Optimal control of quantum systems under different manipulation conditions

In this paper, we explicitly explore how to manipulate single qubits by one-rotation controls under various manipulation conditions. It is revealed that one can construct control Hamiltonian and adjust the control to manipulate quantum states. Furthermore, we comprehensively discuss how to optimize control magnitude in terms of a new kind of weighted time-energy performance. A comparison has been made among the optimal performances under different manipulation conditions. Three concrete examples indicate the feasibility and efficiency of this approach on optimal control of two-level quantum systems.