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Results in Physics

Exponential stabilization of stochastic quantum systems via combined feedback

Jie Wen, Yuanhao Shi, Jianfang Jia, Jianchao Zeng

Published Oct 13, 2021• 4 citations
Publisher

Abstract

We propose a novel control strategy by combining state feedback with noise-assisted feedback to exponentially stabilize the target eigenstate for two-level stochastic quantum systems in this paper. The state space is divided into two subspaces, and the state feedback and noise-assisted feedback work in the corresponding subspace, respectively, to achieve the faster state convergence than that of using the two feedback controls individually. We prove the exponential stabilization of target eigenstate under the combined feedback, whose the effectiveness and superiority are verified in numerical simulations.

DOI
10.1016/j.rinp.2021.104862

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We propose a novel control strategy by combining state feedback with noise-assisted feedback to exponentially stabilize the target eigenstate for two-level stochastic quantum systems in this paper. The state space is divided into two subspaces, and the state feedback and noise-assisted feedback work in the corresponding subspace, respectively, to achieve the faster state convergence than that of using the two feedback controls individually. We prove the exponential stabilization of target eigenstate under the combined feedback, whose the effectiveness and superiority are verified in numerical simulations.
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We propose a novel control strategy by combining state feedback and noise-assisted feedback to exponentially stabilize the target eigenstate for two-level stochastic quantum systems in this paper. The state space is divided into two subspaces, and the state feedback and noise-assisted feedback work in the corresponding subspace, respectively, to achieve the faster state convergence than that of using the two feedback strategies individually. Two kinds of continuous noise-assisted feedback controls are used to form the combined feedback strategies, respectively, and the exponential stabilization of target eigenstate is proved. The effectiveness and superiority of the combined feedback strategies are also verified in numerical simulations.
We propose a novel control strategy by combining state feedback and noise-assisted feedback to exponentially stabilize the target eigenstate for two-level stochastic quantum systems in this paper. The state space is divided into two subspaces, and the state feedback and noise-assisted feedback work in the corresponding subspace, respectively, to achieve the faster state convergence than that of using the two feedback strategies individually. Two kinds of continuous noise-assisted feedback controls are used to form the combined feedback strategies, respectively, and the exponential stabilization of target eigenstate is proved. The effectiveness and superiority of the combined feedback strategies are also verified in numerical simulations.
In this paper, the global exponential stabilization of two-level stochastic quantum systems is achieved by using measurement-based feedback strategies, including state feedback and noise-assisted feedback, and the state convergence rate is improved by dividing the state space. For both the combination of two continuous noise-assisted feedback and the combination of state feedback and noise-assisted feedback, the state space is divided based on the comparison of real-time state convergence rate under different measurement-based feedback strategies, respectively. The global exponential convergence and the effect of dividing state space in improving state convergence rate for two-level quantum systems are proved in theory and verified in numerical simulations.
The exponential stabilization of the eigenstates for two-level quantum systems based on continuous noise-assisted feedback control is investigated in this paper. Due to the symmetric structure of state space, quantum systems may converge to an undesired eigenstate under continuous measurement. In order to overcome the convergence obstacle, the continuous noise-assisted feedback strategy, in which the control signal is driven by an exogenous Brownian noise, is proposed to make the quantum systems converge to the target eigenstates exponentially, and the noise gain is designed as a continuously differentiable function of quantum state, which is negatively related to the distance between system state and the target eigenstate. In particular, the exponential convergence is proved based on the stability theory of stochastic differential equations. Moreover, the numerical simulations on a two-level quantum system are performed to verify the effectiveness of noise-assisted feedback control and study the influences of physical parameters and control parameters on convergence rate.
In this paper, we propose two state feedback strategies to exponentially stabilize eigenstates for quantum spin-1/2 systems, 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-1/2 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-1/2 systems. The effectiveness and the superiority of the improved feedback control are also verified in numerical simulations.