Global stabilization of quantum spin systems via discrete time feedback control

In this paper, a stabilization problem for a quantum 1/2 spin system is discussed. The system is assumed to be observed and controlled with a sampled data system. We introduce a discrete time stochastic model of the dynamics and propose a switching feedback controller. We show that the controller attains global stabilization at the target states under a condition on a sampling time by using a stochastic Lyapunov function for the discrete time systems. Finally, we demonstrate numerical simulations to show the effectiveness of our proposing controller.