  We consider the use of feedback control during a measurement to increase the
rate at which a single qubit is purified, and more generally the rate at which
near-pure states may be prepared. We derive the optimal bang-bang algorithm for
rapid state preparation from an initially completely mixed state when the
measurement basis is unrestricted, and evaluate its performance numerically. We
also consider briefly the case in which the measurement basis is fixed with
respect to the state to be prepared, and describe the qualitative structure of
the optimal bang-bang algorithm.
