{"id":"https://openalex.org/W7214955496","doi":"https://doi.org/10.48550/arxiv.2609.38073","title":"Optimal Quantum-Classical Separations for Exact Learning","display_name":"Optimal Quantum-Classical Separations for Exact Learning","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214955496","doi":"https://doi.org/10.48550/arxiv.2609.38073"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.38073","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.38073","pdf_url":"https://arxiv.org/pdf/2609.38073","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.38073","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153607416","display_name":"Srinivasan Arunachalam","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Arunachalam, Srinivasan","raw_affiliation_strings":["IBM Research"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Research","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018608700","display_name":"Amin Shiraz Gilani","orcid":"https://orcid.org/0000-0003-0859-7254","observed_orcids":["https://orcid.org/0000-0003-0859-7254"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gilani, Amin Shiraz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5027137684","display_name":"Nikhil S. Mande","orcid":"https://orcid.org/0000-0002-9520-7340","observed_orcids":["https://orcid.org/0000-0002-9520-7340"]},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Mande, Nikhil S.","raw_affiliation_strings":["University of Liverpool"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Liverpool","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9922000169754028,"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":0.9922000169754028,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.003800000064074993,"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"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.0007999999797903001,"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/exact-learning","display_name":"exact learning","score":0.8100000023841858},{"id":"https://openalex.org/keywords/membership-queries","display_name":"membership queries","score":0.9869999885559082},{"id":"https://openalex.org/keywords/quantum-query-complexity","display_name":"quantum query complexity","score":0.8939999938011169},{"id":"https://openalex.org/keywords/randomized-query-complexity","display_name":"randomized query complexity","score":0.9879999756813049},{"id":"https://openalex.org/keywords/quantum-advantage","display_name":"quantum advantage","score":0.6620000004768372},{"id":"https://openalex.org/keywords/grover-s-algorithm","display_name":"Grover's algorithm","score":0.8560000061988831},{"id":"https://openalex.org/keywords/bernstein-vazirani-algorithm","display_name":"Bernstein-Vazirani algorithm","score":0.9089999794960022},{"id":"https://openalex.org/keywords/concept-classes","display_name":"concept classes","score":0.7179999947547913},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.4519999921321869}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7832000255584717},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7304999828338623},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.644599974155426},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5640000104904175},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5562999844551086},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43070000410079956},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.414000004529953},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3776000142097473},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.29490000009536743},{"id":"https://openalex.org/C176248197","wikidata":"https://www.wikidata.org/wiki/Q458526","display_name":"Probably approximately correct learning","level":4,"score":0.26510000228881836},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.260699987411499},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.25859999656677246}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.38073","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.38073","pdf_url":"https://arxiv.org/pdf/2609.38073","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2609.38073","doi":"https://doi.org/10.48550/arxiv.2609.38073","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.38073","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.38073","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.38073","pdf_url":"https://arxiv.org/pdf/2609.38073","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214955496.pdf","grobid_xml":"https://content.openalex.org/works/W7214955496.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2966837591","https://openalex.org/W6997115928","https://openalex.org/W2585533438","https://openalex.org/W2727364023","https://openalex.org/W2101429643","https://openalex.org/W1987965590","https://openalex.org/W2009155360","https://openalex.org/W7096073408","https://openalex.org/W2800973926","https://openalex.org/W7127449103"],"abstract_inverted_index":{"We":[0,60],"study":[1],"exact":[2],"learning":[3,157],"with":[4],"membership":[5],"queries":[6],"for":[7,156],"concept":[8,67],"classes":[9,68],"$\\mathcal":[10,69,72],"C\\subseteq\\{0,1\\}^N$,":[11],"focusing":[12],"on":[13,132],"the":[14,50,92,104,107,119,122,137,149,161],"relationships":[15],"among":[16],"their":[17],"deterministic,":[18],"randomized,":[19],"and":[20,29,46,71,112,142,163],"quantum":[21,36,143,154],"query":[22,144],"complexities,":[23],"denoted":[24],"$\\mathsf{D}(\\mathcal":[25],"C)$,":[26,28,31],"$\\mathsf{R}(\\mathcal":[27],"$\\mathsf{Q}(\\mathcal":[30],"respectively.":[32],"The":[33,88],"two":[34],"canonical":[35],"speedups":[37,155],"in":[38,121],"this":[39,63,116],"model":[40],"are":[41,148],"witnessed":[42],"by":[43,65],"Grover":[44,162],"search":[45],"Bernstein-Vazirani,":[47],"leading":[48],"to":[49,100,151],"longstanding":[51],"conjecture":[52,64],"$$":[53,59],"\\mathsf{R}(\\mathcal":[54,76],"C)=O(\\mathsf{Q}(\\mathcal":[55],"C)^2+\\mathsf{Q}(\\mathcal":[56],"C)\\log":[57],"N).":[58,86],"first":[61,89,150],"refute":[62],"constructing":[66],"C$":[70],"C'$":[73],"satisfying":[74],"\\[":[75],"C)=\u03a9\\!\\left(\\frac{\\mathsf{Q}(\\mathcal":[77],"C)^3\\log":[78],"N}{\\log":[79],"\\mathsf{Q}(\\mathcal":[80],"C)}\\right)":[81],"\\qquad\\text{and}\\qquad":[82],"\\mathsf{D}(\\mathcal":[83],"C')=\u03a9(\\mathsf{Q}(\\mathcal":[84],"C')^3\\log":[85],"\\]":[87],"bound":[90,94,109,125],"matches":[91,106],"upper":[93,108,124],"of":[95,110,126],"Arunachalam":[96,127],"et":[97,128],"al.~[Quantum'21]":[98],"up":[99],"constant":[101],"factors,":[102],"while":[103],"second":[105],"Servedio":[111],"Gortler~[SICOMP'04].":[113],"In":[114],"particular,":[115],"shows":[117],"that":[118,153],"saving":[120],"randomized":[123],"al.":[129],"fundamentally":[130],"relies":[131],"randomness.":[133],"Apart":[134],"from":[135],"characterizing":[136],"optimal":[138],"relationship":[139],"between":[140],"classical":[141],"complexity,":[145],"our":[146],"results":[147],"show":[152],"can":[158],"go":[159],"beyond":[160],"Bernstein-Vazirani":[164],"paradigms.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}