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 feedback controller ensuring exponential convergence toward the target state. Moreover, we provide a lower bound of the convergence rate for this case. Then, we discuss the effect of each parameter appearing in the controller in the convergence rate. Finally, we illustrate the efficiency of such feedback controller 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 feedback controller ensuring exponential convergence toward the target state. Moreover, we provide a lower bound of the convergence rate for this case. Then, we discuss the effect of each parameter appearing in the controller in the convergence rate. Finally, we illustrate the efficiency of such feedback controller through simulations.

IEEE Conference on Decision and Control (CDC)Dec 1, 201815 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

On Exponential Stabilization of $N$ -Level Quantum Angular Momentum SystemsOn Exponential Stabilization of $N$-Level Quantum Angular Momentum Systems

Weichao Liang, Nina H. Amini, Paolo Mason

In this paper, we consider the feedback stabilization problem for $N$ -level quantum angular momentum systems undergoing continuous-time measurements. By using stochastic and geometric control tools, we provide sufficient conditions on the feedback control law ensuring almost sure exponential convergence to a predetermined eigenstate of the measurement operator. In order to achieve these results, we establish general features of quantum trajectories which are of interest by themselves. We illustrate the results by designing a class of feedback control laws satisfying the above-mentioned conditions and finally we demonstrate the effectiveness of our methodology through numerical simulations for three-level quantum angular momentum systems.In this paper, we consider the feedback stabilization problem for $N$-level quantum angular momentum systems undergoing continuous-time measurements. By using stochastic and geometric control tools, we provide sufficient conditions on the feedback control law ensuring almost sure exponential convergence to a predetermined eigenstate of the measurement operator. In order to achieve these results, we establish general features of quantum trajectories which are of interest by themselves. We illustrate the results by designing a class of feedback control laws satisfying the above-mentioned conditions and finally we demonstrate the effectiveness of our methodology through numerical simulations for three-level quantum angular momentum systems.

arXiv:1902.05879SIAM Journal on Control and OptimizationJan 1, 201945 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

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

Jie Wen, Fangmin Wang, Yuanhao Shi +2 more

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.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.

Results in PhysicsApr 21, 20220 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.

On Exponential Stabilization of

N

-Level Quantum Angular Momentum Systems

In this paper, we consider the feedback stabilization problem for

N

-level quantum angular momentum systems undergoing continuous-time measurements. By using stochastic and geometric control tools, we provide sufficient conditions on the feedback control law ensuring almost sure exponential convergence to a predetermined eigenstate of the measurement operator. In order to achieve these results, we establish general features of quantum trajectories which are of interest by themselves. We illustrate the results by designing a class of feedback control laws satisfying the above-mentioned conditions and finally we demonstrate the effectiveness of our methodology through numerical simulations for three-level quantum angular momentum systems.