Statistically characterizing robustness and fidelity of quantum controls and quantum control algorithms

Robustness of quantum operations or controls is important to build reliable devices. The robustness-infidelity measure (${\text{RIM}}_{p}$) introduced statistically quantify in a single the robustness and fidelity controller as $p\mathrm{th}$ order Wasserstein distance between distribution under any uncertainty an ideal distribution. ${\text{RIM}}_{p}$ root raw moment infidelity Using metrization argument, we justify why ${\text{RIM}}_{1}$ (the average infidelity) good practical measure. Based on ${\text{RIM}}_{p}$, algorithmic (ARIM) developed expected controllers found by control algorithm. utility RIM ARIM demonstrated energy landscape spin-$\frac{1}{2}$ networks subject Hamiltonian uncertainty. individual well different popular algorithms are characterized. For algorithm comparisons, stochastic nonstochastic optimization objectives considered. Although high often conflicting objectives, some high-fidelity, robust can usually be found, irrespective choice However, for noisy adaptive sequential decision-making approaches, such reinforcement learning, have cost advantage compared standard and, contrast, infidelities obtained more consistent with values low noise levels.