  Quantum control is an essential tool for the operation of quantum
technologies such as quantum computers, simulators, and sensors. Although there
are sophisticated theoretical tools for developing quantum control protocols,
formulating optimal protocols while incorporating experimental conditions
remains a challenge. In this paper, motivated by recent advances in realization
of real-time feedback control in circuit quantum electrodynamics systems, we
study the effect of experimental imperfections on the optimality of qubit
purification protocols. Specifically, we find that the optimal control
solutions in the presence of detector inefficiency and non-negligible
decoherence can be significantly different from the known solutions to
idealized dynamical models. In addition, we present a simplified form of the
verification theorem to examine the global optimality of a control protocol.
