Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics B

Rapid stabilization of stochastic quantum systems in a unified framework

Jie Wen, Fangmin Wang, Yuanhao Shi, Jianfang Jia, Jianchao Zeng

Published Feb 8, 2023• 0 citations
Publisher

Abstract

Rapid stabilization of general stochastic quantum systems is investigated based on the rapid stability of stochastic differential equations. We introduce a Lyapunov–LaSalle-like theorem for a class of nonlinear stochastic systems first, based on which a unified framework of rapidly stabilizing stochastic quantum systems is proposed. According to the proposed unified framework, we design the switching state feedback controls to achieve the rapid stabilization of single-qubit systems, two-qubit systems, and N-qubit systems. From the unified framework, the state space is divided into two state subspaces, and the target state is located in one state subspace, while the other system equilibria are located in the other state subspace. Under the designed state feedback controls, the system state can only transit through the boundary between the two state subspaces no more than two times, and the target state is globally asymptotically stable in probability. In particular, the system state can converge exponentially in (all or part of) the state subspace where the target state is located. Moreover, the effectiveness and rapidity of the designed state feedback controls are shown in numerical simulations by stabilizing GHZ states for a three-qubit system.

DOI
10.1088/1674-1056/acb9f3

Related papers

Rapid Feedback Stabilization of Quantum Systems With Application to Preparation of Multiqubit Entangled States

Sen Kuang, Gan Li, Yanan Liu +2 more

For stochastic quantum systems with measurement feedback, this article proposes a rapid switching control scheme based on state space partition and realizes the rapid stabilization of an eigenstate of an observable operator. Meanwhile, we apply the proposed scheme to the preparation of typical entangled states in multiqubit systems. In view of the convergence obstacle caused by the symmetric structure of the state space, especially in the case with degenerate observable operators, we first partition the state space into a subset containing the target state and its complement to distinguish the target state from its antipodal points, and then design the corresponding control laws in these two subsets, respectively, by using different Lyapunov functions. The interaction Hamiltonians are also constructed to drive the system state to the desired subset first, and further to the target state. In particular, the control law designed in the undesired subset guarantees the strictly monotonic descent of the corresponding Lyapunov function, which makes the system trajectory switch between the two subsets at most twice and has the potential to speed up the convergence process. We also prove the stability of the closed-loop system with the proposed switching control law based on the stochastic Lyapunov stability theory. By applying the proposed switching control scheme to a three-qubit system, we achieve the preparation of a GHZ state and a W state.

IEEE Transactions on Cybernetics•Aug 3, 2021•18 citations

Exponential stabilization of stochastic quantum systems via combined feedback

Jie Wen, Yuanhao Shi, Jianfang Jia +1 more

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.

Results in Physics•Oct 13, 2021•4 citations

Rapid control of two-qubit systems based on measurement feedback

Xiaqing Sun, Sen Kuang, Daoyi Dong

For two-qubit systems with a degenerate measurement operator, this paper presents a control approach to achieve rapid stabilization to a target Bell state. This approach uses two control channels where the control laws associated with these two channels are designed as a constant and a switching control law, respectively. In the control scheme, the system state space is divided into two parts: the set containing the target state, and its complementary set. We design corresponding control laws in these two sets via different Lyapunov functions. In this scheme, the system trajectory switches only one or two times between the two sets and the convergence rate to the target state can be improved. We provide the conditions on the control Hamiltonians to stabilize the target state by analyzing the stability of the closed-loop system.

Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics•Oct 1, 2017•2 citations

Control of Stochastic Quantum Systems with Decomposable Target State

Lei Zhou, Shuang Cong

We propose a Lyapunov-based control method for stochastic quantum systems. The method can make the quantum state converge to a separable mixed target state from an arbitrary initial state. Specifically, the target state can be written as the tensor product of two matrices. Based on a well designed virtual mechanical quantity, a Lyapunov function and two control laws are presented: one can make the system equilibria in the largest invariant set stable according to LaSalle's invariance principle, and the other one can make the target state globally asymptotically stable.

IEEE Information Technology, Networking, Electronic and Automation Control Conference (ITNEC)•May 5, 2020•0 citations

Global stabilization of an eigenstate for stochastic quantum systems

Shuang Cong, Jie Wen, Sen Kuang +1 more

The global stabilization of an eigenstate for finite dimensional stochastic quantum systems with non-diagonal free Hamiltonian and non-regular measurement operator is studied in this paper. A two-part switching control strategy is proposed, in which a constant control is used to steer the system state to enter the convergence domain; another control law, which is designed based on Lyapunov stability theorem is used to attract the system state in convergence domain to the target state. The convergence of the target eigenstate from an arbitrary initial state is strictly proved. Moreover, the numerical experiments on a three dimensional stochastic quantum system are implemented to demonstrate the effectiveness of the control proposed.

