{"id":"https://openalex.org/W3087733736","doi":"https://doi.org/10.22331/q-2021-04-20-436","title":"Lightweight Detection of a Small Number of Large Errors in a Quantum Circuit","display_name":"Lightweight Detection of a Small Number of Large Errors in a Quantum Circuit","publication_year":2021,"publication_date":"2021-04-20","ids":{"openalex":"https://openalex.org/W3087733736","doi":"https://doi.org/10.22331/q-2021-04-20-436","mag":"3087733736"},"language":"en","primary_location":{"id":"doi:10.22331/q-2021-04-20-436","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-04-20-436","pdf_url":"https://quantum-journal.org/papers/q-2021-04-20-436/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-2021-04-20-436/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066895589","display_name":"Noah Linden","orcid":null},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Noah Linden","raw_affiliation_strings":["School of Mathematics, University of Bristol"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Bristol","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066563480","display_name":"Ronald de Wolf","orcid":"https://orcid.org/0000-0001-5147-6090"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832"]},{"id":"https://openalex.org/I4210099082","display_name":"QuSoft","ror":"https://ror.org/00zq3ce72","country_code":"NL","type":"facility","lineage":["https://openalex.org/I4210099082"]},{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Ronald de Wolf","raw_affiliation_strings":["QuSoft, CWI and University of Amsterdam, the Netherlands"],"affiliations":[{"raw_affiliation_string":"QuSoft, CWI and University of Amsterdam, the Netherlands","institution_ids":["https://openalex.org/I1341640284","https://openalex.org/I4210099082","https://openalex.org/I887064364"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066895589"],"corresponding_institution_ids":["https://openalex.org/I36234482"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.5599,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.71546244,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"5","issue":null,"first_page":"436","last_page":"436"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":1.0,"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":1.0,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9941999912261963,"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9873999953269958,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.698273777961731},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47771763801574707},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.43078261613845825},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3543665409088135}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.698273777961731},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47771763801574707},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.43078261613845825},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3543665409088135}],"mesh":[],"locations_count":10,"locations":[{"id":"doi:10.22331/q-2021-04-20-436","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-04-20-436","pdf_url":"https://quantum-journal.org/papers/q-2021-04-20-436/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:dare.uva.nl:openaire_cris_publications/46d44a48-b47c-4bac-ae8e-3dda678e78ec","is_oa":true,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/lightweight-detection-of-a-small-number-of-large-errors-in-a-quantum-circuit(46d44a48-b47c-4bac-ae8e-3dda678e78ec).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Linden, N & de Wolf, R 2021, 'Lightweight detection of a small number of large errors in a quantum circuit', Quantum, vol. 5, 436. https://doi.org/10.22331/q-2021-04-20-436","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire/d2560b4f-dea5-4cc7-8ae9-8a5f77b45f0e","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/d2560b4f-dea5-4cc7-8ae9-8a5f77b45f0e","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Linden, N & de Wolf, R 2021, 'Lightweight detection of a small number of large errors in a quantum circuit', Quantum, vol. 