On the relationship between quantum control landscape structure and optimization complexity

2008 ◽  
Vol 128 (15) ◽  
pp. 154117 ◽  
Author(s):  
Katharine Moore ◽  
Michael Hsieh ◽  
Herschel Rabitz
2013 ◽  
Vol 88 (3) ◽  
Author(s):  
Arun Nanduri ◽  
Ashley Donovan ◽  
Tak-San Ho ◽  
Herschel Rabitz

2021 ◽  
Vol 9 ◽  
Author(s):  
Benjamin Russell ◽  
Re-Bing Wu ◽  
Herschel Rabitz

We investigate the control landscapes of closed n-level quantum systems beyond the dipole approximation by including a polarizability term in the Hamiltonian. The latter term is quadratic in the control field. Theoretical analysis of singular controls is presented, which are candidates for producing landscape traps. The results for considering the presence of singular controls are compared to their counterparts in the dipole approximation (i.e., without polarizability). A numerical analysis of the existence of traps in control landscapes for generating unitary transformations beyond the dipole approximation is made upon including the polarizability term. An extensive exploration of these control landscapes is achieved by creating many random Hamiltonians which include terms linear and quadratic in a single control field. The discovered singular controls are all found not to be local optima. This result extends a great body of recent work on typical landscapes of quantum systems where the dipole approximation is made. We further investigate the relationship between the magnitude of the polarizability and the fluence of the control resulting from optimization. It is also shown that including a polarizability term in an otherwise uncontrollable dipole coupled system removes traps from the corresponding control landscape by restoring controllability. We numerically assess the effect of a polarizability term on a known example of a particular three-level Λ-system with a second order trap in its control landscape. It is found that the addition of the polarizability removes the trap from the landscape. The general practical control implications of these simulations are discussed.


2014 ◽  
Vol 89 (3) ◽  
Author(s):  
Qiuyang Sun ◽  
István Pelczer ◽  
Gregory Riviello ◽  
Re-Bing Wu ◽  
Herschel Rabitz

Author(s):  
Benjamin Russell ◽  
Herschel Rabitz

A common goal in the sciences is optimization of an objective function by selecting control variables such that a desired outcome is achieved. This scenario can be expressed in terms of a control landscape of an objective considered as a function of the control variables. At the most basic level, it is known that the vast majority of quantum control landscapes possess no traps, whose presence would hinder reaching the objective. This paper reviews and extends the quantum control landscape assessment, presenting evidence that the same highly favourable landscape features exist in many other domains of science. The implications of this broader evidence are discussed. Specifically, control landscape examples from quantum mechanics, chemistry and evolutionary biology are presented. Despite the obvious differences, commonalities between these areas are highlighted within a unified mathematical framework. This mathematical framework is driven by the wide-ranging experimental evidence on the ease of finding optimal controls (in terms of the required algorithmic search effort beyond the laboratory set-up overhead). The full scope and implications of this observed common control behaviour pose an open question for assessment in further work. This article is part of the themed issue ‘Horizons of cybernetical physics’.


2014 ◽  
Vol 90 (1) ◽  
Author(s):  
Arun Nanduri ◽  
Ashley Donovan ◽  
Tak-San Ho ◽  
Herschel Rabitz

2012 ◽  
Vol 118 (1) ◽  
pp. 49-56 ◽  
Author(s):  
Tak-San Ho ◽  
Herschel Rabitz ◽  
Gabriel Turinici

2021 ◽  
Author(s):  
Marta Quero Ortega ◽  
Natalia Moreno ◽  
Cristina E. Fernández ◽  
Susana Pascual

Abstract The olive fruit fly, Bactrocera oleae (Rossi) (Diptera: Tephritidae), is a key pest of olive groves. Because of its economic importance and problems associated with chemical control, new approaches to reduce the damage caused by this pest and a deeper knowledge of the biology of the insect and the relationship of landscape structure to different biological parameters are needed. B. oleae can fly long distances and its ability to move within the landscape can determine the damage caused to olive groves. This work evaluates the effect of landscape structure on olive fruit fly abundance, movements and damage at three times of year—spring, early autumn and late autumn—in central Spain. This area is less dominated by olive groves than southern Spain, where the relationship between olive grove area and B. oleae abundance is already known. A cost-distance analysis is used to evaluate the landscape effect on the movement of the fly along the crop cycle. The olive grove area is the landscape composition factor with the greatest effect on the parameters studied, with a decrease in B. oleae abundance in a more complex landscape during spring and early autumn. The cost-distance analysis shows that the olive fruit fly moves mainly in spring, and amongst olive groves. There is no evidence that land uses other than olive groves serve as a summer refuge for B.oleae in the studied landscape context. Olive grove area and land use diversity index had significant effects on olive damage in more than one year.


2009 ◽  
Vol 130 (10) ◽  
pp. 104109 ◽  
Author(s):  
Michael Hsieh ◽  
Rebing Wu ◽  
Herschel Rabitz

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