International Conference on Control and Automation•Jun 1, 2016•3 citations

Global Stabilization of Mixed-states for Stochastic Quantum Systems via Switching Control

Shuang Cong, Jie Wen, Fangfang Meng +1 more

The global stabilization of mixed states for finite dimensional stochastic quantum systems with non-regular measurement operator and non-diagonal free Hamiltonian is investigated in this paper. A two-part switching control strategy is proposed, in which the constant control is used to steer the system state to enter the convergence domain, while the control law which is designed based on Lyapunov stability theorem is used to attract the system state in convergence domain to the target state. The convergence of the switching control is strictly proved. Moreover, the numerical experiments on a three dimensional stochastic quantum system are implemented to demonstrate the effectiveness of the control proposed.

IFAC-PapersOnLine•Jul 1, 2017•0 citations
Rapid stabilization of general stochastic quantum systems is investigated based on the rapid stability of stochastic differential equations. We introduce a Lyapunov–LaSalle-like theorem for a class of nonlinear stochastic systems first, based on which a unified framework of rapidly stabilizing stochastic quantum systems is proposed. According to the proposed unified framework, we design the switching state feedback controls to achieve the rapid stabilization of single-qubit systems, two-qubit systems, and N-qubit systems. From the unified framework, the state space is divided into two state subspaces, and the target state is located in one state subspace, while the other system equilibria are located in the other state subspace. Under the designed state feedback controls, the system state can only transit through the boundary between the two state subspaces no more than two times, and the target state is globally asymptotically stable in probability. In particular, the system state can converge exponentially in (all or part of) the state subspace where the target state is located. Moreover, the effectiveness and rapidity of the designed state feedback controls are shown in numerical simulations by stabilizing GHZ states for a three-qubit system.
For stochastic quantum systems with measurement feedback, this article proposes a rapid switching control scheme based on state space partition and realizes the rapid stabilization of an eigenstate of an observable operator. Meanwhile, we apply the proposed scheme to the preparation of typical entangled states in multiqubit systems. In view of the convergence obstacle caused by the symmetric structure of the state space, especially in the case with degenerate observable operators, we first partition the state space into a subset containing the target state and its complement to distinguish the target state from its antipodal points, and then design the corresponding control laws in these two subsets, respectively, by using different Lyapunov functions. The interaction Hamiltonians are also constructed to drive the system state to the desired subset first, and further to the target state. In particular, the control law designed in the undesired subset guarantees the strictly monotonic descent of the corresponding Lyapunov function, which makes the system trajectory switch between the two subsets at most twice and has the potential to speed up the convergence process. We also prove the stability of the closed-loop system with the proposed switching control law based on the stochastic Lyapunov stability theory. By applying the proposed switching control scheme to a three-qubit system, we achieve the preparation of a GHZ state and a W state.
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.
For two-qubit systems with a degenerate measurement operator, this paper presents a control approach to achieve rapid stabilization to a target Bell state. This approach uses two control channels where the control laws associated with these two channels are designed as a constant and a switching control law, respectively. In the control scheme, the system state space is divided into two parts: the set containing the target state, and its complementary set. We design corresponding control laws in these two sets via different Lyapunov functions. In this scheme, the system trajectory switches only one or two times between the two sets and the convergence rate to the target state can be improved. We provide the conditions on the control Hamiltonians to stabilize the target state by analyzing the stability of the closed-loop system.
We propose a Lyapunov-based control method for stochastic quantum systems. The method can make the quantum state converge to a separable mixed target state from an arbitrary initial state. Specifically, the target state can be written as the tensor product of two matrices. Based on a well designed virtual mechanical quantity, a Lyapunov function and two control laws are presented: one can make the system equilibria in the largest invariant set stable according to LaSalle's invariance principle, and the other one can make the target state globally asymptotically stable.
The global stabilization of an eigenstate for finite dimensional stochastic quantum systems with non-diagonal free Hamiltonian and non-regular measurement operator is studied in this paper. A two-part switching control strategy is proposed, in which a constant control is used to steer the system state to enter the convergence domain; another control law, which is designed based on Lyapunov stability theorem is used to attract the system state in convergence domain to the target state. The convergence of the target eigenstate from an arbitrary initial state is strictly proved. Moreover, the numerical experiments on a three dimensional stochastic quantum system are implemented to demonstrate the effectiveness of the control proposed.
The global stabilization of mixed states for finite dimensional stochastic quantum systems with non-regular measurement operator and non-diagonal free Hamiltonian is investigated in this paper. A two-part switching control strategy is proposed, in which the constant control is used to steer the system state to enter the convergence domain, while the control law which is designed based on Lyapunov stability theorem is used to attract the system state in convergence domain to the target state. The convergence of the switching control is strictly proved. Moreover, the numerical experiments on a three dimensional stochastic quantum system are implemented to demonstrate the effectiveness of the control proposed.