5. https://doi.org/10.22331/q-2021-04-20-436","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:2009.08840","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2009.08840","pdf_url":"https://arxiv.org/pdf/2009.08840","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:cwi.nl:30801","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/30801","pdf_url":"https://ir.cwi.nl/pub/30801/30801.pdf","source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum vol. 5","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:dare.uva.nl:publications/46d44a48-b47c-4bac-ae8e-3dda678e78ec","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2009.08840v3","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:dare.uva.nl:openaire/46d44a48-b47c-4bac-ae8e-3dda678e78ec","is_oa":true,"landing_page_url":"https://hdl.handle.net/11245.1/46d44a48-b47c-4bac-ae8e-3dda678e78ec","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Linden, N & de Wolf, R 2021, 'Lightweight detection of a small number of large errors in a quantum circuit', Quantum, vol. 5, 436. https://doi.org/10.22331/q-2021-04-20-436","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:doaj.org/article:490265f08ee04e1a8b0576f1b0cbad43","is_oa":true,"landing_page_url":"https://doaj.org/article/490265f08ee04e1a8b0576f1b0cbad43","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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 5, p 436 (2021)","raw_type":"article"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/d2560b4f-dea5-4cc7-8ae9-8a5f77b45f0e","is_oa":true,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=85105328922&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Linden, N & de Wolf, R 2021, 'Lightweight detection of a small number of large errors in a quantum circuit', Quantum, vol. 5. https://doi.org/10.22331/q-2021-04-20-436","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:uvapub:oai:dare.uva.nl:publications/46d44a48-b47c-4bac-ae8e-3dda678e78ec","is_oa":true,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/lightweight-detection-of-a-small-number-of-large-errors-in-a-quantum-circuit(46d44a48-b47c-4bac-ae8e-3dda678e78ec).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, 5:436. Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.22331/q-2021-04-20-436","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-04-20-436","pdf_url":"https://quantum-journal.org/papers/q-2021-04-20-436/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/G203500372","display_name":null,"funder_award_id":"EP/R043957/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2503488389","display_name":null,"funder_award_id":"EP/T001062/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5404777626","display_name":null,"funder_award_id":"EP/S005021/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5629409464","display_name":null,"funder_award_id":"EP/R043957/1, EP/S005021/1, EP/T001062/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3087733736.pdf","grobid_xml":"https://content.openalex.org/works/W3087733736.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W47137029","https://openalex.org/W1592648576","https://openalex.org/W1837750740","https://openalex.org/W1848366941","https://openalex.org/W1966842050","https://openalex.org/W2006290558","https://openalex.org/W2017477211","https://openalex.org/W2028406173","https://openalex.org/W2030467629","https://openalex.org/W2039072244","https://openalex.org/W2041555840","https://openalex.org/W2068704276","https://openalex.org/W2072878982","https://openalex.org/W2090368878","https://openalex.org/W2090781531","https://openalex.org/W2107398173","https://openalex.org/W2117593045","https://openalex.org/W2121981260","https://openalex.org/W2128164182","https://openalex.org/W2148118219","https://openalex.org/W2151700290","https://openalex.org/W2228881272","https://openalex.org/W2268604949","https://openalex.org/W2280240002","https://openalex.org/W2601605887","https://openalex.org/W2617434398","https://openalex.org/W2804172638","https://openalex.org/W2811032035","https://openalex.org/W2949847396","https://openalex.org/W2963083276","https://openalex.org/W2963124215","https://openalex.org/W2971898467","https://openalex.org/W2982169647","https://openalex.org/W3036000280","https://openalex.org/W3037687232","https://openalex.org/W3100110742","https://openalex.org/W3100206777","https://openalex.org/W3101479050","https://openalex.org/W3101644211","https://openalex.org/W3103699324","https://openalex.org/W3117113271","https://openalex.org/W3127429871","https://openalex.org/W4307492550"],"related_works":["https://openalex.org/W2961085424","https://openalex.org/W4306674287","https://openalex.org/W3046775127","https://openalex.org/W3107602296","https://openalex.org/W3170094116","https://openalex.org/W4386462264","https://openalex.org/W4364306694","https://openalex.org/W4312192474","https://openalex.org/W4283697347","https://openalex.org/W4210805261"],"abstract_inverted_index":{"Suppose":[0,17],"we":[1,29,66,81,100,133,254,272,297],"want":[2],"to":[3,43,193,204,244,266],"implement":[4],"a":[5,11,22,34,60,105,187,199,206,210,256],"unitary":[6,23],"<mml:math":[7,24,46,53,90,93,116,120,125,144,147,152,170,177,195,249,267,276,284,305,310],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>U</mml:mi></mml:math>,":[8,54],"for":[9,13,78,269,307],"instance":[10],"circuit":[12],"some":[14],"quantum":[15],"algorithm.":[16],"our":[18,237],"actual":[19],"implementation":[20],"is":[21,39,56,172],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow":[25,47,94,148,153,178,196,250,285,311],"class=\"MJX-TeXAtom-ORD\"><mml:mover><mml:mi>U</mml:mi><mml:mo":[26,48,95,149,179,197,251,286,312],"stretchy=\"false\">~</mml:mo></mml:mover></mml:mrow></mml:math>,":[27],"which":[28,99,158],"can":[30,101,181,298],"only":[31,114,183,191,275],"apply":[32,103],"as":[33,104,186],"black-box.":[35],"In":[36,63],"general":[37],"it":[38],"an":[40,83,135],"exponentially-hard":[41],"task":[42],"decide":[44],"whether":[45],"stretchy=\"false\">~</mml:mo></mml:mover></mml:mrow></mml:math>":[49,96,150,180,198,252,287],"equals":[50],"the":[51,87,141,216,234,281],"intended":[52],"or":[55,110,162],"significantly":[57,112],"different":[58,163],"in":[59,113,164,209],"worst-case":[61,211],"norm.":[62,212],"this":[64,79,290],"paper":[65],"consider":[67],"two":[68],"special":[69],"cases":[70],"where":[71,119],"relatively":[72],"efficient":[73,84],"and":[74,92,146,226,228,232,296],"lightweight":[75,138],"procedures":[76,190],"exist":[77],"task.First,":[80],"give":[82,134],"procedure":[85,139,239],"under":[86,140],"assumption":[88,142],"that":[89,143,215,262,274],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>U</mml:mi></mml:math>":[91,145,171,306],"(both":[97],"of":[98,169,202,224,259,280,283,304],"now":[102,173],"black-box)":[106],"are":[107,151,159,288],"either":[108,160],"equal,":[109,161],"differ":[111],"one":[115],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>-qubit":[117],"gate,":[118],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mi>O</mml:mi><mml:mo":[121],"stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo":[122,278],"stretchy=\"false\">)</mml:mo></mml:math>":[123,279],"(the":[124,167],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>":[126],"qubits":[127],"need":[128,192],"not":[129],"be":[130,184,293],"contiguous).":[131],"Second,":[132],"even":[136],"more":[137],"class=\"MJX-TeXAtom-ORD\"><mml:mtext":[154],"class=\"MJX-tex-mathit\"":[155],"mathvariant=\"italic\">Clifford</mml:mtext></mml:mrow></mml:math>":[156],"circuits":[157],"arbitrary":[165],"ways":[166],"specification":[168],"classically":[174],"given":[175],"while":[176],"still":[182],"applied":[185],"black-box).":[188],"Both":[189],"run":[194],"constant":[200,207],"number":[201],"times":[203],"detect":[205],"error":[208],"We":[213],"note":[214],"Clifford":[217,235],"result":[218],"also":[219,240],"follows":[220],"from":[221],"earlier":[222],"work":[223],"Flammia":[225],"Liu,":[227],"da":[229],"Silva,":[230],"Landon-Cardinal,":[231],"Poulin.In":[233],"case,":[236],"error-detection":[238],"allows":[241],"us":[242],"efficiently":[243],"learn":[245],"(and":[246],"hence":[247],"correct)":[248],"if":[253,271],"have":[255,264],"small":[257,295],"list":[258,291],"possible":[260,301],"errors":[261],"could":[263],"happened":[265],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>U</mml:mi></mml:math>;":[268],"example":[270],"know":[273],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>O</mml:mi><mml:mo":[277],"gates":[282],"wrong,":[289],"will":[292],"polynomially":[294],"test":[299],"each":[300],"erroneous":[302],"version":[303],"equality":[308],"with":[309],"stretchy=\"false\">~</mml:mo></mml:mover></mml:mrow></mml:math>.":[313]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2020-09-25T00:00:00"}