Feedback design for quantum state manipulation by measurements

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 successful 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.