{"id":"https://openalex.org/W3161103151","doi":"https://doi.org/10.22331/q-2022-10-13-834","title":"Quantum Proofs of Proximity","display_name":"Quantum Proofs of Proximity","publication_year":2022,"publication_date":"2022-10-13","ids":{"openalex":"https://openalex.org/W3161103151","doi":"https://doi.org/10.22331/q-2022-10-13-834","mag":"3161103151"},"language":"en","primary_location":{"id":"doi:10.22331/q-2022-10-13-834","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-10-13-834","pdf_url":"https://quantum-journal.org/papers/q-2022-10-13-834/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2022-10-13-834/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100480934","display_name":"Marcel Dall apos Agnol","orcid":null},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Marcel Dall&apos;Agnol","raw_affiliation_strings":["Department of Computer Science, University of Warwick, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Warwick, UK","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074192050","display_name":"Tom Gur","orcid":"https://orcid.org/0000-0001-7864-7013"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Tom Gur","raw_affiliation_strings":["Department of Computer Science, University of Warwick, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Warwick, UK","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017675018","display_name":"Subhayan Roy Moulick","orcid":"https://orcid.org/0009-0002-5558-0017"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Subhayan Roy Moulik","raw_affiliation_strings":["Department of Mathematics, UC Berkeley, USA & Department of Computer Science, University of Oxford, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UC Berkeley, USA & Department of Computer Science, University of Oxford, UK","institution_ids":["https://openalex.org/I95457486","https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080601320","display_name":"Justin Thaler","orcid":"https://orcid.org/0009-0009-2234-6225"},"institutions":[{"id":"https://openalex.org/I184565670","display_name":"Georgetown University","ror":"https://ror.org/05vzafd60","country_code":"US","type":"education","lineage":["https://openalex.org/I184565670"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Justin Thaler","raw_affiliation_strings":["Department of Computer Science, Georgetown University, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Georgetown University, USA","institution_ids":["https://openalex.org/I184565670"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.1387,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.50890993,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"6","issue":null,"first_page":"834","last_page":"834"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9995999932289124,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9973000288009644,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.8018059730529785},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.6088629961013794},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.570993959903717},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5572265386581421},{"id":"https://openalex.org/keywords/property-testing","display_name":"Property testing","score":0.5120418667793274},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4889484643936157},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.4866548180580139},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.47017282247543335},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.46166709065437317},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.46158626675605774},{"id":"https://openalex.org/keywords/gas-meter-prover","display_name":"Gas meter prover","score":0.45880356431007385},{"id":"https://openalex.org/keywords/communication-complexity","display_name":"Communication complexity","score":0.4513520300388336},{"id":"https://openalex.org/keywords/quantum-complexity-theory","display_name":"Quantum complexity theory","score":0.450298011302948},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.4444602131843567},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.43501392006874084},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.41945239901542664},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.3988511264324188},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38633060455322266},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35940784215927124},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09353658556938171},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.08235403895378113}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8018059730529785},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.6088629961013794},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.570993959903717},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5572265386581421},{"id":"https://openalex.org/C123842658","wikidata":"https://www.wikidata.org/wiki/Q2918980","display_name":"Property testing","level":2,"score":0.5120418667793274},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4889484643936157},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.4866548180580139},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.47017282247543335},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.46166709065437317},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.46158626675605774},{"id":"https://openalex.org/C159718280","wikidata":"https://www.wikidata.org/wiki/Q5526353","display_name":"Gas