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Quantum control is an essential tool for the operation of quantumtechnologies such as quantum computers, simulators, and sensors. Although thereare sophisticated theoretical tools for developing quantum control protocols,formulating optimal protocols while incorporating experimental conditionsremains a challenge. In this paper, motivated by recent advances in realizationof real-time feedback control in circuit quantum electrodynamics systems, westudy the effect of experimental imperfections on the optimality of qubitpurification protocols. Specifically, we find that the optimal controlsolutions in the presence of detector inefficiency and non-negligibledecoherence can be significantly different from the known solutions toidealized dynamical models. In addition, we present a simplified form of theverification theorem to examine the global optimality of a control protocol.

Optimality of qubit purification protocols in the presence of imperfections