{"id":"https://openalex.org/W4406165543","doi":"https://doi.org/10.22331/q-2025-01-08-1586","title":"Fast algorithms for classical specifications of stabiliser states and Clifford gates","display_name":"Fast algorithms for classical specifications of stabiliser states and Clifford gates","publication_year":2025,"publication_date":"2025-01-08","ids":{"openalex":"https://openalex.org/W4406165543","doi":"https://doi.org/10.22331/q-2025-01-08-1586"},"language":"en","primary_location":{"id":"doi:10.22331/q-2025-01-08-1586","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2025-01-08-1586","pdf_url":"https://quantum-journal.org/papers/q-2025-01-08-1586/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2025-01-08-1586/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037005145","display_name":"Nadish de Silva","orcid":"https://orcid.org/0000-0001-7904-306X"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Nadish de Silva","raw_affiliation_strings":["Department of Mathematics, Simon Fraser University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032927358","display_name":"Wilfred Salmon","orcid":"https://orcid.org/0000-0001-7551-5808"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Wilfred Salmon","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101273683","display_name":"Ming Yin","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Ming Yin","raw_affiliation_strings":["Department of Mathematics, Simon Fraser University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University","institution_ids":["https://openalex.org/I18014758"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5037005145"],"corresponding_institution_ids":["https://openalex.org/I18014758"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":4.5419,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.93244521,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"9","issue":null,"first_page":"1586","last_page":"1586"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9955000281333923,"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":0.9944000244140625,"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/stabiliser","display_name":"Stabiliser","score":0.6094376444816589},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4846521019935608},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48294132947921753},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.43488335609436035},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3272911012172699},{"id":"https://openalex.org/keywords/nanotechnology","display_name":"Nanotechnology","score":0.1272323727607727},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.08316439390182495}],"concepts":[{"id":"https://openalex.org/C2780345374","wikidata":"https://www.wikidata.org/wiki/Q7595716","display_name":"Stabiliser","level":2,"score":0.6094376444816589},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4846521019935608},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48294132947921753},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.43488335609436035},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3272911012172699},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.1272323727607727},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.08316439390182495}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.22331/q-2025-01-08-1586","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2025-01-08-1586","pdf_url":"https://quantum-journal.org/papers/q-2025-01-08-1586/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:doaj.org/article:c3b0837bea1f4c17916948fd3254c589","is_oa":true,"landing_page_url":"https://doaj.org/article/c3b0837bea1f4c17916948fd3254c589","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 9, p 1586 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2025-01-08-1586","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2025-01-08-1586","pdf_url":"https://quantum-journal.org/papers/q-2025-01-08-1586/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/G1207281239","display_name":null,"funder_award_id":"RGPIN-2022-03103","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G1597412403","display_name":null,"funder_award_id":"RGPIN-","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G2862252062","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G5404998627","display_name":null,"funder_award_id":"Chair","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5784215521","display_name":null,"funder_award_id":"Chair","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G6221715925","display_name":null,"funder_award_id":"RGPIN","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G8051717526","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8105784103","display_name":null,"funder_award_id":"RGPIN-202","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322551","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406165543.pdf","grobid_xml":"https://content.openalex.org/works/W4406165543.grobid-xml"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W1551496929","https://openalex.org/W1675244148","https://openalex.org/W1764390522","https://openalex.org/W1789015869","https://openalex.org/W1929354142","https://openalex.org/W1978553093","https