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

Journal of Physics Conference Series

Control Design for State transition of Open Quantum System

Fangfang Meng, Shuang Cong

Published Jan 1, 2022• 1 citation
Publisher

Abstract

Abstract State transition control of open quantum systems is a research hotspot and difficulty. The control method in the light of the Lyapunov stability theory is a common method. Current research shows that if the open quantum systems meet the constraints that the free Hamiltonian is strong regular and the interaction Hamiltonian is fully connected, by devising appropriate control fields in the light of the Lyapunov stability theory, the open quantum system can move to the desired final state. In view of the fact that most practical open quantum systems do not meet these two constraints, this paper propose a control method. The implicit function perturbation terms are introduced into the control fields to resolve the problem that the open quantum systems do not meet these two convergence constraints. And the main control fields are devised in the light of the Lyapunov stability theory to make the state transition of the open quantum systems converging to the desired final state.

DOI
10.1088/1742-6596/2183/1/012005

Related papers

Quantum Lyapunov-based unified control method and verification of simulation experiments

Xiang Zhang, Shuang Cong, Zhou Lei

A Lyapunov-based unified control method for closed quantum systems is proposed, which can transfer the state of closed quantum system from any initial state to any desired target state. In particular, the proposed control method can work under the conditions that free Hamiltonian of the non-ideal quantum system is not strongly regular, and (or) the Hamiltonian is not fully connected. The simulation experiments of the state transition control between different states of three, four and five qubit systems are carried out to verify that the proposed control method is suitable for all kinds of non-ideal quantum systems and the advantages of Lyapunov-based unified control method. The design process of the proposed method, the calculation process of each parameter in each experiment and the analysis of each experimental result are given in detail.

Chinese Control and Decision Conference (CCDC)•Aug 1, 2020•0 citations

Convergent control strategy of state in open quantum systems

Shuang Cong, Fei Yang

A control strategy of quantum states of open quantum system based on Lyapunov method is proposed. On the basis of choosing the average of observable operators as a Lyapunov function, the control laws are designed in interaction picture. We analyze the largest invariant set of the controlled system via Barbalat's Lemma. Based on some assumptions of Hamiltonians, we propose a sufficient condition of the observable operator to guarantee the convergence of the open quantum system, and proof that the proposed strategy can make any pure target state in decoherence-free subspace be globally asymptotic stable under the sufficient condition. Also, we provide a method to construct the observable operator via Schmidt orthogonalization. Numerical experiments on a three-level system validate the effectiveness of the proposed control strategy.

Chinese Control Conference (CCC)•Jul 22, 2011•0 citations

CONVERGENCE OF STATE CONTROL OF OPEN QUANTUM SYSTEM IN DECOHERENCE-FREE SUBSPACES

Fei Yang

A convergent state control strategy of open quantum system based on Lyapunov method is proposed for the target state being a pure state in decoherence-free subspaces. Based on the assumptions of all the transition frequencies being different and all the levels being directly coupled,a sufficient condition is proposed for the observation operator to make that the largest invariant set only contains target state.On the basis of choosing the average of observable operators as a Lyapunov function,the control laws are designed in interaction picture and the largest invariant set of the controlled system is analyzed via Barbalat's Lemma. It is shown that any pure target state in decoherence-free subspace is globally asymptotic stable under the sufficient condition given,and the system controlled could be transferred to target state from arbitrary initial state.Also,a method is provided to construct the observation operator via Schmidt orthogonalization.Numerical experiments on a three-level system verify the validity of the proposed control strategy.

Xitong kexue yu shuxue•Jan 1, 2011•0 citations

Lyapunov-based control of quantum systems

Symeon Grivopoulos, Bassam A. Bamieh

We propose feedback control laws for quantum systems, based on Lyapunov design. These feedback laws locally asymptotically stabilize any desired eigenstate of the system Hamiltonian. The target eigenstate and the size of its region of attraction can be tailored by the choice of design parameters. These feedback control laws are used to design open loop controls for state transfer problems. We illustrate the method with a transfer problem between bound states of a molecular Morse oscillator.

