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In this study, in order to generate a sequence of desired quantum states (or quantum bits) for quantum commu- nication and computation, it is more appealing to formulate a quantum control system as a bilinear state reference tracking system. An optimal tracking control is proposed to achieve the state-tracking by solving a 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 with the HJE to obtain the optimal tracking control in quantum systems from the ap- proximate design perspective. If the quantum system suffers from stochastic parameter variations, it could be modeled as state-dependent noise. In the situation, stochastic optimal tracking control design is also developed for quantum systems. Finally, several examples are given to illustrate the design procedure and to confirm the performance of the proposed tracking control method.

Optimal Tracking Control Design of Quantum Systems via Tensor Formal Power Series Method