meter prover","level":3,"score":0.45880356431007385},{"id":"https://openalex.org/C179145077","wikidata":"https://www.wikidata.org/wiki/Q5154130","display_name":"Communication complexity","level":2,"score":0.4513520300388336},{"id":"https://openalex.org/C92043244","wikidata":"https://www.wikidata.org/wiki/Q7269023","display_name":"Quantum complexity theory","level":4,"score":0.450298011302948},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.4444602131843567},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.43501392006874084},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.41945239901542664},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3988511264324188},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38633060455322266},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35940784215927124},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09353658556938171},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.08235403895378113},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.22331/q-2022-10-13-834","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-10-13-834","pdf_url":"https://quantum-journal.org/papers/q-2022-10-13-834/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:168802","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:2105.03697","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2105.03697","pdf_url":"https://arxiv.org/pdf/2105.03697","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:doaj.org/article:a2b4d27e79564ad39d2c1c806c09657b","is_oa":true,"landing_page_url":"https://doaj.org/article/a2b4d27e79564ad39d2c1c806c09657b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 6, p 834 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2022-10-13-834","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-10-13-834","pdf_url":"https://quantum-journal.org/papers/q-2022-10-13-834/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2291411185","display_name":null,"funder_award_id":"CCF-1845125","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3077665131","display_name":null,"funder_award_id":"2016245","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G394576491","display_name":null,"funder_award_id":"OMA-2016245","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4130051469","display_name":null,"funder_award_id":"MR/S031545/1","funder_id":"https://openalex.org/F4320314731","funder_display_name":"UK Research and Innovation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6795361454","display_name":null,"funder_award_id":"HR00112020022","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G7681175234","display_name":null,"funder_award_id":"CCF-1918989","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8051948103","display_name":"SPX: Automatically Parallelizing Approximate Data Analysis with Mergeable Summaries","funder_award_id":"1918989","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320314731","display_name":"UK Research and Innovation","ror":"https://ror.org/001aqnf71"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320336183","display_name":"Clarendon Fund","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3161103151.pdf","grobid_xml":"https://content.openalex.org/works/W3161103151.grobid-xml"},"referenced_works_count":104,"referenced_works":["https://openalex.org/W1465613978","https://openalex.org/W1602420091","https://openalex.org/W1614234223","https://openalex.org/W1642094981","https://openalex.org/W1837750740","https://openalex.org/W1845834564","https://openalex.org/W1944079109","https://openalex.org/W1971585707","https://openalex.org/W1980816908","https://openalex.org/W1990538552","https://openalex.org/W2000070319","https://openalex.org/W2020029222","https://openalex.org/W2029587304","https://openalex.org/W2031495811","https://openalex.org/W2033016443","https://openalex.org/W2038111284","https://openalex.org/W2043500043","https://openalex.org/W2044199052","https://openalex.org/W2051446825","https://openalex.org/W2053590396","https://openalex.org/W2056168287","https://openalex.org/W2058286540","https://openalex.org/W2061662395","https://openalex.org/W2084157340","https://openalex.org/W2100732817","https://openalex.org/W2100827027","https://openalex.org/W2107398173","https://openalex.org/W2108852611","https://openalex.org/W2114187680","https://openalex.org/W2121981260","https://openalex.org/W2135952940","https://openalex.org/W2144362128","https://openalex.org/W2146443256","https://openalex.org/W2160856947","https://openalex.org/W2193371463","https://openalex.org/W2277746100","https://openalex.org/W2337421628","https://openalex.org/W2347130195","https://openalex.org/W2397531432","https://openalex.org/W2472860399","https://openalex.org/W2473767456","https://openalex.org/W2508833075","https://openalex.org/W2578338218","https://openalex.org/W2610386774","https://openalex.org/W2611398525","https://openalex.org/W2611773579","https://openalex.org/W2649051464","https://openalex.org/W2742040237","https://openalex.org/W2758002822","https://openalex.org/W2769478807","https://openalex.org/W2771519522","https://openalex.org/W2783323265","https://openalex.org/W2784923214","https://openalex.org/W2811282363","https://openalex.org/W2884996813","https://openalex.org/W2887969491","https://openalex.org/W2897264299","https://openalex.org/W2904542722","https://openalex.org/W2912986841","https://openalex.org/W2942051472","https://openalex.org/W2942259633","https://openalex.org/W2943465565","https://openalex.org/W2949645943","https