{"id":"https://openalex.org/W2986104803","doi":"https://doi.org/10.1109/tac.2019.2950559","title":"Sub-Riemannian Geodesics in $SU(n)/S(U(n-1) \\times U(1))$ and Optimal Control of Three Level Quantum Systems","display_name":"Sub-Riemannian Geodesics in $SU(n)/S(U(n-1) \\times U(1))$ and Optimal Control of Three Level Quantum Systems","publication_year":2019,"publication_date":"2019-10-30","ids":{"openalex":"https://openalex.org/W2986104803","doi":"https://doi.org/10.1109/tac.2019.2950559","mag":"2986104803"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2019.2950559","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2019.2950559","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11577/3317320","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042084730","display_name":"Francesca Albertini","orcid":null},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Francesca Albertini","raw_affiliation_strings":["Dipartimento di Tecnica e Gestione dei Sistemi Industriali, Universit\u00e0 di Padova, Padova, Italy"],"raw_orcid":"https://orcid.org/0000-0003-2168-9997","affiliations":[{"raw_affiliation_string":"Dipartimento di Tecnica e Gestione dei Sistemi Industriali, Universit\u00e0 di Padova, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008152552","display_name":"Domenico D\u2019Alessandro","orcid":"https://orcid.org/0000-0003-0179-7157"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Domenico D'Alessandro","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, USA"],"raw_orcid":"https://orcid.org/0000-0003-0179-7157","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, USA","institution_ids":["https://openalex.org/I173911158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068155755","display_name":"Benjamin Sheller","orcid":"https://orcid.org/0000-0001-6699-0797"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Benjamin Sheller","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, USA"],"raw_orcid":"https://orcid.org/0000-0001-6699-0797","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, USA","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5042084730"],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":null,"apc_paid":null,"fwci":0.3312,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.55906418,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"65","issue":"3","first_page":"1176","last_page":"1191"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds","score":0.984499990940094,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.9828000068664551,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5785795450210571},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.5768125057220459},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.5404170155525208},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5291818976402283},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4919254779815674},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4777609407901764},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.46531298756599426},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.4274205267429352},{"id":"https://openalex.org/keywords/quantum-system","display_name":"Quantum system","score":0.42147740721702576},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.3820822238922119},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3735244870185852},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32844656705856323},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3263165354728699},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26284685730934143},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19374167919158936},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.15434712171554565},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1477743685245514}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5785795450210571},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.5768125057220459},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.5404170155525208},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5291818976402283},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4919254779815674},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4777609407901764},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.46531298756599426},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.4274205267429352},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.42147740721702576},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3820822238922119},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3735244870185852},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32844656705856323},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3263165354728699},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26284685730934143},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19374167919158936},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.15434712171554565},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1477743685245514}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tac.2019.2950559","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2019.2950559","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:www.research.unipd.it:11577/3317320","is_oa":true,"landing_page_url":"http://hdl.handle.net/11577/3317320","pdf_url":null,"source":{"id":"https://openalex.org/S4377196283","display_name":"Research