Type of Publication:  Journal article 
Publication status:  Published 
Author:  Ciaramella, Gabriele; Borzì, Alfio; Dirr, Gunther; Wachsmuth, Daniel 
Year of publication:  2015 
Published in:  SIAM Journal on Scientific Computing ; 37 (2015), 1.  pp. A319A346.  ISSN 10648275.  eISSN 10957197 
DOI (citable link):  https://dx.doi.org/10.1137/140966988 
Summary: 
An efficient and robust computational framework for solving closed quantum spin optimalcontrol and exactcontrollability problems with control constraints is presented. Closed spin systems are of fundamental importance in modern quantum technologies such as nuclear magnetic resonance (NMR) spectroscopy, quantum imaging, and quantum computing. These systems are modeled by the Liouvillevon Neumann master (LvNM) equation describing the time evolution of the density operator representing the state of the system. A unifying setting is provided to discuss optimalcontrol and exactcontrollability results. Different controllability results for the LvNM model are given, and necessary optimality conditions for the LvNM control problems are analyzed. Existence and regularity of optimal controls are proved. The computational framework is based on matrixfree reducedHessian semismooth KrylovNewton schemes for solving optimalcontrol problems of the LvNM equation in a real vector space rotatingframe representation. A continuation technique is designed to solve closed spin exactcontrollability problems that is based on the solution of an appropriately formulated optimalcontrol problem. These computational strategies are put into a rigorous theoretical framework, proving convergence to the solutions sought. Results of numerical experiments validate the theoretical results and demonstrate the computational ability of the proposed framework to solve closed quantum spin control problems.

Subject (DDC):  510 Mathematics 
Files  Size  Format  View 

There are no files associated with this item. 
CIARAMELLA, Gabriele, Alfio BORZÌ, Gunther DIRR, Daniel WACHSMUTH, 2015. Newton Methods for the Optimal Control of Closed Quantum Spin Systems. In: SIAM Journal on Scientific Computing. 37(1), pp. A319A346. ISSN 10648275. eISSN 10957197. Available under: doi: 10.1137/140966988
@article{Ciaramella201501Newto41217, title={Newton Methods for the Optimal Control of Closed Quantum Spin Systems}, year={2015}, doi={10.1137/140966988}, number={1}, volume={37}, issn={10648275}, journal={SIAM Journal on Scientific Computing}, pages={A319A346}, author={Ciaramella, Gabriele and Borzì, Alfio and Dirr, Gunther and Wachsmuth, Daniel} }
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22rdfsyntaxns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digitalrepositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.unikonstanz.de/rdf/resource/123456789/41217"> <dc:creator>Borzì, Alfio</dc:creator> <dcterms:abstract xml:lang="eng">An efficient and robust computational framework for solving closed quantum spin optimalcontrol and exactcontrollability problems with control constraints is presented. Closed spin systems are of fundamental importance in modern quantum technologies such as nuclear magnetic resonance (NMR) spectroscopy, quantum imaging, and quantum computing. These systems are modeled by the Liouvillevon Neumann master (LvNM) equation describing the time evolution of the density operator representing the state of the system. A unifying setting is provided to discuss optimalcontrol and exactcontrollability results. Different controllability results for the LvNM model are given, and necessary optimality conditions for the LvNM control problems are analyzed. Existence and regularity of optimal controls are proved. The computational framework is based on matrixfree reducedHessian semismooth KrylovNewton schemes for solving optimalcontrol problems of the LvNM equation in a real vector space rotatingframe representation. A continuation technique is designed to solve closed spin exactcontrollability problems that is based on the solution of an appropriately formulated optimalcontrol problem. These computational strategies are put into a rigorous theoretical framework, proving convergence to the solutions sought. Results of numerical experiments validate the theoretical results and demonstrate the computational ability of the proposed framework to solve closed quantum spin control problems.</dcterms:abstract> <dc:language>eng</dc:language> <dcterms:title>Newton Methods for the Optimal Control of Closed Quantum Spin Systems</dcterms:title> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:contributor>Dirr, Gunther</dc:contributor> <dc:contributor>Ciaramella, Gabriele</dc:contributor> <dc:contributor>Wachsmuth, Daniel</dc:contributor> <dc:creator>Dirr, Gunther</dc:creator> <bibo:uri rdf:resource="https://kops.unikonstanz.de/handle/123456789/41217"/> <dc:creator>Ciaramella, Gabriele</dc:creator> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20180202T13:52:48Z</dcterms:available> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:isPartOf rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/39"/> <dspace:isPartOfCollection rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/39"/> <dc:contributor>Borzì, Alfio</dc:contributor> <dc:creator>Wachsmuth, Daniel</dc:creator> <dcterms:issued>201501</dcterms:issued> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20180202T13:52:48Z</dc:date> </rdf:Description> </rdf:RDF>