• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

On the relationship between the local tracking procedures and monotonic schemes in quantum optimal control

Thumbnail
Date
2006
Dewey
Probabilités et mathématiques appliquées
Sujet
stochastic processes; numerical analysis; optimal control
Journal issue
The Journal of Chemical Physics
Volume
124
Number
7
Publication date
02-2006
Article pages
074102
DOI
http://dx.doi.org/10.1063/1.2170085
URI
https://basepub.dauphine.fr/handle/123456789/931
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Salomon, Julien
Turinici, Gabriel
Type
Article accepté pour publication ou publié
Abstract (EN)
Numerical simulations of (bilinear) quantum control often rely on either monotonically convergent algorithms or tracking schemes. However, despite their mathematical simplicity, very limited intuitive understanding exists at this time to explain the former type of algorithms. Departing from the usual mathematical formalization, we present in this paper an interpretation of the monotonic algorithms as finite horizon, local in time, tracking schemes. Our purpose is not to present a new class of procedures but rather to introduce the necessary rigorous framework that supports this interpretation. As a by-product we show that at each instant, estimates of the future quality of the current control field are available and used in the optimization. When the target is expressed as reaching a prescribed final state, we also present an intuitive geometrical interpretation as the minimization of the distance between two correlated trajectories: one starting from the given initial state and the other backward in time from the target state. As an illustration, a stochastic monotonic algorithm is introduced. Numerical discretizations of the two procedures are also presented.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.