Quantum Interval Bound Propagation for Certified Training of Quantum Neural Networks

TL;DR

This paper introduces Quantum Interval Bound Propagation (QIBP), a method for certified training of quantum neural networks that guarantees robustness against adversarial perturbations.

Contribution

It adapts classical IBP to quantum models, enabling certified robustness in quantum machine learning for the first time.

Findings

QIBP achieves robust decision boundaries in quantum models.

Interval and affine arithmetic implementations trade off accuracy and computational considerations.

Certified models predict correctly within adversarial bounds.

Abstract

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.