Quantum Optimal Control Problems with a Sparsity Cost Functional. (2nd August 2016)

• Record Type: Journal Article
• Authors: Ciaramella, Gabriele; Borzì, Alfio
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 8(2016)
• Page Start: 938
• Page End: 965
• Publication Date: 2016-08-02
• Subjects: Nonsmooth optimization -- optimal control theory -- quantum control problems -- semi-smooth Newton method; 70Q05 -- 81V99 -- 35Q40 -- 49J52 -- 49J15 -- 49K15 -- 65L05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1184166
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, the investigation of a class of quantum optimal control problems with L 1 sparsity cost functionals is presented. The focus is on quantum systems modeled by Schrödinger-type equations with a bilinear control structure as it appears in many applications in nuclear magnetic resonance spectroscopy, quantum imaging, quantum computing, and in chemical and photochemical processes. In these problems, the choice of L 1 control spaces promotes sparse optimal control functions that are conveniently produced by laboratory pulse shapers. The characterization of L 1 quantum optimal controls and an efficient numerical semi-smooth Newton solution procedure are discussed.