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

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2008

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Borzì, Alfio
Salomon, Julien

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https://doi.org/10.1016/j.cam.2007.04.029
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Journal of Computational and Applied Mathematics. 2008, 216(1), pp. 170-197. ISSN 0377-0427. eISSN 1879-1778. Available under: doi: 10.1016/j.cam.2007.04.029

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Optimal control of finite-level quantum systems is investigated, and iterative solution schemes for the optimization of a control representing laser pulses are developed. The purpose of this external field is to channel the system's wavefunction between given states in its most efficient way. Physically motivated constraints, such as limited laser resources or population suppression of certain states, are accounted for through an appropriately chosen cost functional. First-order necessary optimality conditions and second-order sufficient optimality conditions are investigated. For solving the optimal control problems, a cascadic non-linear conjugate gradient scheme and a monotonic scheme are discussed. Results of numerical experiments with a representative finite-level quantum system demonstrate the effectiveness of the optimal control formulation and efficiency and robustness of the proposed approaches.

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510 Mathematik

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ISO 690BORZÌ, Alfio, Julien SALOMON, Stefan VOLKWEIN, 2008. Formulation and numerical solution of finite-level quantum optimal control problems. In: Journal of Computational and Applied Mathematics. 2008, 216(1), pp. 170-197. ISSN 0377-0427. eISSN 1879-1778. Available under: doi: 10.1016/j.cam.2007.04.029
BibTex
@article{Borzi2008-06Formu-41168,
  year={2008},
  doi={10.1016/j.cam.2007.04.029},
  title={Formulation and numerical solution of finite-level quantum optimal control problems},
  number={1},
  volume={216},
  issn={0377-0427},
  journal={Journal of Computational and Applied Mathematics},
  pages={170--197},
  author={Borzì, Alfio and Salomon, Julien and Volkwein, Stefan}
}
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