IEEE Conference on Decision and Control (CDC)•Jul 8, 2004•91 citations

Lyapunov control on quantum open systems in decoherence-free subspaces

Wei Wang, L. C. Wang, X. X. Yi

A scheme to drive and manipulate a finite-dimensional quantum system in decoherence-free subspaces (DFSs) by Lyapunov control is proposed. Control fields are established by the Lyapunov function. This proposal can drive the open quantum system into DFSs and manipulate it to any desired eigenstate of the free Hamiltonian. An example which consists of a four-level system with three long-lived states driven by two lasers is presented to demonstrate the scheme. We have performed numerical simulations of the dynamics of the four-level system, which show that the scheme works well.

arXiv:1005.2446•Physical Review A•Sep 30, 2010•51 citations

Implicit Lyapunov control of multi-control Hamiltonian systems in degenerate cases

Shuang Cong, Fangfang Meng

In closed quantum systems, if controlled systems are not strongly regular or there exists at least one eigenstate that is directly uncoupled to the target state, then such systems control will become degenerate cases. This paper proposes a quantum control method designed by an implicit Lyapunov function to transfer states of the quantum systems in these two degenerate cases, especially the method proposed is suitable for multi-control Hamiltonian systems. The state distance is selected as the Lyapunov function in this paper. Numerical simulation experiments on a 4-level system are done, and the experiment results indicate the effectiveness of the implicit Lyapunov control method proposed for degenerate cases and multi-control Hamiltonians.

IFAC-PapersOnLine•Jan 1, 2024•0 citations
Abstract State transition control of open quantum systems is a research hotspot and difficulty. The control method in the light of the Lyapunov stability theory is a common method. Current research shows that if the open quantum systems meet the constraints that the free Hamiltonian is strong regular and the interaction Hamiltonian is fully connected, by devising appropriate control fields in the light of the Lyapunov stability theory, the open quantum system can move to the desired final state. In view of the fact that most practical open quantum systems do not meet these two constraints, this paper propose a control method. The implicit function perturbation terms are introduced into the control fields to resolve the problem that the open quantum systems do not meet these two convergence constraints. And the main control fields are devised in the light of the Lyapunov stability theory to make the state transition of the open quantum systems converging to the desired final state.
A Lyapunov-based unified control method for closed quantum systems is proposed, which can transfer the state of closed quantum system from any initial state to any desired target state. In particular, the proposed control method can work under the conditions that free Hamiltonian of the non-ideal quantum system is not strongly regular, and (or) the Hamiltonian is not fully connected. The simulation experiments of the state transition control between different states of three, four and five qubit systems are carried out to verify that the proposed control method is suitable for all kinds of non-ideal quantum systems and the advantages of Lyapunov-based unified control method. The design process of the proposed method, the calculation process of each parameter in each experiment and the analysis of each experimental result are given in detail.
A control strategy of quantum states of open quantum system based on Lyapunov method is proposed. On the basis of choosing the average of observable operators as a Lyapunov function, the control laws are designed in interaction picture. We analyze the largest invariant set of the controlled system via Barbalat's Lemma. Based on some assumptions of Hamiltonians, we propose a sufficient condition of the observable operator to guarantee the convergence of the open quantum system, and proof that the proposed strategy can make any pure target state in decoherence-free subspace be globally asymptotic stable under the sufficient condition. Also, we provide a method to construct the observable operator via Schmidt orthogonalization. Numerical experiments on a three-level system validate the effectiveness of the proposed control strategy.
A convergent state control strategy of open quantum system based on Lyapunov method is proposed for the target state being a pure state in decoherence-free subspaces. Based on the assumptions of all the transition frequencies being different and all the levels being directly coupled,a sufficient condition is proposed for the observation operator to make that the largest invariant set only contains target state.On the basis of choosing the average of observable operators as a Lyapunov function,the control laws are designed in interaction picture and the largest invariant set of the controlled system is analyzed via Barbalat's Lemma. It is shown that any pure target state in decoherence-free subspace is globally asymptotic stable under the sufficient condition given,and the system controlled could be transferred to target state from arbitrary initial state.Also,a method is provided to construct the observation operator via Schmidt orthogonalization.Numerical experiments on a three-level system verify the validity of the proposed control strategy.
A scheme to drive and manipulate a finite-dimensional quantum system in decoherence-free subspaces (DFSs) by Lyapunov control is proposed. Control fields are established by the Lyapunov function. This proposal can drive the open quantum system into DFSs and manipulate it to any desired eigenstate of the free Hamiltonian. An example which consists of a four-level system with three long-lived states driven by two lasers is presented to demonstrate the scheme. We have performed numerical simulations of the dynamics of the four-level system, which show that the scheme works well.
In closed quantum systems, if controlled systems are not strongly regular or there exists at least one eigenstate that is directly uncoupled to the target state, then such systems control will become degenerate cases. This paper proposes a quantum control method designed by an implicit Lyapunov function to transfer states of the quantum systems in these two degenerate cases, especially the method proposed is suitable for multi-control Hamiltonian systems. The state distance is selected as the Lyapunov function in this paper. Numerical simulation experiments on a 4-level system are done, and the experiment results indicate the effectiveness of the implicit Lyapunov control method proposed for degenerate cases and multi-control Hamiltonians.