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Title
A globalized Newton method for the accurate solution of a dipole quantum control problem
Authorvon Winckel, Greg ; Borzì, Alfio In der Gemeinsamen Normdatei der DNB nachschlagen ; Volkwein, Stefan In der Gemeinsamen Normdatei der DNB nachschlagen
Published in
SIAM Journal on Scientific Computing, Philadelphia, Pa., 2009, Vol. 31, Issue 6, page 4176-4203
PublishedSIAM, 2009
Edition
Preprint
LanguageEnglish
Document typeJournal Article
Keywords (EN)Optimal control theory / Schrödinger equation / Newton method
ISSN1064-8275
URNurn:nbn:at:at-ubg:3-3648 Persistent Identifier (URN)
DOI10.1137/09074961X 
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 The work is publicly available
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Abstract (English)

A theoretical and computational framework is presented to obtain accurate controls for fast quantum state transitions that are needed in a host of applications such as nanoelectronic devices and quantum computing. This method is based on a reduced Hessian KrylovNewton scheme applied to a norm-preserving discrete model of a dipole quantum control problem. The use of second-order numerical methods for solving the control problem is justified, proving the existence of optimal solutions and analyzing first- and second-order optimality conditions. Criteria for the discretization of the nonconvex optimization problem and for the formulation of the Hessian are given to ensure accurate gradients and a symmetric Hessian. Robustness of the Newton approach is obtained using a globalization strategy with a robust linesearch procedure. Results of numerical experiments demonstrate that the Newton approach presented in this paper is able to provide fast and accurate controls for high-energy state transitions.

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