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

Keji daobao

Applications of Averaging Optimal Control in Quantum System

Shuang Cong

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The control time is supposed to be relative large, the averaged system is obtained by using of the averaging theorem in the quantum system. The control field of averaged system is designed by classical optimal control theorem, then analytic expression for the control field is acquired within optimal energy. As a result, the normal iterative solution of a two-point boundary value problem is avoided by the use of averaging optimal control. At last, the method is used to a three-level quantum system. The some analysis are given according to the simulation test results.

Related papers

Optimal control of quantum system under bilinear systems

Qixing Zheng

By means of the achievement of bilinear systems theory research in the macroscopic fields, associated with the characteristic that the mathematical model of quantum mechanical system is bilinear, an iterative optimal controller for a quantum mechanical system is designed through the derivation of the optimal controller with two points boundary values problem. Also by the simulation experiment of states transfer control of the designed quantum system, the effects to control results with different control parameters are detailly analyzed.

Chinese Journal of Quantum Electronics•Jan 1, 2005•0 citations

OPTIMAL CONTROL ALGORITHMS FOR QUANTUM SYSTEMS AND THEIR LIMITATIONS

S. G. Schirmer, Pierre de Fouquieres, Xiaoting Wang

Some of the limitations of popular optimal control algorithms such as Lyapunov control, the Krotov method and other iterative algorithms based on functional gradients are considered. Lyapunov control, while elegant and generally effective for ideal systems, struggles for realistic systems. Iterative techniques such as the Krotov method tend to be more effective, but the inclusion of an energy penalty term implies that the resulting solutions are not critical points of the objective functional alone, and do not maximize it. These problems can be avoided by using functional gradients without penalty terms, but even these techniques fail for some problems.

•Jan 1, 2009•0 citations

Quantum Optimal Control Based on the Constrained Control Field

Ze-Xia Huang, You-Hong Yu

According to the specialty of quantum systems, the reliability or the efficiency of a general optimal control scheme leave much to be desired. In this paper, we develop a special improved quantum optimal control method for using dynamic control field, which can be implemented as fast convergent algorithms. The relations among, convergence speed and iteration step parameters are analyzed in detail through a three-level ¦® system simulation experiments. Theoretical analysis show that this new algorithm exhibits significantly superior to the classical quantum optimal control method and the Krotov method in reliability and convergence rate.

International Conference on Electronics, Communications and Control•Oct 16, 2012•0 citations

Optimal quantum control based on Lyapunov stability theorem

Shuang Cong

By means of the design method for bilinear systems in the macroscopic field in association with the characteristic that the mathematical model of pure state quantum system is bilinear,and of selecting the performance index of the controlled system,the optimal control strategy in quantum systems was proposed based on the Lyapunov stability theorem.The detailed design process of optimal control law was derived.Some simulation experiments were performed on a spin-1/2 particle system.Experimental results demonstrate the effectiveness of the method proposed.At the same time,the influence of different parameters on the system control effects is analyzed.

•Jan 1, 2008•1 citation

Averaging simplifies optimal population transfer problems

Symeon Grivopoulos, Bassam A. Bamieh

We consider energy-optimal population transfer problems for isolated finite dimensional quantum systems. In the limit when the transfer time is large compared to the time scale of the free dynamics, we show how the associated two-point boundary-value problem (TPBVP) can be reduced to a corresponding "averaged" TPBVP where the free dynamics has been averaged over. This approach offers significant computational and conceptual advantages to the solution of such problems

IEEE Conference on Decision and Control (CDC)•Jan 1, 2006•0 citations

Algebraic and computational aspects of quantum control and applications.

I. C. H. Pullen

We investigate the problem of control of quantum systems. Various notions of controllability of quantum systems are discussed and Lie algebraic techniques are employed to derive necessary and sufficient conditions for the resulting degrees of controllability. The results are employed to study the degree of controllability for various model systems. The problem of optimal control is formulated as a problem of maximisation of the expectation value of an observable of the system subject to dynamical constraints and costs. A class of iterative algorithms is discussed, and shown to converge to a solution of the Euler-Lagrange equations, which is a necessary condition for optimality of a solution. A numerical realisation of the algorithm is presented and potential implementation of the resulting control fields in the laboratory is discussed. The algorithm is applied to find optimal control fields for a variety of applications including selective and simultaneous excitation of individual quantum dots in a globally addressed ensemble, creation of superposition states, and selective excitation of certain vibrational modes of a simple molecule such as Hydrogen Fluoride. In each case we systematically explore the parameter space of the algorithm to select solutions with desirable physical features from the multitude of possible choices. As there are many possible optimal control fields which give similar yields the question of whether some are more robust than others is investigated. A number of optimal fields are analysed quantitatively in terms of robustness with regard to temporal and spectral noise affecting the fields, uncertainty in the model parameters and the effect of experimental limitations such as restrictions on the bandwidth of the fields. It is shown that whilst the solutions tend to be sensitive to uncertainty in the energy levels chosen for the model, they appear to be surprisingly tolerant to even severe bandwidth limitations.

