Arbitrary State Transition of Open Qubit System Based on Switching Control

Abstract: We present a switching control strategy based on Lyapunov control for arbitrary state transitions in open qubit systems. With coherent vector representation, we propose a switching control strategy, which can prevent the state of the qubit from entering invariant sets and singular value sets, effectively driving the system ultimately to a sufficiently small neighborhood of target states. In comparison to existing works, this control strategy relaxes the strict constraints on system models imposed by special target states. Furthermore, we identify conditions under which the open qubit system achieves finite-time stability (FTS) and finite-time contractive stability (FTCS), respectively. This represents a critical improvement in quantum state transitions, especially considering the asymptotic stability of arbitrary target states is unattainable in open quantum systems. The effectiveness of our proposed method is convincingly demonstrated through its application in a qubit system affected by various types of decoherence, including amplitude, dephasing and polarization decoherence.