Arbitrary state transition of open qubit system based on switching control

We present a switching control strategy based on Lyapunov control for arbitrary state transitions in open qubit systems. This strategy can prevent the state from entering invariant or singularity sets, effectively driving the system ultimately to a sufficiently small neighborhood of target states, which relaxes strict constraints on system models imposed by special target states compared to existing works. For the arbitrary transition, practical finite-time stability (PFTS) and its contractive version (PFTCS) conditions are given, respectively, where asymptotic stability is unattainable in open quantum systems in general. The efficacy of our method is demonstrated in examples of a qubit affected by amplitude damping, dephasing, and depolarizing decoherence.