# Robustness Verification of Quantum Classifiers

arXiv: https://arxiv.org/abs/2008.07230 · HTML: https://mlsanity.com/paper/2008.07230/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2020.

## Built on by (most cited first, 18 of 18)

- [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)
- [Training robust and generalizable quantum models](https://mlsanity.com/paper/2311.11871/) (2023)
- [Enhancing Quantum Adversarial Robustness by Randomized Encodings](https://mlsanity.com/paper/2212.02531/) (2022)
- [Verifying Fairness in Quantum Machine Learning](https://mlsanity.com/paper/2207.11173/) (2022)
- [Detecting Violations of Differential Privacy for Quantum Algorithms](https://mlsanity.com/paper/2309.04819/) (2023)
- [Adversarial Robustness of Partitioned Quantum Classifiers](https://mlsanity.com/paper/2502.20403/) (2025)
- [Universal adversarial perturbations for multiple classification tasks with quantum classifiers](https://mlsanity.com/paper/2306.11974/) (2023)
- [A Quantum Convolutional Neural Network Approach for Object Detection and Classification](https://mlsanity.com/paper/2307.08204/) (2023)
- [Quadratic Advantage with Quantum Randomized Smoothing Applied to Time-Series Analysis](https://mlsanity.com/paper/2407.18021/) (2024)
- [On the Generalization of Adversarially Trained Quantum Classifiers](https://mlsanity.com/paper/2504.17690/) (2025)
- [Experimental robustness benchmarking of quantum neural networks on a superconducting quantum processor](https://mlsanity.com/paper/2505.16714/) (2025)
- [Entangled Threats: A Unified Kill Chain Model for Quantum Machine Learning Security](https://mlsanity.com/paper/2507.08623/) (2025)
- [Detecting underdetermination in parameterized quantum circuits](https://mlsanity.com/paper/2504.03315/) (2025)
- [The interplay of robustness and generalization in quantum machine learning](https://mlsanity.com/paper/2506.08455/) (2025)
- [Formal Verification of Noisy Quantum Reinforcement Learning Policies](https://mlsanity.com/paper/2512.01502/) (2025)
- [Quantifying Quanvolutional Neural Networks Robustness for Speech in Healthcare Applications](https://mlsanity.com/paper/2601.02432/) (2026)
- [QShield: Securing Neural Networks Against Adversarial Attacks using Quantum Circuits](https://mlsanity.com/paper/2604.10933/) (2026)

## Abstract (arXiv)

Several important models of machine learning algorithms have been successfully generalized to the quantum world, with potential speedup to training classical classifiers and applications to data analytics in quantum physics that can be implemented on the near future quantum computers. However, quantum noise is a major obstacle to the practical implementation of quantum machine learning. In this work, we define a formal framework for the robustness verification and analysis of quantum machine learning algorithms against noises. A robust bound is derived and an algorithm is developed to check whether or not a quantum machine learning algorithm is robust with respect to quantum training data. In particular, this algorithm can find adversarial examples during checking. Our approach is implemented on Google's TensorFlow Quantum and can verify the robustness of quantum machine learning algorithms with respect to a small disturbance of noises, derived from the surrounding environment. The effectiveness of our robust bound and algorithm is confirmed by the experimental results, including quantum bits classification as the "Hello World" example, quantum phase recognition and cluster excitation detection from real world intractable physical problems, and the classification of MNIST from the classical world.