dc.contributor.author
Reich, Daniel M.
dc.contributor.author
Ndong, Mamadou
dc.contributor.author
Koch, Christiane P.
dc.date.accessioned
2018-06-08T03:52:40Z
dc.date.available
2015-11-03T13:57:00.935Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/16106
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-20290
dc.description.abstract
The non-linear optimization method developed by A. Konnov and V. Krotov
[Autom. Remote Cont. (Engl. Transl.)60, 1427 (1999)] has been used previously
to extend the capabilities of optimal control theory from the linear to the
non-linear Schrödinger equation[S. E. Sklarz and D. J. Tannor, Phys. Rev. A66,
053619 (2002)]10.1103/PhysRevA.66.053619. Here we show that based on the
Konnov-Krotov method, monotonically convergent algorithms are obtained for a
large class of quantum control problems. It includes, in addition to nonlinear
equations of motion, control problems that are characterized by non-unitary
time evolution, nonlinear dependencies of the Hamiltonian on the control,
time-dependent targets, and optimizationfunctionals that depend to higher than
second order on the time-evolving states. We furthermore show that the
nonlinear (second order) contribution can be estimated either analytically or
numerically, yielding readily applicable optimization algorithms. We
demonstrate monotonic convergence for an optimizationfunctional that is an
eighth-degree polynomial in the states. For the “standard” quantum control
problem of a convex final-time functional,linear equations of motion and
linear dependency of the Hamiltonian on the field, the second-order
contribution is not required for monotonic convergence but can be used to
speed up convergence. We demonstrate this by comparing the performance of
first- and second-order algorithms for two examples.
en
dc.rights.uri
http://publishing.aip.org/authors/web-posting-guidelines
dc.subject.ddc
500 Naturwissenschaften und Mathematik::530 Physik
dc.title
Monotonically convergent optimization in quantum control using Krotov's method
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation
Journal of Chemical Physics. - 136 (2012), 10, Artikel Nr. 104103
dcterms.bibliographicCitation.doi
10.1063/1.3691827
dcterms.bibliographicCitation.url
http://dx.doi.org/10.1063/1.3691827
refubium.affiliation
Physik
de
refubium.funding
OpenAccess Publikation in Allianzlizenz
refubium.mycore.fudocsId
FUDOCS_document_000000023405
refubium.resourceType.isindependentpub
no
refubium.mycore.derivateId
FUDOCS_derivate_000000005621
dcterms.accessRights.openaire
open access