# Quantum Interval Bound Propagation for Certified Training of Quantum Neural Networks

arXiv: https://arxiv.org/abs/2605.00747 · HTML: https://mlsanity.com/paper/2605.00747/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Large-Margin Softmax Loss for Convolutional Neural Networks](https://mlsanity.com/paper/1612.02295/) (2016)
- [Training robust neural networks using Lipschitz bounds](https://mlsanity.com/paper/2005.02929/) (2020)
- [Quantum Adversarial Machine Learning](https://mlsanity.com/paper/2001.00030/) (2019)
- [Understanding Certified Training with Interval Bound Propagation](https://mlsanity.com/paper/2306.10426/) (2023)
- [Boosting the Certified Robustness of L-infinity Distance Nets](https://mlsanity.com/paper/2110.06850/) (2021)
- [Training robust and generalizable quantum models](https://mlsanity.com/paper/2311.11871/) (2023)
- [A Comparative Analysis of Adversarial Robustness for Quantum and Classical Machine Learning Models](https://mlsanity.com/paper/2404.16154/) (2024)
- [Formal Verification of Variational Quantum Circuits](https://mlsanity.com/paper/2507.10635/) (2025)

## Abstract (arXiv)

Quantum machine learning is a promising field for efficiently learning features of a dataset to perform a specified task, such as classification. Interval bound propagation (IBP) is a popular certified training method in classical machine learning, where the lower and upper bounds are tracked throughout the model. These bounds are used during training to ensure that the model is certified to predict the correct label even under adversarial perturbations. While IBP is successful in classical domain, there are limited certified training efforts in quantum domain. In this paper, we present quantum interval bound propagation (QIBP) to establish a certified training routine for quantum machine learning, certifying the accuracy of models under adversarial perturbations. We implement QIBP using both interval and affine arithmetic to explore the tradeoffs between the two implementations in terms of accuracy and other design considerations. Extensive evaluation demonstrates that the resulting certified trained models have robust decision boundaries, guaranteed to predict the correct class for the samples within the trained adversarial robustness bounds.