Global exponential stabilization of quantum spin-[formula omitted] systems via improved feedback control

Abstract

In this paper, we propose two state feedback strategies to exponentially stabilize eigenstates for quantum spin-12 systems based on the state feedback designed in Liang et al. (2018)[1] and Wen et al. (2022)[2], respectively. In order to obtain faster state convergence, we improve the state feedback by increasing the real-time state convergence rate, and prove the exponential convergence. On this basis, we present the way of achieving global exponential stabilization of quantum spin-12 systems under the improved state feedback with the help of noise-assisted feedback. Besides, we redesign the division of state space to improve the state convergence rate further, and compare the state convergence rates of all state feedback strategies that can exponentially stabilize eigenstates for quantum spin-12 systems. The effectiveness and the superiority of the improved feedback control are also verified in numerical simulations.