Local Stabilization of Quantum Spin Systems with Discrete Feedback Control

Abstract

A stabilization problem for a quantum system is discussed. The states of the system have been described with 1/2 spin variables, and in discrete time domain. Firstly, we introduce the stochastic equation that the system obeys and then, derive an approximated equation for that stochastic dynamics. Secondly, some local stabilities for the approximated and non-approximated target spin systems are analyzed using stochastic Lyapunov function. In the last, we demonstrate those stabilities with numerical simulations.