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

CRM proceedings & lecture notes

Development of solution algorithms for quantum optimal control equations in product spaces

Yukiyoshi Ohtsuki, HERSCHEL A. RABITZ

Published Dec 17, 2003• 6 citations
Publisher
DOI
10.1090/crmp/033/10

Related papers

Quantum control : mathematical and numerical challenges : CRM workshop, October 6-11, 2002, Montréal, Canada

André D. Bandrauk, Michel C. Delfour, Claude Le Bris

Molecular alignment and orientation: From laser-induced mechanisms to optimal control by O. Atabek and C. M. Dion Overview and software guide of evolutionary algorithms A case study in quantum control by A. Auger, A. Ben Haj-Yedder, and M. Schoenauer Laser control of molecular states--Nonperturbative examples by A. D. Bandrauk, F. Legare, and H. T. Yu Coherent control: Principles and semiclassical implementations by V. S. Batista and P. Brumer Mathematical models of contemporary elementary quantum computing devices by G. Chen, D. A. Church, B.-G. Englert, and M. S. Zubairy Addendum and remarks on doubly conservative numerical schemes for the nonlinear Schrodinger equation and its control by M. C. Delfour A note on the exact internal control of nonlinear Schrodinger equations by R. Illner, H. Lange, and H. Teismann Towards efficient numerical approaches for quantum control by C. Le Bris, Y. Maday, and G. Turinici Multichannel quantum defect study of the control in the frequency domain: Example of HI by H. Lefebvre-Brion Development of solution algorithms for quantum optimal control equations in product spaces by Y. Ohtsuki and H. Rabitz Using contracted basis functions to solve the Schrodinger equation by X.-G. Wang and T. Carrington, Jr. Remarks on the controllability of the Schrodinger equation by E. Zuazua.

American Mathematical Society eBooks•Jan 1, 2003•1 citation

Formulation and numerical solution of finite-level quantum optimal control problems

Alfio Borzı̀, Julien Salomon, Stefan Volkwein

Journal of Computational and Applied Mathematics•May 9, 2007•32 citations

Formulation and Numerical Solution of Quantum Control Problems

Alfio Borzı̀, Gabriele Ciaramella, M. Sprengel

Society for Industrial and Applied Mathematics eBooks•Jul 6, 2017•57 citations

Fourier compression: A customization method for quantum control protocols

Martín Larocca, Esteban Calzetta, Diego A. Wisniacki

Quantum optimal control (QOC) is the field devoted to the production of external control protocols that actively guide quantum dynamics. Solutions to QOC problems were shown to constitute continuous submanifolds of control space. A solution navigation method exploiting this property to achieve secondary features in the control protocols was proposed [Larocca, Calzetta, and Wisniacki, Phys. Rev. A 101, 023410 (2020)]. Here, we present a navigation-powered protocol postprocessing mechanism allowing naturally inflexible optimization algorithms to produce user-customized solutions, for example, in terms of a Fourier decomposition. We test the performance of the method in two inherently different models: the two-level Landau-Zener system and the quantum harmonic oscillator.

arXiv:2001.05941•Physical Review A•Sep 16, 2020•7 citations

Optimal control equations for the one dimensional quantum harmonic oscillator under the influence of external dipole effects

Muzaffer Ayvaz, Metin Demіralp

This study focuses on the construction of the optimal control equations for one dimensional quantum harmonic oscillator under the influence of external dipol effects and the solution of these equations by using Fluctuationlessness Theorem and a recently developed scheme called Characteristic Evolutions Method. The dipole function of the system has been taken as odd cubic spatial polynomial. Optimal control equations of the system under consideration are constructed by using expectation values of the position and the momentum operators instead of the wave and costate evolutions. It is shown that, the resulting equations are systems of ordinary differential equations and there are infinitely many ODEs. The solution strategy is based on the approximation of the expectation values for the operator products in the sense of Fluctuationlessness Theorem.

AIP conference proceedings•Jan 1, 2012•0 citations

Quantum Optimal Control: Practical Aspects and Diverse Methods

T. S. Mahesh, Priya Batra, M. Harshanth Ram

arXiv:2205.15574•Journal of the Indian Institute of Science•Sep 7, 2022•11 citations
Molecular alignment and orientation: From laser-induced mechanisms to optimal control by O. Atabek and C. M. Dion Overview and software guide of evolutionary algorithms A case study in quantum control by A. Auger, A. Ben Haj-Yedder, and M. Schoenauer Laser control of molecular states--Nonperturbative examples by A. D. Bandrauk, F. Legare, and H. T. Yu Coherent control: Principles and semiclassical implementations by V. S. Batista and P. Brumer Mathematical models of contemporary elementary quantum computing devices by G. Chen, D. A. Church, B.-G. Englert, and M. S. Zubairy Addendum and remarks on doubly conservative numerical schemes for the nonlinear Schrodinger equation and its control by M. C. Delfour A note on the exact internal control of nonlinear Schrodinger equations by R. Illner, H. Lange, and H. Teismann Towards efficient numerical approaches for quantum control by C. Le Bris, Y. Maday, and G. Turinici Multichannel quantum defect study of the control in the frequency domain: Example of HI by H. Lefebvre-Brion Development of solution algorithms for quantum optimal control equations in product spaces by Y. Ohtsuki and H. Rabitz Using contracted basis functions to solve the Schrodinger equation by X.-G. Wang and T. Carrington, Jr. Remarks on the controllability of the Schrodinger equation by E. Zuazua.
Quantum optimal control (QOC) is the field devoted to the production of external control protocols that actively guide quantum dynamics. Solutions to QOC problems were shown to constitute continuous submanifolds of control space. A solution navigation method exploiting this property to achieve secondary features in the control protocols was proposed [Larocca, Calzetta, and Wisniacki, Phys. Rev. A 101, 023410 (2020)]. Here, we present a navigation-powered protocol postprocessing mechanism allowing naturally inflexible optimization algorithms to produce user-customized solutions, for example, in terms of a Fourier decomposition. We test the performance of the method in two inherently different models: the two-level Landau-Zener system and the quantum harmonic oscillator.
This study focuses on the construction of the optimal control equations for one dimensional quantum harmonic oscillator under the influence of external dipol effects and the solution of these equations by using Fluctuationlessness Theorem and a recently developed scheme called Characteristic Evolutions Method. The dipole function of the system has been taken as odd cubic spatial polynomial. Optimal control equations of the system under consideration are constructed by using expectation values of the position and the momentum operators instead of the wave and costate evolutions. It is shown that, the resulting equations are systems of ordinary differential equations and there are infinitely many ODEs. The solution strategy is based on the approximation of the expectation values for the operator products in the sense of Fluctuationlessness Theorem.