{"id":"https://openalex.org/W2124282981","doi":null,"title":"Complexity for the approximation of Sobolev imbeddings in the quantum computation model","display_name":"Complexity for the approximation of Sobolev imbeddings in the quantum computation model","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2124282981","mag":"2124282981"},"language":"en","primary_location":{"id":"mag:3143448286","doi":null,"is_oa":false,"landing_page_url":"http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.ieee-000006000458","pdf_url":null,"source":{"id":"https://openalex.org/S4363607703","display_name":"Chinese Control Conference (CCC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Chinese Control Conference","raw_type":null},"volume":null,"type":"conference-paper","indexed_in":[],"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/A5003009611","display_name":"Jingfan Long","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I78675632","display_name":"Beijing Information Science & Technology University","ror":"https://ror.org/04xnqep60","country_code":"CN","type":"education","lineage":["https://openalex.org/I78675632"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jingfan Long","raw_affiliation_strings":["Beijing Information Science and Technology University, 100101, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Information Science and Technology University, 100101, China","institution_ids":["https://openalex.org/I78675632"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010523186","display_name":"Peixin Ye","orcid":"https://orcid.org/0000-0002-4706-3223","observed_orcids":["https://orcid.org/0000-0002-4706-3223"]},"institutions":[{"id":"https://openalex.org/I78675632","display_name":"Beijing Information Science & Technology University","ror":"https://ror.org/04xnqep60","country_code":"CN","type":"education","lineage":["https://openalex.org/I78675632"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peixin Ye","raw_affiliation_strings":["Beijing Information Science and Technology University, 100101, China"],"raw_orcid":"https://orcid.org/0000-0002-4706-3223","affiliations":[{"raw_affiliation_string":"Beijing Information Science and Technology University, 100101, China","institution_ids":["https://openalex.org/I78675632"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101804839","display_name":"Xiuhua Yuan","orcid":"https://orcid.org/0000-0003-3300-6639","observed_orcids":["https://orcid.org/0000-0003-3300-6639","https://orcid.org/0000-0002-5648-031X"]},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiuhua Yuan","raw_affiliation_strings":["School of Mathematics and LPMC, Nankai University, Tianjin 300071, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and LPMC, Nankai University, Tianjin 300071, China#TAB#","institution_ids":["https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18663254,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"5319","last_page":"5323"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9883000254631042,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9883000254631042,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.006200000178068876,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0012000000569969416,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-complexity","display_name":"quantum complexity","score":0.6930000185966492},{"id":"https://openalex.org/keywords/sobolev-embeddings","display_name":"Sobolev embeddings","score":0.8059999942779541},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.7300000190734863},{"id":"https://openalex.org/keywords/quantum-algorithms","display_name":"quantum algorithms","score":0.7950000166893005},{"id":"https://openalex.org/keywords/approximation-algorithms","display_name":"approximation algorithms","score":0.4569999873638153},{"id":"https://openalex.org/keywords/quantum-advantage","display_name":"quantum advantage","score":0.5260000228881836},{"id":"https://openalex.org/keywords/function-spaces","display_name":"function spaces","score":0.3230000138282776}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7305837273597717},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6963689923286438},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.593456506729126},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.5863204598426819},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5764565467834473},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5196660757064819},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4946300685405731},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4761476516723633},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.457492470741272},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4405204951763153},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4188215732574463},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4124721586704254},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34195733070373535},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30069804191589355},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2705078721046448},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.23363429307937622},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22658005356788635},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1847957968711853},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"mag:3143448286","doi":null,"is_oa":false,"landing_page_url":"http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.ieee-000006000458","pdf_url":null,"source":{"id":"https://openalex.org/S4363607703","display_name":"Chinese Control Conference (CCC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Chinese Control Conference","raw_type":null},{"id":"mag:2124282981","doi":null,"is_oa":false,"landing_page_url":"http://ieeexplore.ieee.org/iel5/5980617/6000362/06000458.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4363607703","display_name":"Chinese Control Conference (CCC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Chinese Control Conference","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1500118058","https://openalex.org/W1545025828","https://openalex.org/W1631356911","https://openalex.org/W1967601378","https://openalex.org/W1981183585","https://openalex.org/W1984361215","https://openalex.org/W1990788918","https://openalex.org/W2008891665","https://openalex.org/W2018527921","https://openalex.org/W2018655598","https://openalex.org/W2029029634","https://openalex.org/W2033084728","https://openalex.org/W2067134471","https://openalex.org/W2146537406","https://openalex.org/W2148132004","https://openalex.org/W2179731956","https://openalex.org/W2970070367","https://openalex.org/W3106123690"],"related_works":["https://openalex.org/W1984321582","https://openalex.org/W2159311700","https://openalex.org/W2102247346","https://openalex.org/W2000191983","https://openalex.org/W1963539121","https://openalex.org/W2170939697","https://openalex.org/W1971275002","https://openalex.org/W2023347923","https://openalex.org/W567136971","https://openalex.org/W2156536167"],"abstract_inverted_index":{"Using":[0],"a":[1,9],"new":[2],"and":[3,84],"elegant":[4],"reduction":[5],"approach":[6],"we":[7,73],"derive":[8],"lower":[10],"bound":[11,49],"of":[12,18],"quantum":[13,56,76],"complexity":[14],"for":[15,36],"the":[16,55,63,81,92],"approximation":[17],"imbeddings":[19],"from":[20],"anisotropic":[21,29],"Sobolev":[22,30],"classes":[23],"B(W":[24],"p":[25,33,45,70],"r([0,":[26],"1]d))":[27],"to":[28],"space":[31],"W":[32],"s([0,":[34],"1]d)":[35],"all":[37],"1":[38],"\u2264":[39,42],"p,":[40],"q":[41,47,72],"\u221e.":[43],"When":[44,69],"\u2265":[46,71],"this":[48,53],"is":[50],"optimal.":[51],"In":[52],"case":[54],"algorithms":[57,77],"are":[58],"not":[59],"significantly":[60],"better":[61],"than":[62],"classical":[64,82],"deterministic":[65,83],"or":[66],"randomized":[67,85],"algorithms.":[68],"conjecture":[74,88],"that":[75],"bring":[78],"speed-up":[79],"over":[80],"ones.":[86],"This":[87],"was":[89],"confirmed":[90],"in":[91],"situation":[93],"s":[94],"=":[95],"0.":[96]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2016-06-24T00:00:00"}