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All quantum systems are subject to noise from the environment or external controls. This noise is a major obstacle to the realization of quantum technology. For example, noise limits the fidelity of quantum gates. Employing optimal control theory, we study the generation of quantum single and two-qubit gates. Specifically, we explore a Markovian model of phase and amplitude noise, leading to the degradation of the gate fidelity. We show that optimal control with such noise models generates control solutions to mitigate the loss of gate fidelity. The problem is formulated in Liouville space employing an extremely accurate numerical solver and the Krotov algorithm for solving the optimal control equations.
Aroch et al. (Wed,) studied this question.