{"id":"https://openalex.org/W2738602703","doi":"https://doi.org/10.1109/tac.2017.2727225","title":"The $K\\hbox{--}P$ Problem on Tensor Products of Lie Groups and Time-Optimal Control of $n$ Quantum Bits With a Bounded Field","display_name":"The $K\\hbox{--}P$ Problem on Tensor Products of Lie Groups and Time-Optimal Control of $n$ Quantum Bits With a Bounded Field","publication_year":2017,"publication_date":"2017-07-25","ids":{"openalex":"https://openalex.org/W2738602703","doi":"https://doi.org/10.1109/tac.2017.2727225","mag":"2738602703"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2017.2727225","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2727225","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042084730","display_name":"Francesca Albertini","orcid":"https://orcid.org/0000-0003-2168-9997"},"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"],"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":"last","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, IA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, IA, USA","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042084730"],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":null,"apc_paid":null,"fwci":0.3441,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.57103471,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"63","issue":"2","first_page":"518","last_page":"524"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10566","display_name":"Laser-Matter Interactions and Applications","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11414","display_name":"Quantum optics and atomic interactions","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7240834832191467},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5553221702575684},{"id":"https://openalex.org/keywords/quantum-control","display_name":"Quantum control","score":0.5495043992996216},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5306899547576904},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5146511793136597},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.4892001152038574},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.4889291822910309},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.45762619376182556},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4158349335193634},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.35031676292419434},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34988540410995483},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3252905011177063},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.27160152792930603},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22866004705429077}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7240834832191467},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5553221702575684},{"id":"https://openalex.org/C2984281365","wikidata":"https://www.wikidata.org/wiki/Q906781","display_name":"Quantum control","level":3,"score":0.5495043992996216},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5306899547576904},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5146511793136597},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.4892001152038574},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4889291822910309},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.45762619376182556},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4158349335193634},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.35031676292419434},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34988540410995483},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3252905011177063},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.27160152792930603},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22866004705429077}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2017.2727225","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2727225","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:11577/3257019","is_oa":false,"landing_page_url":"http://hdl.handle.net/11577/3257019","pdf_url":null,"source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.800000011920929}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W99367046","https://openalex.org/W168467620","https://openalex.org/W807650025","https://openalex.org/W1515066108","https://openalex.org/W1631356911","https://openalex.org/W1778500158","https://openalex.org/W1839422797","https://openalex.org/W1865865506","https://openalex.org/W1965743188","https://openalex.org/W1968085281","https://openalex.org/W1970803190","https://openalex.org/W1981989554","https://openalex.org/W1983894121","https://openalex.org/W1995990462","https://openalex.org/W2035225569","https://openalex.org/W2048130943","https://openalex.org/W2052997814","https://openalex.org/W2083978792","https://openalex.org/W2106693271","https://openalex.org/W2114265982","https://openalex.org/W2147733222","https://openalex.org/W2171971045","https://openalex.org/W2501142942","https://openalex.org/W2592232225","https://openalex.org/W2764347725","https://openalex.org/W2963565741","https://openalex.org/W2963864580","https://openalex.org/W3100690666","https://openalex.org/W3104824685","https://openalex.org/W4250514131","https://openalex.org/W6606808333","https://openalex.org/W6630964717","https://openalex.org/W6638990656","https://openalex.org/W6719291779"],"related_works":["https://openalex.org/W3013085049","https://openalex.org/W1560496689","https://openalex.org/W4386900933","https://openalex.org/W4385301946","https://openalex.org/W4297797135","https://openalex.org/W3125672081","https://openalex.org/W1673581201","https://openalex.org/W2991991550","https://openalex.org/W4386687603","https://openalex.org/W4307007469"],"abstract_inverted_index":{"We":[0],"use":[1],"properties":[2],"of":[3,26,60,99],"sub-Riemannian":[4],"<inline-formula":[5,16,27,46],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[6,17,28,47,82],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[7,18,29,48],"notation=\"LaTeX\">$K\\hbox{--}P$</tex-math>":[8],"</inline-formula>":[9,20,31],"problems":[10],"and":[11],"the":[12,23,57,61,71,80,87,97,107],"optimal":[13],"synthesis":[14],"on":[15],"notation=\"LaTeX\">$SU(2)$</tex-math>":[19],"to":[21],"solve":[22],"time-optimal":[24],"control":[25,42,98,108],"notation=\"LaTeX\">$n$</tex-math>":[30],"noninteracting":[32],"two-level":[33,100],"quantum":[34],"systems":[35,101],"(qubits)":[36],"controlled":[37,54],"in":[38,45],"parallel":[39],"with":[40,102],"a":[41,113],"field":[43],"bounded":[44,117],"notation=\"LaTeX\">$L_2$</tex-math></inline-formula>":[49],"norm.":[50],"Every":[51],"qubit":[52],"is":[53,64,94],"independently,":[55],"but":[56],"total":[58],"energy":[59],"controls":[62],"used":[63],"bounded.":[65],"For":[66],"this":[67],"system,":[68],"we":[69,78],"describe":[70],"reachable":[72],"set":[73],"at":[74],"every":[75],"time.":[76,90],"Moreover,":[77],"compute":[79],"<italic":[81],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">diameter</i>":[83],",":[84],"that":[85],"is,":[86],"worst-case":[88],"minimum":[89],"The":[91],"mathematical":[92],"problem":[93],"motivated":[95],"by":[96],"different":[103],"resonance":[104],"frequencies,":[105],"where":[106],"fields":[109],"are":[110],"obtained":[111],"from":[112],"single":[114],"signal":[115],"having":[116],"energy.":[118]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}