Orbit tracking of quantum state in open quantum systems based on Lyapunov control method

In quantum state transfer and tracking, control of quantum states are effective against decoherence caused by external environment and information processing. In this paper, based on model reference adaptive control theory, the orbit tracking based on Lyapunov approach in Liouville equation for open quantum systems is investigated under various dissipative modes. Meanwhile, through counteracting the shift term by simplification, 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.