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Nanoscale Systems: Mathematical Modeling, Theory and Applications

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Quantum optimal control using the adjoint method

Alfio Borzì
  • Institut für Mathematik, Universität Würzburg Emil-Fischer-Strasse 30, 97074 Würzburg, Germany
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Published Online: 2012-11-29 | DOI: https://doi.org/10.2478/nsmmt-2012-0007

Abstract

Control of quantum systems is central in a variety of present and perspective applications ranging from quantum optics and quantum chemistry to semiconductor nanostructures, including the emerging fields of quantum computation and quantum communication. In this paper, a review of recent developments in the field of optimal control of quantum systems is given with a focus on adjoint methods and their numerical implementation. In addition, the issues of exact controllability and optimal control are discussed for finite- and infinitedimensional quantum systems. Some insight is provided considering ’two-level’ models. This work is completed with an outlook to future developments.

Keywords: Quantum systems; Schrödinger equation; Optimal control theory; Numerical optimization

PACS: 03.65.-w; 32.80.Qk; 37.90+j; 82.37.Gk; 82.53.-k

MSC: 35Q40; 49K20; 65H10; 65M06; 65N06; 90C53

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About the article

Received: 2012-09-26

Revised: 2012-11-07

Accepted: 2012-11-24

Published Online: 2012-11-29



Citation Information: Nanoscale Systems: Mathematical Modeling, Theory and Applications, ISSN (Online) 2299-3290, DOI: https://doi.org/10.2478/nsmmt-2012-0007. Export Citation

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