On the Cost of Training Adversarially-Robust Quantum Models

Explore the computational cost analysis of training parametrized quantum circuits (PQCs) in variational quantum algorithms through this 20-minute conference presentation from QTML 2025. Examine how the number of circuit evaluations directly impacts both monetary and temporal training expenses, with particular focus on achieving epsilon-stationary solutions of objective functions. Learn about tightened bounds on Lipschitz-smoothness constants that generalize beyond expectation values to arbitrary loss functions. Discover how gradient-free algorithms, specifically the adapted Stochastic Three Points method, can reduce circuit evaluations by a factor of d compared to stochastic gradient descent, achieving a sesquilinear cost reduction from O(d^3.5) to O(d^2) for circuits with d optimizable parameters. Investigate the inherent adversarial robustness properties of quantum models, where adversarial loss remains bounded by scalar multiples of non-adversarial loss, potentially eliminating expensive overheads associated with input-gradient estimation and adversarial example augmentation in traditional adversarial training approaches.