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We perform a functional expansion of the fidelity between two unitarymatrices in order to find the necessary conditions for the robustimplementation of a target gate. Comparison of these conditions with thoseobtained from the Magnus expansion and Dyson series shows that they areequivalent in first order. By exploiting techniques from robust designoptimization, we account for issues of experimental feasibility by introducingan additional criterion to the search for control pulses. This search isaccomplished by exploring the competition between the multiple objectives inthe implementation of the NOT gate by means of evolutionary multi-objectiveoptimization.

Fidelity Between Unitary Operators and the Generation of Gates Robust Against Off-Resonance Perturbations