In this paper, we study the stabilization problem of quantum spin-1/2 systems under continuous-time measurements. In the case without feedback, we show exponential stabilization around the excited and ground state by providing a lower bound of the convergence rate. Based on stochastic Lyapunov techniques, we propose a parametrized measurement-based feedback which ensures exponential convergence toward the excited state. Moreover, we give a lower bound of the convergence rate for this case. Then, we discuss the effect of each parameter appeared in the control law in the convergence rate. Finally, we illustrate the efficiency of such feedback law through simulations.In this paper, we study the stabilization problem of quantum spin-1/2 systems under continuous-time measurements. In the case without feedback, we show exponential stabilization around the excited and ground state by providing a lower bound of the convergence rate. Based on stochastic Lyapunov techniques, we propose a parametrized measurement-based feedback which ensures exponential convergence toward the excited state. Moreover, we give a lower bound of the convergence rate for this case. Then, we discuss the effect of each parameter appeared in the control law in the convergence rate. Finally, we illustrate the efficiency of such feedback law through simulations.

arXiv:1803.10632Mar 28, 201812 citations

On exponential stabilization of two-qubit systems

Weichao Liang, Nina H. Amini, Paolo Mason

In this paper, we consider a two-qubit system undergoing continuous-time measurements. In presence of multiple channels, we provide sufficient conditions on the continuous feedback control law ensuring almost sure exponential convergence to a predetermined Bell state. This is obtained by applying stochastic tools, Lyapunov methods and geometric control tools. With one channel, we establish asymptotic convergence towards a predetermined Bell state. In both cases, we provide explicit expressions of feedback control laws satisfying the above-mentioned conditions. Finally, we demonstrate the effectiveness of our methodology through numerical simulations.In this paper, we consider a two-qubit system undergoing continuous-time measurements. In presence of multiple channels, we provide sufficient conditions on the continuous feedback control law ensuring almost sure exponential convergence to a predetermined Bell state. This is obtained by applying stochastic tools, Lyapunov methods and geometric control tools. With one channel, we establish asymptotic convergence towards a predetermined Bell state. In both cases, we provide explicit expressions of feedback control laws satisfying the above-mentioned conditions. Finally, we demonstrate the effectiveness of our methodology through numerical simulations.

arXiv:1903.07470IEEE Conference on Decision and Control (CDC)Dec 1, 20197 citations

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

Jie Wen, Yuanhao Shi, Jianfang Jia +1 more

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.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.

Mar 11, 20210 citations

Exponential stabilization of two-level quantum systems based on continuous noise-assisted feedback

Jie Wen, Yuanhao Shi, Jianfang Jia +1 more

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.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.

Results in PhysicsFeb 21, 202115 citations

Global exponential stabilization of quantum spin-1/2 systems via improved feedback control

Jie Wen, Yuanhao Shi, Xiaoqiong Pang +2 more

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.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.

Mar 10, 20220 citations

Global stabilization of quantum spin systems via discrete time feedback control

Daisuke Matsuna, Koji Tsumura

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.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.

IEEE Conference on Decision and Control (CDC)Dec 1, 20100 citations

On Exponential Stabilization of Spin

-\frac{1}{2}

Systems

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.