{"id":"https://openalex.org/W2985257503","doi":"https://doi.org/10.1145/3357713.3384332","title":"Interactive shallow Clifford circuits: Quantum advantage against NC\u00b9 and beyond","display_name":"Interactive shallow Clifford circuits: Quantum advantage against NC\u00b9 and beyond","publication_year":2020,"publication_date":"2020-06-06","ids":{"openalex":"https://openalex.org/W2985257503","doi":"https://doi.org/10.1145/3357713.3384332","mag":"2985257503"},"language":"en","primary_location":{"id":"doi:10.1145/3357713.3384332","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3357713.3384332","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1911.02555","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074338298","display_name":"Daniel Grier","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Daniel Grier","raw_affiliation_strings":["University of Waterloo, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022444482","display_name":"Luke Schaeffer","orcid":"https://orcid.org/0000-0002-5413-8131"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Luke Schaeffer","raw_affiliation_strings":["University of Waterloo, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00632208,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"875","last_page":"888"},"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":0.9918000102043152,"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":0.9904999732971191,"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/circuit-complexity","display_name":"Circuit complexity","score":0.5966569185256958},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5848332643508911},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5613850355148315},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.5589815974235535},{"id":"https://openalex.org/keywords/quantum-circuit","display_name":"Quantum circuit","score":0.5230497121810913},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47263190150260925},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.4314480423927307},{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.430826336145401},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.4102051854133606},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4071057438850403},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.36837464570999146},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"Quantum error correction","score":0.2833220362663269},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.25449612736701965},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1780993640422821},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11144018173217773}],"concepts":[{"id":"https://openalex.org/C90702460","wikidata":"https://www.wikidata.org/wiki/Q1055112","display_name":"Circuit complexity","level":3,"score":0.5966569185256958},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5848332643508911},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5613850355148315},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.5589815974235535},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.5230497121810913},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47263190150260925},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.4314480423927307},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.430826336145401},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4102051854133606},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4071057438850403},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.36837464570999146},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.2833220362663269},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.25449612736701965},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1780993640422821},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11144018173217773},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3357713.3384332","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3357713.3384332","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1911.02555","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.02555","pdf_url":"https://arxiv.org/pdf/1911.02555","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,"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":"mag:2985257503","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1911.02555v1","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,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1911.02555","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1911.02555","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,"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1911.02555","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.02555","pdf_url":"https://arxiv.org/pdf/1911.02555","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,"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":[{"id":"https://openalex.org/G1911632812","display_name":null,"funder_award_id":"1122374","funder_id":"https://openalex.org/F4320315254","funder_display_name":"Innovative Research Group Project of the National Natural Science Foundation of China"},{"id":"https://openalex.org/G3526151021","display_name":"Graduate Research Fellowship Program","funder_award_id":"1122374","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/F4320315254","display_name":"Innovative Research Group Project of the National Natural Science Foundation of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2985257503.pdf","grobid_xml":"https://content.openalex.org/works/W2985257503.