Learning to control quantum systems robustly

Quantum control provides methods to steer the dynamics of quantum systems. The robustness of such controls, in addition to high fidelity, is important for practical applications due to the presence of uncertainties arising from limited knowledge about system and control Hamiltonians, initial state preparation errors, and interactions with the environment leading to decoherence. We introduce a novel robustness measure based on the Wasserstein distance, and discuss structured singular value analysis and log-sensitivity approaches from classical robust control. This is employed to analyse the robustness of controllers found by reinforcement learning and gradient-based optimisation algorithms. Some, not all, high-fidelity controllers are also robust and controllers found by reinforcement learning appear less affected by noise than those found by gradient-based optimisation. We briefly discuss applications in information transfer in spin networks and magnetic resonance spectroscopy