Robust Quantum Control for Set-Membership Hamiltonian Uncertainty

We provide a brief review of a recently proposed approach to robust quantum control which rests on three theoretical foundations: the classic method of averaging, set-membership uncertainty modeling, and the known topological properties of the quantum control landscape. Application of the method of averaging directly results in a multi-criterion optimization problem consisting of the uncertainty-free fidelity competing with a generic robustness measure, the latter being a norm of a time-domain product of a function of the uncertainty-free system and the character of the uncertainty set. If this term is sufficiently small, then at most, only fourth order error effects can accrue. Lastly, the topological features promote a two-stage algorithm: in stage-1 the uncertainty-free fidelity is set to a high threshold, then in stage-2 the robustness measure is minimized while maintaing the threshold. Each stage-2 control update is found by solving a convex optimization problem.