Abstract
In this study, in order to specify quantum state to any desired state we need for the use of communication and computation, the quantum control system is formulated as a bilinear state space tracking system. An optimal tracking control is proposed to achieve state-tracking by solving the Hamilton-Jacobi equation (HJE). In order to avoid the difficulty in solving the HJE with a closed-form solution, the technique of formal tensor power series is employed to treat the partial differential equation HJE to obtain the optimal tracking control in quantum systems from the approximate perspective. If the quantum system suffers from stochastic parameter variations, it could be modeled as state-dependent noise. In this situation, stochastic optimal tracking control design is also developed for quantum systems. Finally, several examples are given to illustrate the design procedure and proposed method.