  Quantum feedback control protocols can improve the operation of quantum
devices. Here we examine the performance of a purification protocol when there
are imperfections in the controls. The ideal feedback protocol produces an $x$
eigenstate from a mixed state in the minimum time, and is known as rapid state
preparation. The imperfections we examine include time delays in the feedback
loop, finite strength feedback, calibration errors, and inefficient detection.
We analyse these imperfections using the Wiseman-Milburn feedback master
equation and related formalism. We find that the protocol is most sensitive to
time delays in the feedback loop. For systems with slow dynamics, however, our
analysis suggests that inefficient detection would be the bigger problem. We
also show how system imperfections, such as dephasing and damping, can be
included in model via the feedback master equation.
