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Feedback control of quantum systems via continuous measurement involvescomplex nonlinear dynamics. Except in very special cases, even for a singlequbit optimal feedback protocols are unknown. Not even do intuitive candidatesexist for choosing the measurement basis, which is the primary non-trivialingredient in the feedback control of a qubit. Here we present a series ofarguments that suggest a particular form for the optimal protocol for a broadclass of noise sources in the regime of good control. This regime is defined asthat in which the control is strong enough to keep the system close to thedesired state. With the assumption of this form the remaining parameters can bedetermined via a numerical search. The result is a non-trivial feedbackprotocol valid for all feedback strengths in the regime of good control. Weconjecture that this protocol is optimal to leading order in the smallparameters that define this regime. The protocol can be described relativelysimply, and as a notable feature contains a discontinuity as a function of thefeedback strength.

Optimal measurement-based feedback control for a single qubit: a candidate protocol