Padua  Archive (University of Padua)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:zenodo.org:103083","is_oa":true,"landing_page_url":"https://www.openaccessrepository.it/record/103083","pdf_url":null,"source":{"id":"https://openalex.org/S4306402478","display_name":"INFM-OAR (INFN Catania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210116497","host_organization_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Catania","host_organization_lineage":["https://openalex.org/I4210116497"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:www.research.unipd.it:11577/3317320","is_oa":true,"landing_page_url":"http://hdl.handle.net/11577/3317320","pdf_url":null,"source":{"id":"https://openalex.org/S4377196283","display_name":"Research Padua  Archive (University of Padua)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"score":0.8700000047683716,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G2910434282","display_name":null,"funder_award_id":"1710558","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3030888803","display_name":null,"funder_award_id":"ECCS 1710558","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5604743328","display_name":null,"funder_award_id":"1710558","funder_id":"https://openalex.org/F4320337392","funder_display_name":"Division of Electrical, Communications and Cyber Systems"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337392","display_name":"Division of Electrical, Communications and Cyber Systems","ror":"https://ror.org/01krpsy48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W567358997","https://openalex.org/W1511073412","https://openalex.org/W1515066108","https://openalex.org/W1595765050","https://openalex.org/W1631356911","https://openalex.org/W1778500158","https://openalex.org/W1865865506","https://openalex.org/W1983894121","https://openalex.org/W2005656891","https://openalex.org/W2024283190","https://openalex.org/W2047758537","https://openalex.org/W2052997814","https://openalex.org/W2057285417","https://openalex.org/W2083802218","https://openalex.org/W2084545094","https://openalex.org/W2084864304","https://openalex.org/W2100799692","https://openalex.org/W2103901535","https://openalex.org/W2364556952","https://openalex.org/W2496556349","https://openalex.org/W2501142942","https://openalex.org/W2764347725","https://openalex.org/W2963160845","https://openalex.org/W2963565741","https://openalex.org/W2969707820","https://openalex.org/W3037952079","https://openalex.org/W3161114015","https://openalex.org/W4210956211","https://openalex.org/W4292743191","https://openalex.org/W6767772469"],"related_works":["https://openalex.org/W1978591761","https://openalex.org/W2941285539","https://openalex.org/W4287661821","https://openalex.org/W4353103777","https://openalex.org/W2950657073","https://openalex.org/W2951269968","https://openalex.org/W2946352054","https://openalex.org/W3127827089","https://openalex.org/W4386555091","https://openalex.org/W2953331129"],"abstract_inverted_index":{"We":[0,118,136,147,173],"study":[1],"the":[2,8,17,20,24,82,112,130,144,149,154,162,167,175],"time":[3],"optimal":[4,151],"control":[5,21,152],"problem":[6,42,113,177,183],"for":[7,153,191],"evolution":[9],"operator":[10],"of":[11,84,123,132,140,156,195],"an":[12,120,179],"n-level":[13],"quantum":[14,159],"system.":[15],"For":[16],"considered":[18],"models,":[19],"couples":[22],"all":[23],"energy":[25,170],"levels":[26,171],"to":[27,34,105,178],"a":[28,44,71,93,107,115,125,133,192],"given":[29,145],"one":[30],"and":[31,56,77,110],"is":[32,43,64,165],"assumed":[33],"be":[35],"bounded":[36],"in":[37,50],"Euclidean":[38],"norm.":[39],"The":[40],"resulting":[41],"sub-Riemannian":[45,141],"K-P":[46],"problem,":[47],"(as":[48],"introduced":[49,73],"articles":[51],"by":[52,57,74],"U.":[53],"Boscain":[54],"etal.":[55],"V.":[58],"Jurdjevic),":[59],"whose":[60],"underlying":[61],"symmetric":[62],"space":[63,127],"SU(n)/S(U(n":[65],"-":[66,86],"1)":[67,87],"\u00d7":[68,88],"U(1)).":[69],"Following":[70],"method":[72],"F.":[75],"Albertini":[76],"D.":[78],"D'Alessandro,":[79],"we":[80,188],"consider":[81,111],"action":[83],"S(U(n":[85],"U(1))":[89],"on":[90,114,166],"SU(n)":[91],"as":[92],"conjugation":[94],"X":[95],"\u2192":[96],"KXK":[97],"<sup":[98],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[99],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-1</sup>":[100],".":[101],"This":[102],"allows":[103],"us":[104],"do":[106],"symmetry":[108],"reduction":[109],"quotient":[116,126],"space.":[117,135],"give":[119],"explicit":[121,150],"description":[122],"such":[124],"which":[128,187],"has":[129],"structure":[131],"stratified":[134],"prove":[137],"several":[138],"properties":[139],"problems":[142],"with":[143,184],"structure.":[146],"derive":[148],"case":[155],"three":[157],"level":[158],"systems":[160],"where":[161],"desired":[163],"operation":[164],"lowest":[168],"two":[169],"(A-systems).":[172],"reduce":[174],"latter":[176],"integer":[180],"quadratic":[181],"optimization":[182],"linear":[185],"constraints,":[186],"solve":[189],"completely":[190],"specific":[193],"set":[194],"final":[196],"data.":[197]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}