://openalex.org/W1993292204","https://openalex.org/W1993688167","https://openalex.org/W2009169733","https://openalex.org/W2012264492","https://openalex.org/W2015179126","https://openalex.org/W2017156903","https://openalex.org/W2020725861","https://openalex.org/W2027998831","https://openalex.org/W2033909248","https://openalex.org/W2044338030","https://openalex.org/W2046826122","https://openalex.org/W2050334794","https://openalex.org/W2052146120","https://openalex.org/W2070421562","https://openalex.org/W2079294297","https://openalex.org/W2117584890","https://openalex.org/W2135830616","https://openalex.org/W2170620327","https://openalex.org/W2336770924","https://openalex.org/W2765753692","https://openalex.org/W2885845431","https://openalex.org/W2950267153","https://openalex.org/W2988981135","https://openalex.org/W3006823398","https://openalex.org/W3042832883","https://openalex.org/W3048559261","https://openalex.org/W3096796582","https://openalex.org/W3100204248","https://openalex.org/W3103870741","https://openalex.org/W3106326670","https://openalex.org/W3112719526","https://openalex.org/W3118856128","https://openalex.org/W3135510046","https://openalex.org/W3181290353","https://openalex.org/W3183885798","https://openalex.org/W3201107990","https://openalex.org/W3212908997","https://openalex.org/W4287711460","https://openalex.org/W4311604156","https://openalex.org/W4380881148","https://openalex.org/W4386874848","https://openalex.org/W4387390353","https://openalex.org/W4388667510","https://openalex.org/W4394647518","https://openalex.org/W4394672652","https://openalex.org/W4396818866","https://openalex.org/W6931031300","https://openalex.org/W6931422814"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W2078468767","https://openalex.org/W4324357120","https://openalex.org/W2185973892","https://openalex.org/W2052643798","https://openalex.org/W2892236424","https://openalex.org/W1977573875","https://openalex.org/W2060804077"],"abstract_inverted_index":{"The":[0],"stabiliser":[1,23,67,74,113,161,167,204],"formalism":[2],"plays":[3],"a":[4,109,112,122,126,137,142,152,160,170,177,197],"central":[5],"role":[6],"in":[7,35,54,180,218,228,247],"quantum":[8,36,46],"computing,":[9],"error":[10],"correction,":[11],"and":[12,17,25,44,61,76,115,125,145,155,233],"fault":[13],"tolerance.":[14],"Conversions":[15],"between":[16,117,148],"verifications":[18],"of":[19,22,31,151,169,196,221,225],"different":[20],"specifications":[21],"states":[24,75],"Clifford":[26,77,143,153,178,198],"gates":[27,78],"are":[28,51,131],"important":[29],"components":[30],"many":[32],"classical":[33],"algorithms":[34,93,227,246],"information,":[37],"e.g.":[38],"for":[39],"gate":[40,144,154,199],"synthesis,":[41],"circuit":[42],"optimisation,":[43],"simulating":[45],"circuits.":[47],"These":[48,129],"core":[49],"functions":[50],"also":[52],"used":[53],"the":[55,66,149,166,194,212,219,248],"numerical":[56],"experiments":[57],"critical":[58],"to":[59,88,105,133,146,175,191,201],"formulating":[60],"testing":[62],"mathematical":[63,71],"conjectures":[64],"on":[65],"formalism.We":[68],"develop":[69],"novel":[70],"insights":[72],"concerning":[73],"that":[79,108,215,238],"significantly":[80],"clarify":[81],"their":[82],"descriptions.":[83],"We":[84,102],"then":[85],"utilise":[86],"these":[87],"provide":[89,223],"ten":[90],"new":[91],"fast":[92],"which":[94],"offer":[95],"asymptotic":[96,209],"advantages":[97],"over":[98,211,244],"any":[99],"existing":[100,245],"implementations.":[101],"show":[103],"how":[104],"rapidly":[106,134],"verify":[107],"vector":[110],"is":[111,141,188,207,216],"state,":[114],"interconvert":[116,147],"its":[118,156,203],"specification":[119,158],"as":[120,159],"amplitudes,":[121],"quadratic":[123],"form,":[124],"check":[127,135],"matrix.":[128],"methods":[130],"leveraged":[132],"if":[136],"given":[138],"unitary":[139],"matrix":[140,150,200],"compact":[157],"tableau.For":[162],"example,":[163],"we":[164],"extract":[165,202],"tableau":[168],"<mml:math":[171,181,229,234],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:msup><mml:mo>&amp;#x00D7;</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:msup></mml:math>":[172],"matrix,":[173],"promised":[174],"be":[176],"gate,":[179],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>O</mml:mi><mml:mo":[182],"stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:msup><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:msup><mml:mo":[183],"stretchy=\"false\">)</mml:mo></mml:math>":[184],"time.":[185],"Remarkably,":[186],"it":[187],"not":[189],"necessary":[190],"read":[192],"all":[193],"elements":[195],"tableau.":[205],"This":[206],"an":[208],"speedup":[210],"best-known":[213],"method":[214],"exponential":[217],"number":[220],"qubits.We":[222],"implementations":[224],"our":[226],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow":[230,235],"class=\"MJX-TeXAtom-ORD\"><mml:mtext":[231,236],"mathvariant=\"monospace\">Python</mml:mtext></mml:mrow></mml:math>":[232],"mathvariant=\"monospace\">C++</mml:mtext></mml:mrow></mml:math>":[237],"exhibit":[239],"vastly":[240],"improved":[241],"practical":[242],"performance":[243],"cases":[249],"where":[250],"they":[251],"exist.":[252]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}