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

Chemical engineering transactions

Trajectory Tracking for Quantum Systems with Impulsive Control Fields

Wei Yang

Published Jul 1, 2017• 0 citations
Publisher

Abstract

Quantum Lyapunov control is a feedback control methodology to determine control fields applied to control quantum systems. In this paper, with the help of the invariant principle of impulsive systems, we investigate the trajectory tracking for quantum systems with impulsive control fields by two Lyapunov functions based on the distance of quantum states and the average value of Hermitian operator which can be regarded as an observable of a quantum system, propose new control fields to drive the quantum systems in the form of sufficient conditions. One numerical simulation is presented to illustrate the effectiveness of the proposed control method.

DOI
10.3303/cet1759112

Related papers

Trajectory tracking for quantum systems based on Lyapunov control method

Wei Yang

We investigat the trajectory tracking problem of quantum systems governed by Liouville equation.With the help of Lyapunov function and LaSlle invariance principle, impulsive control fields are given, which drive the quantum state to a time-variant target state.A numerical simulation experiment on a two-level quantum system shows the rationality of the obtained theoretical results, and the advantage compared to traditional control method.

IEEE Workshop on Advanced Research and Technology in Industry Applications (WARTIA)•Jan 1, 2016•0 citations

Lyapunov Control of Quantum Systems with Impulsive Control Fields

Wei Yang, Jitao Sun

We investigate the Lyapunov control of finite-dimensional quantum systems with impulsive control fields, where the studied quantum systems are governed by the Schrödinger equation. By three different Lyapunov functions and the invariant principle of impulsive systems, we study the convergence of quantum systems with impulsive control fields and propose new results for the mentioned quantum systems in the form of sufficient conditions. Two numerical simulations are presented to illustrate the effectiveness of the proposed control method.

The Scientific World JOURNAL•Jan 1, 2013•1 citation

Finite-time Target Function Tracking of Quantum Systems with Impulsive Control Fields

Xueming Qian, Baotong Cui

In this paper, the finite time tracking issue for a class of closed quantum systems under the action of impulsive control fields is addressed. The aim is to steer the state of the quantum system to the trajectory of a periodic time-varying target. By using the Lyapunov direct method and considering a finite-time control strategy, the modified impulsive tracking controllers are designed such that the error dynamical system converges to zero in finite time. While finite-time tracking implies optimality in convergence time and has better disturbance rejection. Numerical simulations are given to illustrate the effects of system’s trajectory tracking, and also given to demonstrate the superiority of the control laws which are proposed.

Chinese Control and Decision Conference (CCDC)•May 20, 2023•0 citations

Trajectory tracking of quantum states based on Lyapunov method

Jianxiu Liu, Shuang Cong

A Lyapunov-based approach of trajectory tracking in Liouville equation for quantum systems is proposed. By selecting density matrix of controlled system as the system state, and defining the error between controlled state and target one as an error state, the paper regards this error as a new controlled state of system. In such a way the quantum state trajectory tracking problem is changed into the state regulation problem by driving the error state to zero. The control law is designed according to the Lyapunov stability theorem, which can be applied to track different kinds of quantum states including pure state, superposition state and mixed-state. Finally, numerical simulation experiments and results analysis are given.

International Conference on Control and Automation•Dec 1, 2011•10 citations

Trajectory tracking control of quantum systems

Shuang Cong, Jianxiu Liu

For quantum state trajectory tracking of density matrix in Liouville equation of quantum systems, with the help of concept in quantum system control, one can apply unitary transformation both to controlled system and free-evolutionary target system such as to change the time-variant and non-stationary target system into a stationary state. Therefore, the quantum state trajectory tracking problem becomes a steering one. State steering control law of the system transformed is designed by means of the Lyapunov stability theorem. Finally, numerical simulation experiments are given for a five-level energy quantum system. The comparison analysis of original system’s trajectory tracking with other method illustrates the advantage in control time of the method proposed.

Chinese Science Bulletin•May 3, 2012•6 citations

Adaptive trajectory tracking of quantum systems

Jianxiu Liu, Shuang Cong, Zhu Yaping

A control strategy for tracking the trajectory of a time-variant objective function in closed quantum systems is proposed in this paper. The Lyapunov stability theorem is used to design the control law. Meanwhile, the issue of singularity is discussed and the problem of large value of control field occurred during the process of tracking are solved by using an adaptive regulation algorithm of objective function. Simulation results demonstrate the effectiveness and feasibility of the method proposed. We also explore the relationship of effect between control parameters and the error of the control system.

International Conference on Control, Automation and Systems (ICCAS)•Dec 31, 2012•4 citations
Quantum Lyapunov control is a feedback control methodology to determine control fields applied to control quantum systems. In this paper, with the help of the invariant principle of impulsive systems, we investigate the trajectory tracking for quantum systems with impulsive control fields by two Lyapunov functions based on the distance of quantum states and the average value of Hermitian operator which can be regarded as an observable of a quantum system, propose new control fields to drive the quantum systems in the form of sufficient conditions. One numerical simulation is presented to illustrate the effectiveness of the proposed control method.
We investigate the Lyapunov control of finite-dimensional quantum systems with impulsive control fields, where the studied quantum systems are governed by the Schrödinger equation. By three different Lyapunov functions and the invariant principle of impulsive systems, we study the convergence of quantum systems with impulsive control fields and propose new results for the mentioned quantum systems in the form of sufficient conditions. Two numerical simulations are presented to illustrate the effectiveness of the proposed control method.
In this paper, the finite time tracking issue for a class of closed quantum systems under the action of impulsive control fields is addressed. The aim is to steer the state of the quantum system to the trajectory of a periodic time-varying target. By using the Lyapunov direct method and considering a finite-time control strategy, the modified impulsive tracking controllers are designed such that the error dynamical system converges to zero in finite time. While finite-time tracking implies optimality in convergence time and has better disturbance rejection. Numerical simulations are given to illustrate the effects of system’s trajectory tracking, and also given to demonstrate the superiority of the control laws which are proposed.
A Lyapunov-based approach of trajectory tracking in Liouville equation for quantum systems is proposed. By selecting density matrix of controlled system as the system state, and defining the error between controlled state and target one as an error state, the paper regards this error as a new controlled state of system. In such a way the quantum state trajectory tracking problem is changed into the state regulation problem by driving the error state to zero. The control law is designed according to the Lyapunov stability theorem, which can be applied to track different kinds of quantum states including pure state, superposition state and mixed-state. Finally, numerical simulation experiments and results analysis are given.
For quantum state trajectory tracking of density matrix in Liouville equation of quantum systems, with the help of concept in quantum system control, one can apply unitary transformation both to controlled system and free-evolutionary target system such as to change the time-variant and non-stationary target system into a stationary state. Therefore, the quantum state trajectory tracking problem becomes a steering one. State steering control law of the system transformed is designed by means of the Lyapunov stability theorem. Finally, numerical simulation experiments are given for a five-level energy quantum system. The comparison analysis of original system’s trajectory tracking with other method illustrates the advantage in control time of the method proposed.
A control strategy for tracking the trajectory of a time-variant objective function in closed quantum systems is proposed in this paper. The Lyapunov stability theorem is used to design the control law. Meanwhile, the issue of singularity is discussed and the problem of large value of control field occurred during the process of tracking are solved by using an adaptive regulation algorithm of objective function. Simulation results demonstrate the effectiveness and feasibility of the method proposed. We also explore the relationship of effect between control parameters and the error of the control system.