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1552645895","https://openalex.org/W1965035185","https://openalex.org/W1971094383","https://openalex.org/W1984108045","https://openalex.org/W1991877988","https://openalex.org/W1993292204","https://openalex.org/W2009005793","https://openalex.org/W2009994177","https://openalex.org/W2010465749","https://openalex.org/W2016443801","https://openalex.org/W2069280326","https://openalex.org/W2070678975","https://openalex.org/W2097087591","https://openalex.org/W2103368228","https://openalex.org/W2137147061","https://openalex.org/W2472883538","https://openalex.org/W2482126025","https://openalex.org/W2604467189","https://openalex.org/W2880299821","https://openalex.org/W2952456716","https://openalex.org/W3104500086","https://openalex.org/W6659368035","https://openalex.org/W6703106485"],"related_works":["https://openalex.org/W3035484803","https://openalex.org/W3133452729","https://openalex.org/W3157884677","https://openalex.org/W2964939752","https://openalex.org/W3107610151","https://openalex.org/W2952270869","https://openalex.org/W3105834216","https://openalex.org/W3101424970","https://openalex.org/W2895919397","https://openalex.org/W2766602260","https://openalex.org/W3080688664","https://openalex.org/W2604467189","https://openalex.org/W3035743436","https://openalex.org/W3161821612","https://openalex.org/W2894798306","https://openalex.org/W3099009889","https://openalex.org/W2951518814","https://openalex.org/W1683743514","https://openalex.org/W3163186218","https://openalex.org/W2949864545"],"abstract_inverted_index":{"Recent":[0],"work":[1,8],"of":[2,52,74,85,93,120,144,211,228],"Bravyi":[3],"et":[4,12],"al.":[5,13],"and":[6,47,166,202,214],"follow-up":[7],"by":[9,108],"Bene":[10],"Watts":[11],"demonstrates":[14],"a":[15,26,70,101,109,121,140,224],"quantum":[16,22,42,75,111],"advantage":[17,39],"for":[18,150,183],"shallow":[19],"circuits:":[20],"constant-depth":[21,29,62,110,145],"circuits":[23,33,64,147,165],"can":[24],"perform":[25,156,171],"task":[27,104,173],"which":[28,105,207],"classical":[30,63,95,131,146,209,232],"(i.e.,":[31],"0)":[32],"cannot.":[34],"Their":[35],"results":[36,182,220],"have":[37],"the":[38,41,83,86,91,94,157,172,176,231],"that":[40,129],"circuit":[43,112,190],"is":[44,57,100,106],"fairly":[45],"practical,":[46],"their":[48],"proofs":[49],"are":[50,65,221],"free":[51],"hardness":[53,181,219],"assumptions":[54],"(e.g.,":[55,148],"factoring":[56],"classically":[58],"hard,":[59],"etc.).":[60],"Unfortunately,":[61],"too":[66],"weak":[67],"to":[68,79,82,223],"yield":[69],"convincing":[71],"real-world":[72],"demonstration":[73],"advantage.":[76],"We":[77],"attempt":[78],"hold":[80],"on":[81,198],"advantages":[84],"above":[87],"results,":[88],"while":[89],"increasing":[90],"power":[92,212],"model.":[96],"Our":[97],"main":[98],"result":[99],"two-round":[102],"interactive":[103,196],"solved":[107],"(using":[113],"only":[114],"Clifford":[115],"gates,":[116],"between":[117],"neighboring":[118],"qubits":[119],"2D":[122],"grid,":[123],"with":[124],"Pauli":[125],"measurements),":[126],"but":[127],"such":[128],"any":[130,151],"solution":[132],"would":[133],"necessarily":[134],"solve":[135],"-hard":[136],"problems.":[137],"This":[138],"implies":[139],"more":[141,188],"powerful":[142],"class":[143],"0[p]":[149],"prime":[152],"p)":[153],"unconditionally":[154],"cannot":[155,170],"task.":[158],"Furthermore,":[159],"under":[160,187],"standard":[161],"complexity-theoretic":[162],"conjectures,":[163],"log-depth":[164],"log-space":[167],"Turing":[168],"machines":[169],"either.":[174],"Using":[175],"same":[177],"techniques,":[178],"we":[179,193],"prove":[180],"weaker":[184],"complexity":[185],"classes":[186],"restrictive":[189],"topologies.":[191],"Specifically,":[192],"give":[194],"0":[195],"tasks":[197],"2":[199],"\u00d7":[200,204],"n":[201,205],"1":[203,213],"grids":[206],"require":[208],"simulations":[210],"0[6],":[215],"respectively.":[216],"Moreover,":[217],"these":[218],"robust":[222],"small":[225],"constant":[226],"fraction":[227],"error":[229],"in":[230],"simulation.":[233]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}