Abstract
The problem of quantum state control in open quantum systems based on the Lyapunov method is studied. The control laws are designed to drive the system to a pure target state in decoherence-free subspace (DFS) in the interaction picture, where the average of an observable operator P is chosen as a Lyapunov function. By analyzing the positive limit set via Barbalat's lemma, we propose a sufficient condition on the observable operator such that the positive limit set only contains the target state. Under this condition, it is proved that the control laws can drive the open system to any pure target state in DFS in the interaction picture. Also, we provide a method to construct the observable operator via Schmidt orthogonalization. Numerical simulations on a three-level system validate the effectiveness of the proposed control strategy.
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