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

Ho, Tak-San; Rabitz, Herschel; Turinici, Gabriel

Ho, Tak-San; Rabitz, Herschel; Turinici, Gabriel (2012), Critical points of the optimal quantum control landscape: a propagator approach, Acta Applicandae Mathematicae, 118, 1, p. 49-56. http://dx.doi.org/10.1007/s10440-012-9677-3

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00630263/fr/

Date

2012

Journal name

Acta Applicandae Mathematicae

Volume

118

Number

Publisher

Springer

Pages

49-56

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.

Subjects / Keywords

landscape analysis in quatum control; quantum control; singular control