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We investigat the trajectory tracking problem of quantum systems governed by Liouville equation. With the help of Lyapunov function and LaSlle invariance principle, impulsive control fields are given, which drive the quantum state to a time-variant target state. A numerical simulation experiment on a two-level quantum system shows the rationality of the obtained theoretical results, and the advantage compared to traditional control method.

Trajectory tracking for quantum systems based on Lyapunov control method