  In this paper, we propose feedback designs for manipulating a quantum state
to a target state by performing sequential measurements. In light of Belavkin's
quantum feedback control theory, for a given set of (projective or
non-projective) measurements and a given time horizon, we show that finding the
measurement selection policy that maximizes the probability of successful state
manipulation is an optimal control problem for a controlled Markovian process.
The optimal policy is Markovian and can be solved by dynamical programming.
Numerical examples indicate that making use of feedback information
significantly improves the success probability compared to classical scheme
without taking feedback. We also consider other objective functionals including
maximizing the expected fidelity to the target state as well as minimizing the
expected arrival time. The connections and differences among these objectives
are also discussed.
