Abstract

In quantum state transfer and tracking, control of quantum states are effective against decoherence caused by external environment and information processing. In this paper, utilizing model reference adaptive control theory and Lyapunov stability theorem, we derive the adaptive law for the model reference adaptive system. Then we design the Lyapunov control law by double control functions and we investigate the orbit tracking of quantum state for Markovian quantum system. Meanwhile, through counteracting the shift term by simplization, the control law avoids oscillating state trajectory in a two-level Markovian quantum system. Finally, numerical simulations for a two-level open quantum system validate the effectiveness of the method.

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