Near-optimal measurement-based feedback control for a single qubit

Feedback control of quantum systems via continuous measurements involves complex nonlinear dynamics. As a result, even for a single qubit the optimal measurement for feedback control is known only in very special cases. We show here that for a broad class of noise processes, a series of compelling arguments can be applied to greatly simplify the problem of steady-state preparation of the ground-state, while loosing little in the way of optimality. Using numerical optimization to solve this simplified control problem, we obtain for the first time a non-trivial feedback protocol valid for all feedback strengths in the regime of good control. The protocol can be described relatively simply, and contains a discontinuity as a function of feedback strength.