{"id":"https://openalex.org/W4404417871","doi":"https://doi.org/10.3390/e26110978","title":"Quantum Control Design by Lyapunov Trajectory Tracking and Optimal Control","display_name":"Quantum Control Design by Lyapunov Trajectory Tracking and Optimal Control","publication_year":2024,"publication_date":"2024-11-15","ids":{"openalex":"https://openalex.org/W4404417871","doi":"https://doi.org/10.3390/e26110978","pmid":"https://pubmed.ncbi.nlm.nih.gov/39593922"},"language":"en","primary_location":{"id":"doi:10.3390/e26110978","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26110978","pdf_url":"https://www.mdpi.com/1099-4300/26/11/978/pdf?version=1731651718","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/26/11/978/pdf?version=1731651718","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102884345","display_name":"Hongli Yang","orcid":"https://orcid.org/0000-0002-8259-5241"},"institutions":[{"id":"https://openalex.org/I4210155952","display_name":"Qingdao Huanghai University","ror":"https://ror.org/05e1zbn94","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210155952"]},{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongli Yang","raw_affiliation_strings":["College of Big Data, Qingdao Huanghai University, Qingdao 266427, China","College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"],"raw_orcid":"https://orcid.org/0000-0002-8259-5241","affiliations":[{"raw_affiliation_string":"College of Big Data, Qingdao Huanghai University, Qingdao 266427, China","institution_ids":["https://openalex.org/I4210155952"]},{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5098444914","display_name":"Guohui Yu","orcid":null},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guohui Yu","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101948369","display_name":"Ivan Ivanov","orcid":"https://orcid.org/0000-0002-9019-072X"},"institutions":[{"id":"https://openalex.org/I58918642","display_name":"Sofia University \"St. Kliment Ohridski\"","ror":"https://ror.org/02jv3k292","country_code":"BG","type":"education","lineage":["https://openalex.org/I58918642"]}],"countries":["BG"],"is_corresponding":true,"raw_author_name":"Ivan Ganchev Ivanov","raw_affiliation_strings":["Faculty of Economics and Business Administration, St. Kl. Ohridski Sofia University, 1113 Sofia, Bulgaria"],"raw_orcid":"https://orcid.org/0000-0002-9019-072X","affiliations":[{"raw_affiliation_string":"Faculty of Economics and Business Administration, St. Kl. Ohridski Sofia University, 1113 Sofia, Bulgaria","institution_ids":["https://openalex.org/I58918642"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101948369","https://openalex.org/A5102884345"],"corresponding_institution_ids":["https://openalex.org/I4210155952","https://openalex.org/I58918642","https://openalex.org/I80143920"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17970401,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"11","first_page":"978","last_page":"978"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11993","display_name":"Atomic and Subatomic Physics Research","score":0.9976000189781189,"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/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.9968000054359436,"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":0.6582812666893005},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.62516188621521},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6032187342643738},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5250943899154663},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5210644602775574},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.5204855799674988},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5096347332000732},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.50932776927948},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5023422241210938},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4448798894882202},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.44398626685142517},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4281010031700134},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3815552890300751},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32320863008499146},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.28716790676116943},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23725083470344543},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09015971422195435},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08490639925003052}],"concepts":[{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6582812666893005},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.62516188621521},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6032187342643738},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5250943899154663},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5210644602775574},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.5204855799674988},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5096347332000732},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.50932776927948},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5023422241210938},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4448798894882202},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.44398626685142517},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4281010031700134},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3815552890300751},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32320863008499146},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28716790676116943},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23725083470344543},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09015971422195435},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08490639925003052},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e26110978","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26110978","pdf_url":"https://www.mdpi.com/1099-4300/26/11/978/pdf?version=1731651718","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:39593922","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39593922","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:11592483","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11592483","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11592483/pdf/entropy-26-00978.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:00124cb73fad4002b77742511ecdd3ca","is_oa":true,"landing_page_url":"https://doaj.org/article/00124cb73fad4002b77742511ecdd3ca","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 26, Iss 11, p 978 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e26110978","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26110978","pdf_url":"https://www.mdpi.com/1099-4300/26/11/978/pdf?version=1731651718","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8100000023841858}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4404417871.pdf"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1964074791","https://openalex.org/W1984122837","https://openalex.org/W2054931070","https://openalex.org/W2068209810","https://openalex.org/W2082468028","https://openalex.org/W2083494341","https://openalex.org/W2096501535","https://openalex.org/W2113593438","https://openalex.org/W2147733222","https://openalex.org/W2158618715","https://openalex.org/W2373107819","https://openalex.org/W2769672765","https://openalex.org/W2991597955","https://openalex.org/W3011988735","https://openalex.org/W3023938623","https://openalex.org/W3103348503","https://openalex.org/W3135030843","https://openalex.org/W3170955435","https://openalex.org/W4251770864","https://openalex.org/W4280620545","https://openalex.org/W4286001073","https://openalex.org/W4309789893","https://openalex.org/W4311329525","https://openalex.org/W4322502335","https://openalex.org/W4323044391","https://openalex.org/W4377691672","https://openalex.org/W4387523773","https://openalex.org/W4387883299","https://openalex.org/W4387924856","https://openalex.org/W4389326479","https://openalex.org/W4391154628","https://openalex.org/W4391813211","https://openalex.org/W6629075117","https://openalex.org/W6671192538"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W2030955003","https://openalex.org/W2374426356","https://openalex.org/W2059628530","https://openalex.org/W2164487476","https://openalex.org/W3194517843","https://openalex.org/W1977987201","https://openalex.org/W2106169668","https://openalex.org/W2534107666"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,49,56],"investigate":[4],"a":[5,13,17,45,83,88],"Lyapunov":[6],"trajectory":[7],"tracking":[8],"design":[9],"method":[10],"that":[11,25,39],"incorporates":[12],"Schr\u00f6dinger":[14],"equation":[15],"with":[16],"dipole":[18],"subterm":[19],"and":[20,61,87],"polarizability.":[21],"Our":[22],"findings":[23,75],"suggest":[24],"the":[26,32,66],"proposed":[27],"control":[28,37,53],"law":[29],"can":[30],"overcome":[31],"limitations":[33],"of":[34],"certain":[35],"existing":[36],"laws":[38],"do":[40],"not":[41],"converge.":[42],"By":[43],"integrating":[44],"quadratic":[46],"performance":[47],"index,":[48],"introduce":[50],"an":[51],"optimal":[52],"law,":[54],"which":[55],"subsequently":[57],"analyze":[58],"for":[59],"stability":[60],"optimality.":[62],"We":[63],"also":[64],"simulate":[65],"spin-1/2":[67,89],"particle":[68,90],"system":[69],"to":[70],"illustrate":[71],"our":[72],"results.":[73],"These":[74],"are":[76],"further":[77],"validated":[78],"through":[79],"numerical":[80],"illustrations":[81],"involving":[82],"3D,":[84],"5D":[85],"system,":[86],"system.":[91]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
