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Title: Searching for quantum optimal controls under severe constraints

Abstract

The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is of full rank, and (3) there are no constraints on the control field. This paper investigates how the violation of assumption (3) affects gradient searches for globally optimal control fields. The satisfaction of assumptions (1) and (2) ensures that the control landscape lacks fundamental traps, but certain control constraints can still prevent successful optimization of the objective. Using optimal control simulations, we show that the most severe field constraints are those that limit essential control resources, such as the number of control variables, the control duration, and the field strength. Proper management of these resources is an issue of great practical importance for optimization in the laboratory. For each resource, we show that constraints exceeding quantifiable limits can introduce artificial traps to the control landscape and prevent gradient searches from reaching a globally optimal solution. These results demonstrate that careful choice of relevant control parameters helpsmore » to eliminate artificial traps and facilitate successful optimization.« less

Authors:
 [1];  [2];  [3];  [1];  [4];  [1];  [1]
  1. Princeton Univ., NJ (United States). Dept. of Chemistry
  2. Princeton Univ., NJ (United States). Dept. of Chemistry; Temple Univ., Philadelphia, PA (United States). Dept. of Chemistry
  3. Sandia National Lab. (SNL-CA), Livermore, CA (United States). Dept. of Scalable & Secure Systems Research
  4. Tsinghua Univ., Beijing (China). Center for Quantum Information Science and Technology, Dept. of Automation
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); US Army Research Office (ARO); NSFC
OSTI Identifier:
1340253
Alternate Identifier(s):
OSTI ID: 1179324
Report Number(s):
SAND-2014-19558J
Journal ID: ISSN 1050-2947; PLRAAN; 642791
Grant/Contract Number:  
AC04-94AL85000; FG02-02ER15344; W911NF-13-1-0237; 61374091; 61134008; 60904034
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 91; Journal Issue: 4; Journal ID: ISSN 1050-2947
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Riviello, Gregory, Tibbetts, Katharine Moore, Brif, Constantin, Long, Ruixing, Wu, Re-Bing, Ho, Tak-San, and Rabitz, Herschel. Searching for quantum optimal controls under severe constraints. United States: N. p., 2015. Web. doi:10.1103/PhysRevA.91.043401.
Riviello, Gregory, Tibbetts, Katharine Moore, Brif, Constantin, Long, Ruixing, Wu, Re-Bing, Ho, Tak-San, & Rabitz, Herschel. Searching for quantum optimal controls under severe constraints. United States. doi:10.1103/PhysRevA.91.043401.
Riviello, Gregory, Tibbetts, Katharine Moore, Brif, Constantin, Long, Ruixing, Wu, Re-Bing, Ho, Tak-San, and Rabitz, Herschel. Mon . "Searching for quantum optimal controls under severe constraints". United States. doi:10.1103/PhysRevA.91.043401. https://www.osti.gov/servlets/purl/1340253.
@article{osti_1340253,
title = {Searching for quantum optimal controls under severe constraints},
author = {Riviello, Gregory and Tibbetts, Katharine Moore and Brif, Constantin and Long, Ruixing and Wu, Re-Bing and Ho, Tak-San and Rabitz, Herschel},
abstractNote = {The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is of full rank, and (3) there are no constraints on the control field. This paper investigates how the violation of assumption (3) affects gradient searches for globally optimal control fields. The satisfaction of assumptions (1) and (2) ensures that the control landscape lacks fundamental traps, but certain control constraints can still prevent successful optimization of the objective. Using optimal control simulations, we show that the most severe field constraints are those that limit essential control resources, such as the number of control variables, the control duration, and the field strength. Proper management of these resources is an issue of great practical importance for optimization in the laboratory. For each resource, we show that constraints exceeding quantifiable limits can introduce artificial traps to the control landscape and prevent gradient searches from reaching a globally optimal solution. These results demonstrate that careful choice of relevant control parameters helps to eliminate artificial traps and facilitate successful optimization.},
doi = {10.1103/PhysRevA.91.043401},
journal = {Physical Review. A},
number = 4,
volume = 91,
place = {United States},
year = {2015},
month = {4}
}

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