Designing Robust Quantum Neural Networks via Optimized Circuit Metrics

In this study, the robustness of Quanvolutional Neural Networks (QuNNs) is investigated in comparison to their classical counterparts, Convolutional Neural Networks (CNNs), against two adversarial attacks: the Fast Gradient Sign Method (FGSM) and the Projected Gradient Descent (PGD), for the image classification task on both the Modified National Institute of Standards and Technology (MNIST) and Fashion-MNIST (FMNIST) datasets. To enhance the robustness of QuNNs, a novel methodology is developed that utilizes three quantum circuit metrics: expressibility, entanglement capability, and controlled rotation gate selection. This analysis shows that these metrics significantly influence data representation within the Hilbert space, thereby directly affecting QuNN robustness. It is rigorously established that circuits with higher expressibility and lower entanglement capability generally exhibit enhanced robustness under adversarial conditions, particularly at low-spectrum perturbation strengths where most attacks occur. Furthermore, these findings challenge the prevailing assumption that expressibility alone dictates circuit robustness; instead, it is demonstrated that the inclusion of controlled rotation gates around the Z-axis generally enhances the resilience of QuNNs. These results demonstrate that QuNNs exhibit up to 60% greater robustness on the MNIST dataset and 40% on the Fashion-MNIST dataset compared to CNNs. Collectively, this work elucidates the relationship between quantum circuit metrics and robust data feature extraction, advancing the field by improving the adversarial robustness of QuNNs.