On the relationship between quantum control landscape structure and optimization complexity

The Journal of Chemical Physics
Katharine W MooreHerschel Rabitz

Abstract

It has been widely observed in optimal control simulations and experiments that state preparation is surprisingly easy to achieve, regardless of the dimension N of the system Hilbert space. In contrast, simulations for the generation of targeted unitary transformations indicate that the effort increases exponentially with N. In order to understand such behavior, the concept of quantum control landscapes was recently introduced, where the landscape is defined as the physical objective, as a function of the control variables. The present work explores how the local structure of the control landscape influences the effectiveness and efficiency of quantum optimal control search efforts. Optimizations of state and unitary transformation preparation using kinematic control variables (i.e., the elements of the action matrix) are performed with gradient, genetic, and simplex algorithms. The results indicate that the search effort scales weakly, or possibly independently, with N for state preparation, while the search effort for the unitary transformation objective increases exponentially with N. Analysis of the mean path length traversed during a search trajectory through the space of action matrices and the local structure along this ...Continue Reading

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Citations

Mar 25, 2011·Physical Chemistry Chemical Physics : PCCP·A DonovanH Rabitz
Oct 9, 2012·The Journal of Chemical Physics·Katharine W Moore, Herschel Rabitz
Oct 15, 2013·The Journal of Chemical Physics·Katharine Moore TibbettsHerschel Rabitz
May 24, 2011·The Journal of Chemical Physics·Vincent BeltraniHerschel Rabitz
Nov 3, 2010·The Journal of Chemical Physics·Stefan RuetzelDavid J Tannor
Nov 8, 2014·Physical Chemistry Chemical Physics : PCCP·Arun NanduriHerschel Rabitz
Dec 18, 2014·Physical Chemistry Chemical Physics : PCCP·Katharine Moore Tibbetts, Herschel Rabitz
May 8, 2009·Journal of Computational Chemistry·Traci Strohecker, Herschel Rabitz

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