Quantum Sharpness-Aware Minimization

Quantum neural networks (QNNs) deployed on noisy intermediate-scale quantum (NISQ) devices often suffer from severe performance degradation due to intrinsic hardware noise. By spotlighting this challenge from a deep neural network (DNN) perspective, we raise an intriguing question: *Can we incorporate a concept of flat minima in DNNs into QNNs for quantum noise robustness?* As our answer, we propose quantum sharpness-aware minimization (Q-SAM), which integrates the flat minima concept into the Riemannian quantum parameter space to seek minima that remain *flat* or invariant under quantum state perturbations induced by hardware noise. We formally connect a bounded perturbation in the quantum state manifold to a bound in the Riemannian quantum parameter space, providing theoretical ground for Q-SAM's state noise robustness. Across image classification tasks, including MNIST-10, Fashion-MNIST, and CIFAR-10, Q-SAM with 4-, 6-, and 8-qubit QNNs consistently exhibit superior robustness against diverse noise channels compared to baselines, also validated on real IBM quantum hardware.