•Jan 1, 2006•0 citations
The control time is supposed to be relative large, the averaged system is obtained by using of the averaging theorem in the quantum system. The control field of averaged system is designed by classical optimal control theorem, then analytic expression for the control field is acquired within optimal energy. As a result, the normal iterative solution of a two-point boundary value problem is avoided by the use of averaging optimal control. At last, the method is used to a three-level quantum system. The some analysis are given according to the simulation test results.
By means of the achievement of bilinear systems theory research in the macroscopic fields, associated with the characteristic that the mathematical model of quantum mechanical system is bilinear, an iterative optimal controller for a quantum mechanical system is designed through the derivation of the optimal controller with two points boundary values problem. Also by the simulation experiment of states transfer control of the designed quantum system, the effects to control results with different control parameters are detailly analyzed.
Some of the limitations of popular optimal control algorithms such as Lyapunov control, the Krotov method and other iterative algorithms based on functional gradients are considered. Lyapunov control, while elegant and generally effective for ideal systems, struggles for realistic systems. Iterative techniques such as the Krotov method tend to be more effective, but the inclusion of an energy penalty term implies that the resulting solutions are not critical points of the objective functional alone, and do not maximize it. These problems can be avoided by using functional gradients without penalty terms, but even these techniques fail for some problems.
According to the specialty of quantum systems, the reliability or the efficiency of a general optimal control scheme leave much to be desired. In this paper, we develop a special improved quantum optimal control method for using dynamic control field, which can be implemented as fast convergent algorithms. The relations among, convergence speed and iteration step parameters are analyzed in detail through a three-level ¦® system simulation experiments. Theoretical analysis show that this new algorithm exhibits significantly superior to the classical quantum optimal control method and the Krotov method in reliability and convergence rate.
By means of the design method for bilinear systems in the macroscopic field in association with the characteristic that the mathematical model of pure state quantum system is bilinear,and of selecting the performance index of the controlled system,the optimal control strategy in quantum systems was proposed based on the Lyapunov stability theorem.The detailed design process of optimal control law was derived.Some simulation experiments were performed on a spin-1/2 particle system.Experimental results demonstrate the effectiveness of the method proposed.At the same time,the influence of different parameters on the system control effects is analyzed.
We investigate the problem of control of quantum systems. Various notions of controllability of quantum systems are discussed and Lie algebraic techniques are employed to derive necessary and sufficient conditions for the resulting degrees of controllability. The results are employed to study the degree of controllability for various model systems. The problem of optimal control is formulated as a problem of maximisation of the expectation value of an observable of the system subject to dynamical constraints and costs. A class of iterative algorithms is discussed, and shown to converge to a solution of the Euler-Lagrange equations, which is a necessary condition for optimality of a solution. A numerical realisation of the algorithm is presented and potential implementation of the resulting control fields in the laboratory is discussed. The algorithm is applied to find optimal control fields for a variety of applications including selective and simultaneous excitation of individual quantum dots in a globally addressed ensemble, creation of superposition states, and selective excitation of certain vibrational modes of a simple molecule such as Hydrogen Fluoride. In each case we systematically explore the parameter space of the algorithm to select solutions with desirable physical features from the multitude of possible choices. As there are many possible optimal control fields which give similar yields the question of whether some are more robust than others is investigated. A number of optimal fields are analysed quantitatively in terms of robustness with regard to temporal and spectral noise affecting the fields, uncertainty in the model parameters and the effect of experimental limitations such as restrictions on the bandwidth of the fields. It is shown that whilst the solutions tend to be sensitive to uncertainty in the energy levels chosen for the model, they appear to be surprisingly tolerant to even severe bandwidth limitations.