VeriQR: A Robustness Verification Tool for quantum Machine Learning Models

Abstract Adversarial noise attacks present a significant threat to quantum machine learning (QML) models, similar to their classical counterparts. This is especially true in the current Noisy Intermediate-Scale Quantum era, where noise is unavoidable. Therefore, it is essential to ensure the robustness of QML models before their deployment. To address this challenge, we introduce VeriQR, the first tool designed specifically for formally verifying and improving the robustness of QML models, to the best of our knowledge. This tool mimics real-world quantum hardware’s noisy impacts by incorporating random noise to formally validate a QML model’s robustness. VeriQR supports exact (sound and complete) algorithms for both local and global robustness verification. For enhanced efficiency, it implements an under-approximate (complete) algorithm and a tensor network-based algorithm to verify local and global robustness, respectively. As a formal verification tool, VeriQR can detect adversarial examples and utilize them for further analysis and to enhance the local robustness through adversarial training, as demonstrated by experiments on real-world quantum machine learning models. Moreover, it permits users to incorporate customized noise. Based on this feature, we assess VeriQR using various real-world examples, and experimental outcomes confirm that the addition of specific quantum noise can enhance the global robustness of QML models. These processes are made accessible through a user-friendly graphical interface provided by VeriQR, catering to general users without requiring a deep understanding of the counter-intuitive probabilistic nature of quantum computing.