Exponential stabilization of spin-1/2 systems based on switching state feedback

Abstract

The exponential stabilization of eigenstates by using switching state feedback strategy for quantum spin-$\frac{1}{2}$ systems is considered in this paper. In order to obtain faster state exponential convergence, we divide the state space into two subspaces, and use two different continuous state feedback controls in the corresponding subspace. The two continuous state feedback controls form the switching state feedback, under which the state convergence is faster than that under continuous state feedback. The exponential convergence and the superiority of switching state feedback are proved in theory and verified in numerical simulations. Besides, the influence of the control parameter on the state convergence rate is also studied.

Global exponential stabilization of quantum spin-12 systems via improved feedback control

“…According to the continuous state feedback proposed in [1], we designed switching state feedback to obtain faster exponential convergence of eigenstates for quantum spin- 1 2 systems in [2]. In this paper, we propose two state feedback strategies, which are denoted as improved state feedback, to further improve the state convergence rate and achieve the exponential stabilization of the target eigenstate for quantum spin- 1 2 systems based on the state feedback in [1] and [2], respectively. The main idea of designing improved state feedback is to increase the real-time state convergence rate.…”

“…The main idea of designing improved state feedback is to increase the real-time state convergence rate. Specifically, we design new switching state feedback by modifying the state feedback in [1] and [2], respectively. Based on the designed switching state feedback, we divide the state space into two subspaces and use different state feedback in the corresponding subspace to obtain a larger real-time state convergence rate.…”

“…To our knowledge, the improved state feedback proposed in this paper are the state feedback that achieves the fastest exponential stabilization of eigenstates for quantum spin- 1 2 systems. Moreover, the state feedback in [1] and [2] as well as the improved state feedback in this paper can only exponentially stabilize eigenstates in a state subspace, so we have the aid of noise-assisted feedback, which were proposed in [26], to achieve the global exponential stabilization. The rest of this paper is organized as follows.…”

“…Section 2 presents the model of quantum spin-1 2 systems and the exponential stabilization of eigenstates. In Section 3, we give the methods of improving the state feedback strategies in [1] and [2], prove the exponential convergence and compare the state convergence rates under different state feedback. The way of achieving global exponential stabilization with the help of noiseassisted feedback is presented in Section 4.…”

Feedback exponential stabilization of stochastic quantum systems based on state space division

“…Different from state feedback, Cardona et al proposed the switching noise-assisted feedback, whose noise gain function is saturating function, to achieve the exponential stabilization of N -level quantum systems in [26], from which we proposed two continuous noise-assisted feedback strategies for the same goal in [27], where the noise gain functions are constructed as continuous functions in linear form and exponential form, respectively. Moreover, we designed switching state feedback from [20] to obtain faster exponential convergence for quantum spin- 1 2 systems in [28].…”