://openalex.org/W2950457543","https://openalex.org/W2951169248","https://openalex.org/W2963498695","https://openalex.org/W2967514345","https://openalex.org/W2973719433","https://openalex.org/W2982087871","https://openalex.org/W2990961515","https://openalex.org/W2997631494","https://openalex.org/W2998650203","https://openalex.org/W3003478940","https://openalex.org/W3016651332","https://openalex.org/W3021291082","https://openalex.org/W3021472282","https://openalex.org/W3036000280","https://openalex.org/W3084524042","https://openalex.org/W3092562962","https://openalex.org/W3095535646","https://openalex.org/W3097401090","https://openalex.org/W3100524017","https://openalex.org/W3101287583","https://openalex.org/W3101644211","https://openalex.org/W3101738067","https://openalex.org/W3102621335","https://openalex.org/W3104065018","https://openalex.org/W3106278932","https://openalex.org/W3115192023","https://openalex.org/W3122725086","https://openalex.org/W3126276693","https://openalex.org/W3126688003","https://openalex.org/W3156157822","https://openalex.org/W3168770271","https://openalex.org/W3185089760","https://openalex.org/W3194732277","https://openalex.org/W3217033513","https://openalex.org/W4213235348","https://openalex.org/W4235805661","https://openalex.org/W4239261415","https://openalex.org/W4247494971","https://openalex.org/W4289433287","https://openalex.org/W4300718172","https://openalex.org/W4307492550"],"related_works":["https://openalex.org/W2338630033","https://openalex.org/W4301013907","https://openalex.org/W2951836800","https://openalex.org/W2045590835","https://openalex.org/W2121507438","https://openalex.org/W2120210041","https://openalex.org/W2950910290","https://openalex.org/W4298273595","https://openalex.org/W2100732817","https://openalex.org/W2128158983"],"abstract_inverted_index":{"We":[0,198],"initiate":[1],"the":[2,9,75,103,180],"systematic":[3],"study":[4],"of":[5,11,25,71,78,93,105,140,160,171,182,213],"QMA":[6,19,176,202],"algorithms":[7,32],"in":[8,131],"setting":[10],"property":[12,50,116,209],"testing,":[13],"to":[14,37,45,113,178],"which":[15,217],"we":[16,101],"refer":[17],"as":[18],"<mml:math":[20,51,59,62,86,167,184,188],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow":[21],"class=\"MJX-TeXAtom-ORD\"><mml:mtext":[22],"class=\"MJX-tex-mathit\"":[23],"mathvariant=\"italic\">proofs":[24],"proximity</mml:mtext></mml:mrow></mml:math>":[26],"(QMAPs).":[27],"These":[28],"are":[29,43,58,165],"quantum":[30,96,115,153,221],"query":[31],"that":[33,57,82,151,164,210],"receive":[34],"explicit":[35],"access":[36],"a":[38,49,68,128,146,175,201,208,220],"sublinear-size":[39],"untrusted":[40],"proof":[41,196],"and":[42,54,95,108,135,195],"required":[44],"accept":[46],"inputs":[47,56],"having":[48],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi":[52,63],"mathvariant=\"normal\">&amp;#x03A0;</mml:mi></mml:math>":[53],"reject":[55],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>&amp;#x03B5;</mml:mi></mml:math>-far":[60],"from":[61,122],"mathvariant=\"normal\">&amp;#x03A0;</mml:mi></mml:math>,":[64],"while":[65],"only":[66],"probing":[67],"minuscule":[69],"portion":[70],"their":[72],"input.We":[73],"investigate":[74],"complexity":[76],"landscape":[77],"this":[79,99,172,214],"model,":[80],"showing":[81],"QMAPs":[83],"can":[84],"be":[85],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>e</mml:mi><mml:mi>x</mml:mi><mml:mi>p</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>l</mml:mi><mml:mi>y</mml:mi></mml:math>":[87],"stronger":[88],"than":[89],"both":[90],"classical":[91],"proofs":[92],"proximity":[94],"testers.":[97],"To":[98],"end,":[100],"extend":[102],"methodology":[104],"Blais,":[106],"Brody,":[107],"Matulef":[109],"(Computational":[110],"Complexity,":[111],"2012)":[112],"prove":[114],"testing":[117,156,205],"lower":[118],"bounds":[119],"via":[120],"reductions":[121],"communication":[123],"complexity.":[124],"This":[125],"also":[126,199],"resolves":[127],"question":[129],"raised":[130],"2013":[132],"by":[133],"Montanaro":[134],"de":[136],"Wolf":[137],"(cf.":[138],"Theory":[139],"Computing,":[141],"2016).Our":[142],"algorithmic":[143,149],"results":[144],"include":[145],"purpose":[147],"an":[148,157,183],"framework":[150,173],"enables":[152],"speedups":[154],"for":[155,204,216],"expressive":[158],"class":[159],"properties,":[161],"namely,":[162],"those":[163],"succinctly":[166],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>d</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>m</mml:mi><mml:mi>p</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mi>a</mml:mi><mml:mi>b</mml:mi><mml:mi>l</mml:mi><mml:mi>e</mml:mi></mml:math>.":[168],"A":[169],"consequence":[170],"is":[174,219],"algorithm":[177,203],"verify":[179],"Parity":[181],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>n</mml:mi></mml:math>-bit":[185],"string":[186],"with":[187],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>O</mml:mi><mml:mo":[189],"stretchy=\"false\">(</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mrow":[190],"class=\"MJX-TeXAtom-ORD\"><mml:mn>2</mml:mn><mml:mrow":[191],"class=\"MJX-TeXAtom-ORD\"><mml:mo>/</mml:mo></mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:mo":[192],"stretchy=\"false\">)</mml:mo></mml:math>":[193],"queries":[194],"length.":[197],"propose":[200],"graph":[206],"bipartitneness,":[207],"lies":[211],"outside":[212],"family,":[215],"there":[218],"speedup.":[222]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2021-05-24T00:00:00"}