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Title: Landscape for optimal control of quantum-mechanical unitary transformations

Abstract

The optimal creation of a targeted unitary transformation W is considered under the influence of an external control field. The controlled dynamics produces the unitary transformation U and the goal is to seek a control field that minimizes the cost J= parallel W-U parallel . The optimal control landscape is the cost J as a functional of the control field. For a controllable quantum system with N states and without restrictions placed on the controls, the optimal control landscape is shown to have extrema with N+1 possible distinct values, where the desired transformation at U=W is a minimum and the maximum value is at U=-W. The other distinct N-1 extrema values of J are saddle points. The results of this analysis have significance for the practical construction of unitary transformations.

Authors:
;  [1];  [2]
  1. Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States)
  2. Department of Chemistry, Drexel University, Philadelphia, Pennsylvania 19104 (United States)
Publication Date:
OSTI Identifier:
20786489
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.052337; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; OPTIMAL CONTROL; QUANTUM COMPUTERS; QUANTUM MECHANICS; TRANSFORMATIONS; UNITARITY

Citation Formats

Rabitz, Herschel, Hsieh, Michael, and Rosenthal, Carey. Landscape for optimal control of quantum-mechanical unitary transformations. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Rabitz, Herschel, Hsieh, Michael, & Rosenthal, Carey. Landscape for optimal control of quantum-mechanical unitary transformations. United States. doi:10.1103/PHYSREVA.72.0.
Rabitz, Herschel, Hsieh, Michael, and Rosenthal, Carey. Tue . "Landscape for optimal control of quantum-mechanical unitary transformations". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786489,
title = {Landscape for optimal control of quantum-mechanical unitary transformations},
author = {Rabitz, Herschel and Hsieh, Michael and Rosenthal, Carey},
abstractNote = {The optimal creation of a targeted unitary transformation W is considered under the influence of an external control field. The controlled dynamics produces the unitary transformation U and the goal is to seek a control field that minimizes the cost J= parallel W-U parallel . The optimal control landscape is the cost J as a functional of the control field. For a controllable quantum system with N states and without restrictions placed on the controls, the optimal control landscape is shown to have extrema with N+1 possible distinct values, where the desired transformation at U=W is a minimum and the maximum value is at U=-W. The other distinct N-1 extrema values of J are saddle points. The results of this analysis have significance for the practical construction of unitary transformations.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 5,
volume = 72,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}