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Critical points of the optimal quantum control landscape: a propagator approach

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Date
2012
Link to item file
http://hal.archives-ouvertes.fr/hal-00630263/fr/
Dewey
Sciences connexes (physique, astrophysique)
Sujet
landscape analysis in quatum control; quantum control; singular control
Journal issue
Acta Applicandae Mathematicae
Volume
118
Number
1
Publication date
2012
Article pages
49-56
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s10440-012-9677-3
URI
https://basepub.dauphine.fr/handle/123456789/7257
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Ho, Tak-San
Rabitz, Herschel
Turinici, Gabriel
Type
Article accepté pour publication ou publié
Abstract (EN)
Numerical and experimental realizations of quantum control are closely connected to the properties of the mapping from the control to the unitary propagator. For bilinear quantum control problems, no general results are available to fully determine when this mapping is singular or not. In this paper we give suffcient conditions, in terms of elements of the evolution semigroup, for a trajectory to be non-singular. We identify two lists of "way-points" that, when reached, ensure the non-singularity of the control trajectory. It is found that under appropriate hypotheses one of those lists does not depend on the values of the coupling operator matrix.

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