Core Concepts
A switching control strategy based on Lyapunov control is proposed to enable arbitrary state transitions in open qubit systems, preventing the system state from entering invariant sets and singular value sets, and achieving finite-time stability and finite-time contractive stability.
Abstract
The paper presents a switching control strategy based on Lyapunov control for arbitrary state transitions in open qubit systems. The key highlights are:
The authors propose a switching control strategy that 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. This is in contrast to existing works that require the target states to be eigenstates of the system Hamiltonian or observables.
The authors 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 the proposed method is demonstrated through its application in a qubit system affected by various types of decoherence, including amplitude, dephasing and polarization decoherence. The simulation results show that the switching control strategy can effectively drive the system state to a small neighborhood of the arbitrary target state.
An improved switching control strategy with shrink thresholds is proposed to further enhance the convergence performance. The shrink thresholds allow the control strategy to adapt to the evolving system state, prolonging the duration of the switching control and achieving better control performance.