{"id":"https://openalex.org/W4225086382","doi":"https://doi.org/10.48550/arxiv.2204.12051","title":"Complexity of quantum circuits via sensitivity, magic, and coherence","display_name":"Complexity of quantum circuits via sensitivity, magic, and coherence","publication_year":2022,"publication_date":"2022-04-26","ids":{"openalex":"https://openalex.org/W4225086382","doi":"https://doi.org/10.48550/arxiv.2204.12051"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2204.12051","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2204.12051","pdf_url":"https://arxiv.org/pdf/2204.12051","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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2204.12051","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083926771","display_name":"Kaifeng Bu","orcid":"https://orcid.org/0000-0001-8419-8736"},"institutions":[{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bu, Kaifeng","raw_affiliation_strings":[") Harvard University, Cambridge, Massachusetts 02138, USA"],"affiliations":[{"raw_affiliation_string":") Harvard University, Cambridge, Massachusetts 02138, USA","institution_ids":["https://openalex.org/I2801851002"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070173582","display_name":"Roy J. Garcia","orcid":"https://orcid.org/0000-0003-0861-873X"},"institutions":[{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Garcia, Roy J.","raw_affiliation_strings":[") Harvard University, Cambridge, Massachusetts 02138, USA"],"affiliations":[{"raw_affiliation_string":") Harvard University, Cambridge, Massachusetts 02138, USA","institution_ids":["https://openalex.org/I2801851002"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103278449","display_name":"Arthur Jaffe","orcid":"https://orcid.org/0000-0003-4236-4833"},"institutions":[{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jaffe, Arthur","raw_affiliation_strings":[") Harvard University, Cambridge, Massachusetts 02138, USA"],"affiliations":[{"raw_affiliation_string":") Harvard University, Cambridge, Massachusetts 02138, USA","institution_ids":["https://openalex.org/I2801851002"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046561636","display_name":"Dax Enshan Koh","orcid":"https://orcid.org/0000-0002-8968-591X"},"institutions":[{"id":"https://openalex.org/I3004594783","display_name":"Institute of High Performance Computing","ror":"https://ror.org/02n0ejh50","country_code":"SG","type":"facility","lineage":["https://openalex.org/I115228651","https://openalex.org/I3004594783","https://openalex.org/I91275662"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Koh, Dax Enshan","raw_affiliation_strings":["COMPLEXITY OF QUANTUM CIRCUITS",") Institute of High Performance Computing, Agency for Science, Technology and Re-search (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore"],"affiliations":[{"raw_affiliation_string":"COMPLEXITY OF QUANTUM CIRCUITS","institution_ids":[]},{"raw_affiliation_string":") Institute of High Performance Computing, Agency for Science, Technology and Re-search (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore","institution_ids":["https://openalex.org/I3004594783"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100386329","display_name":"Lu Li","orcid":"https://orcid.org/0000-0002-6550-0626"},"institutions":[{"id":"https://openalex.org/I1328775524","display_name":"Zhejiang Sci-Tech University","ror":"https://ror.org/03893we55","country_code":"CN","type":"education","lineage":["https://openalex.org/I1328775524"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Lu","raw_affiliation_strings":[") Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China"],"affiliations":[{"raw_affiliation_string":") Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China","institution_ids":["https://openalex.org/I1328775524"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5083926771"],"corresponding_institution_ids":["https://openalex.org/I2801851002"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":7,"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":0.9976999759674072,"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":0.9976999759674072,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9591000080108643,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9347000122070312,"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/quantum-computer","display_name":"Quantum computer","score":0.612586259841919},{"id":"https://openalex.org/keywords/magic","display_name":"MAGIC (telescope)","score":0.5338296294212341},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5321862697601318},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5114537477493286},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.49341192841529846},{"id":"https://openalex.org/keywords/quantum-circuit","display_name":"Quantum circuit","score":0.4808369576931},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.4645504653453827},{"id":"https://openalex.org/keywords/quantum-information","display_name":"Quantum information","score":0.4637758135795593},{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.43114349246025085},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4193432629108429},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"Quantum error correction","score":0.3831775486469269},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.37410759925842285},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.35268300771713257},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.34234434366226196}],"concepts":[{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.612586259841919},{"id":"https://openalex.org/C2777704519","wikidata":"https://www.wikidata.org/wiki/Q45732","display_name":"MAGIC (telescope)","level":2,"score":0.5338296294212341},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5321862697601318},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5114537477493286},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.49341192841529846},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.4808369576931},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4645504653453827},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.4637758135795593},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.43114349246025085},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4193432629108429},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.3831775486469269},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.37410759925842285},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.35268300771713257},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.34234434366226196}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2204.12051","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2204.12051","pdf_url":"https://arxiv.org/pdf/2204.12051","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":"doi:10.48550/arxiv.2204.12051","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2204.12051","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2204.12051","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2204.12051","pdf_url":"https://arxiv.org/pdf/2204.12051","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":87,"referenced_works":["https://openalex.org/W112858668","https://openalex.org/W1529556207","https://openalex.org/W1530936416","https://openalex.org/W1599190397","https://openalex.org/W1604065510","https://openalex.org/W1616620037","https://openalex.org/W1619293558","https://openalex.org/W1636149824","https://openalex.org/W1683743514","https://openalex.org/W1763793949","https://openalex.org/W1860626550","https://openalex.org/W1891181203","https://openalex.org/W1899006432","https://openalex.org/W1923824182","https://openalex.org/W1967883933","https://openalex.org/W1974411071","https://openalex.org/W2018064694","https://openalex.org/W2023232348","https://openalex.org/W2024588775","https://openalex.org/W2027595342","https://openalex.org/W2028914943","https://openalex.org/W2032292489","https://openalex.org/W2048691322","https://openalex.org/W2052146120","https://openalex.org/W2059846772","https://openalex.org/W2084019889","https://openalex.org/W2088559598","https://openalex.org/W2103749128","https://openalex.org/W2117660206","https://openalex.org/W2150670192","https://openalex.org/W2152587816","https://openalex.org/W2170608991","https://openalex.org/W2203723895","https://openalex.org/W2267486489","https://openalex.org/W2520347247","https://openalex.org/W2524307097","https://openalex.org/W2582495643","https://openalex.org/W2626769593","https://openalex.org/W2740297979","https://openalex.org/W2741759353","https://openalex.org/W2760053505","https://openalex.org/W2885303178","https://openalex.org/W2902892742","https://openalex.org/W2903183678","https://openalex.org/W2939719762","https://openalex.org/W2944913150","https://openalex.org/W2949864545","https://openalex.org/W2963713365","https://openalex.org/W2963902134","https://openalex.org/W2965824167","https://openalex.org/W2981310591","https://openalex.org/W2981369791","https://openalex.org/W2996387336","https://openalex.org/W3006412606","https://openalex.org/W3037333478","https://openalex.org/W3037637275","https://openalex.org/W3083257226","https://openalex.org/W3097999405","https://openalex.org/W3098820533","https://openalex.org/W3099009889","https://openalex.org/W3100496348","https://openalex.org/W3101000235","https://openalex.org/W3101548872","https://openalex.org/W3101822725","https://openalex.org/W3103115193","https://openalex.org/W3103453378","https://openalex.org/W3103699324","https://openalex.org/W3105530994","https://openalex.org/W3105782957","https://openalex.org/W3106326670","https://openalex.org/W3122177224","https://openalex.org/W3124733274","https://openalex.org/W3127340234","https://openalex.org/W3133630681","https://openalex.org/W3142194265","https://openalex.org/W3197058083","https://openalex.org/W3209710634","https://openalex.org/W3211028885","https://openalex.org/W3211718387","https://openalex.org/W4224317822","https://openalex.org/W4225637011","https://openalex.org/W4280579466","https://openalex.org/W4293404412","https://openalex.org/W4293861557","https://openalex.org/W4295351844","https://openalex.org/W4316881890","https://openalex.org/W4383263854"],"related_works":["https://openalex.org/W4281550036","https://openalex.org/W3206120658","https://openalex.org/W1996213744","https://openalex.org/W3092615945","https://openalex.org/W4390992964","https://openalex.org/W3131420525","https://openalex.org/W2771474912","https://openalex.org/W2045780663","https://openalex.org/W2037426566","https://openalex.org/W2578586822"],"abstract_inverted_index":{"Quantum":[0],"circuit":[1],"complexity-a":[2],"measure":[3,105],"of":[4,8,32,39,49,55,69,82,129,142],"the":[5,29,37,47,53,67,80,115,130,140],"minimum":[6],"number":[7],"gates":[9],"needed":[10],"to":[11,35,106,113],"implement":[12],"a":[13,17,98,126],"given":[14],"unitary":[15],"transformation-is":[16],"fundamental":[18],"concept":[19],"in":[20,147],"quantum":[21,33,50,88,99,108,127,148],"computation,":[22],"with":[23,71,79],"widespread":[24],"applications":[25],"ranging":[26],"from":[27],"determining":[28],"running":[30],"time":[31],"algorithms":[34],"understanding":[36,139],"physics":[38],"black":[40],"holes.":[41],"In":[42],"this":[43,123],"work,":[44],"we":[45,90],"study":[46],"complexity":[48],"circuits":[51],"using":[52],"notions":[54],"sensitivity,":[56,143],"average":[57],"sensitivity":[58,73,94],"(also":[59],"called":[60],"influence),":[61],"magic,":[62,144],"and":[63,74,119,145],"coherence.":[64],"We":[65,121],"characterize":[66],"set":[68],"unitaries":[70],"vanishing":[72],"show":[75],"that":[76,93],"it":[77,110],"coincides":[78],"family":[81],"matchgates.":[83],"Since":[84],"matchgates":[85],"are":[86,136],"tractable":[87],"circuits,":[89],"have":[91],"proved":[92],"is":[95,103,111],"necessary":[96],"for":[97,138],"speedup.":[100],"As":[101],"magic":[102,118],"another":[104],"quantify":[107],"advantage,":[109],"interesting":[112],"understand":[114],"relation":[116],"between":[117],"sensitivity.":[120],"do":[122],"by":[124],"introducing":[125],"version":[128],"Fourier":[131],"entropy-influence":[132],"relation.":[133],"Our":[134],"results":[135],"pivotal":[137],"role":[141],"coherence":[146],"computation.":[149]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}