wittek.