Fidelity between unitary operators and the generation of robust gates against off-resonance perturbations

We perform a functional expansion of the fidelity between two unitary matrices in order to find necessary conditions for the robust implementation of a target gate. Comparison of these conditions with those obtained from the the Magnus expansion and Dyson series shows that they are equivalent in the first order. By exploiting techniques from robust design optimization, we account for issues of experimental feasibility by introducing an additional criterion to the search for control pulses. This search is accomplished by exploring the competition between the multiple objectives in the implementation of the NOT gate by means of evolutionary multi-objective optimization.