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We consider the use of feedback control during a measurement to increase therate at which a single qubit is purified, and more generally the rate at whichnear-pure states may be prepared. We derive the optimal bang-bang algorithm forrapid state preparation from an initially completely mixed state when themeasurement basis is unrestricted, and evaluate its performance numerically. Wealso consider briefly the case in which the measurement basis is fixed withrespect to the state to be prepared, and describe the qualitative structure ofthe optimal bang-bang algorithm.Comment: 8 pages, revtex4, 3 eps figure

Optimal feedback control for rapid preparation of a qubit