{"id":"https://openalex.org/W2140283128","doi":"https://doi.org/10.1109/cdc.2005.1582652","title":"Time Minimal Trajectories for two-level Quantum Systems with Drift","display_name":"Time Minimal Trajectories for two-level Quantum Systems with Drift","publication_year":2006,"publication_date":"2006-10-04","ids":{"openalex":"https://openalex.org/W2140283128","doi":"https://doi.org/10.1109/cdc.2005.1582652","mag":"2140283128"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2005.1582652","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2005.1582652","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 44th IEEE Conference on Decision and Control","raw_type":"proceedings-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/A5012657462","display_name":"Ugo Boscain","orcid":"https://orcid.org/0000-0001-5450-275X"},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"U. Boscain","raw_affiliation_strings":["SISSA, Trieste, Italy","SISSA, via Beirut 2-4 34014 Trieste, Italy. e-mail boscain@sissa.it"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SISSA, Trieste, Italy","institution_ids":["https://openalex.org/I138549579"]},{"raw_affiliation_string":"SISSA, via Beirut 2-4 34014 Trieste, Italy. e-mail boscain@sissa.it","institution_ids":["https://openalex.org/I138549579"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053579534","display_name":"Paolo Mason","orcid":"https://orcid.org/0000-0002-2583-9991"},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"P. Mason","raw_affiliation_strings":["SISSA, Trieste, Italy","International School for Advanced Studies"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SISSA, Trieste, Italy","institution_ids":["https://openalex.org/I138549579"]},{"raw_affiliation_string":"International School for Advanced Studies","institution_ids":["https://openalex.org/I138549579"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2586,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.61987084,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"43","issue":null,"first_page":"3188","last_page":"3193"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11414","display_name":"Quantum optics and atomic interactions","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T11414","display_name":"Quantum optics and atomic interactions","score":0.9984999895095825,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10566","display_name":"Laser-Matter Interactions and Applications","score":0.9962999820709229,"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/trajectory","display_name":"Trajectory","score":0.6672878265380859},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.642848789691925},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.5785062909126282},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5612350106239319},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5174063444137573},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5083484053611755},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.49884676933288574},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.48603349924087524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46997541189193726},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.41071081161499023},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3933750092983246},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35208016633987427},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2996578812599182},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28202277421951294},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22280481457710266},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1997033655643463},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.19668981432914734},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18872708082199097},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.16677409410476685}],"concepts":[{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6672878265380859},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.642848789691925},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.5785062909126282},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5612350106239319},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5174063444137573},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5083484053611755},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.49884676933288574},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.48603349924087524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46997541189193726},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.41071081161499023},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3933750092983246},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35208016633987427},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2996578812599182},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28202277421951294},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22280481457710266},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1997033655643463},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.19668981432914734},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18872708082199097},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.16677409410476685},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cdc.2005.1582652","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2005.1582652","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 44th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.251.5359","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.251.5359","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/quant-ph/0502151v1.pdf","raw_type":"text"},{"id":"pmh:oai:cds.cern.ch:824563","is_oa":false,"landing_page_url":"http://cds.cern.ch/record/824563","pdf_url":null,"source":{"id":"https://openalex.org/S4306402194","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W598851308","https://openalex.org/W1490418572","https://openalex.org/W1580797458","https://openalex.org/W1587799944","https://openalex.org/W1595765050","https://openalex.org/W1968195054","https://openalex.org/W2004953010","https://openalex.org/W2091697047","https://openalex.org/W2147733222","https://openalex.org/W2166662778","https://openalex.org/W2985141412","https://openalex.org/W3206777520","https://openalex.org/W4365787134"],"related_works":["https://openalex.org/W4323768008","https://openalex.org/W1941703695","https://openalex.org/W4248382324","https://openalex.org/W3131574667","https://openalex.org/W4360995134","https://openalex.org/W3023605104","https://openalex.org/W2039473718","https://openalex.org/W2387529410","https://openalex.org/W2383578611","https://openalex.org/W3013085049"],"abstract_inverted_index":{"On":[0,32,138],"a":[1,38,98],"two-level":[2],"quantum":[3],"system":[4],"driven":[5],"by":[6],"an":[7],"external":[8],"field,":[9],"we":[10,77,166,185],"consider":[11],"the":[12,17,20,24,33,58,64,67,79,83,88,92,118,126,129,139,146,151,155,173,178,203],"population":[13],"transfer":[14],"problem":[15,43],"from":[16],"first":[18],"to":[19,91,154,176,182],"second":[21],"level,":[22],"minimizing":[23],"time":[25,84,110,147,174],"of":[26,49,73,82,97,125,128,193],"transfer,":[27],"with":[28,47,123,160,189,199],"bounded":[29],"field":[30,68],"amplitude.":[31,69],"Bloch":[34],"sphere":[35],"(i.e.":[36],"after":[37],"suitable":[39],"Hopf":[40],"projection),":[41],"this":[42],"can":[44],"be":[45,57,102],"attacked":[46],"techniques":[48],"optimal":[50,85,111,148],"syntheses":[51],"on":[52,66],"2-D":[53],"manifolds.":[54],"Let":[55],"(\u2212E,E)":[56],"two":[59,94,157,180],"energy":[60],"levels,":[61],"and":[62,75,115,196,198],"[equacion]":[63],"bound":[65],"For":[70,105],"each":[71],"values":[72],"E":[74,145,165],"M,":[76],"provide":[78],"explicit":[80],"expression":[81],"trajectory":[86,112,149],"steering":[87,150],"state":[89,93,152,156,179],"one":[90,153,162],"in":[95,116,202],"terms":[96],"parameter":[99],"that":[100,169],"should":[101],"computed":[103],"numerically.":[104],"M":[106,143,171],"<<":[107],"E,":[108],"every":[109],"is":[113,121,158],"bang-bang":[114,159],"particular":[117],"corresponding":[119],"control":[120],"periodic":[122],"frequency":[124,131],"order":[127],"resonance":[130],"\u03c9":[132],"<inf":[133],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[134],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">R</inf>":[135],"=":[136],"2E.":[137],"other":[140],"side,":[141],"for":[142,170],">":[144],"exactly":[161],"switching.":[163],"Fixed":[164],"also":[167],"prove":[168],"\u2192\u221e":[172],"needed":[175],"reach":[177],"tends":[181],"zero.":[183],"Finally":[184],"compare":[186],"these":[187],"results":[188,192],"some":[190],"known":[191],"Khaneja,":[194],"Brockett":[195],"Glaser":[197],"those":[200],"obtained":[201],"Rotating":[204],"Wave":[205],"Approximation.":[206]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}