{"id":"https://openalex.org/W2094848842","doi":"https://doi.org/10.1109/tit.2015.2422294","title":"Hardness of Decoding Quantum Stabilizer Codes","display_name":"Hardness of Decoding Quantum Stabilizer Codes","publication_year":2015,"publication_date":"2015-04-28","ids":{"openalex":"https://openalex.org/W2094848842","doi":"https://doi.org/10.1109/tit.2015.2422294","mag":"2094848842"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2015.2422294","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2422294","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014971904","display_name":"Pavithran Iyer","orcid":"https://orcid.org/0000-0003-2977-0490"},"institutions":[{"id":"https://openalex.org/I135117807","display_name":"Universit\u00e9 de Sherbrooke","ror":"https://ror.org/00kybxq39","country_code":"CA","type":"education","lineage":["https://openalex.org/I135117807"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Pavithran Iyer","raw_affiliation_strings":["D\u00e9partement de Physique, Universit\u00e9 de Sherbrooke, Sherbrooke, QC, Canada","departement de physique, Universite de Sherbrooke, Sherbrooke QC, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Physique, Universit\u00e9 de Sherbrooke, Sherbrooke, QC, Canada","institution_ids":["https://openalex.org/I135117807"]},{"raw_affiliation_string":"departement de physique, Universite de Sherbrooke, Sherbrooke QC, Canada","institution_ids":["https://openalex.org/I135117807"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110289759","display_name":"David Poulin","orcid":null},"institutions":[{"id":"https://openalex.org/I135117807","display_name":"Universit\u00e9 de Sherbrooke","ror":"https://ror.org/00kybxq39","country_code":"CA","type":"education","lineage":["https://openalex.org/I135117807"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"David Poulin","raw_affiliation_strings":["D\u00e9partement de Physique, Universit\u00e9 de Sherbrooke, Sherbrooke, QC, Canada","departement de physique, Universite de Sherbrooke, Sherbrooke QC, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Physique, Universit\u00e9 de Sherbrooke, Sherbrooke, QC, Canada","institution_ids":["https://openalex.org/I135117807"]},{"raw_affiliation_string":"departement de physique, Universite de Sherbrooke, Sherbrooke QC, Canada","institution_ids":["https://openalex.org/I135117807"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I135117807"],"apc_list":null,"apc_paid":null,"fwci":0.4451,"has_fulltext":false,"cited_by_count":80,"citation_normalized_percentile":{"value":0.77023531,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"61","issue":"9","first_page":"5209","last_page":"5223"},"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9958999752998352,"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":0.9945999979972839,"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/decoding-methods","display_name":"Decoding methods","score":0.7726154327392578},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.6580976247787476},{"id":"https://openalex.org/keywords/sequential-decoding","display_name":"Sequential decoding","score":0.5532320737838745},{"id":"https://openalex.org/keywords/berlekamp\u2013welch-algorithm","display_name":"Berlekamp\u2013Welch algorithm","score":0.5263784527778625},{"id":"https://openalex.org/keywords/quantum-convolutional-code","display_name":"Quantum convolutional code","score":0.50909823179245},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4784945845603943},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4668116569519043},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.45958322286605835},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.4332837462425232},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4223608374595642},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3822545111179352},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.3473152816295624},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3260614275932312},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.32144153118133545}],"concepts":[{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.7726154327392578},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.6580976247787476},{"id":"https://openalex.org/C193969084","wikidata":"https://www.wikidata.org/wiki/Q7452500","display_name":"Sequential decoding","level":4,"score":0.5532320737838745},{"id":"https://openalex.org/C132727834","wikidata":"https://www.wikidata.org/wiki/Q4892328","display_name":"Berlekamp\u2013Welch algorithm","level":5,"score":0.5263784527778625},{"id":"https://openalex.org/C69497775","wikidata":"https://www.wikidata.org/wiki/Q7269025","display_name":"Quantum convolutional code","level":5,"score":0.50909823179245},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4784945845603943},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4668116569519043},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.45958322286605835},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.4332837462425232},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4223608374595642},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3822545111179352},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.3473152816295624},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3260614275932312},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.32144153118133545},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2015.2422294","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2422294","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320307763","display_name":"Lockheed Martin Corporation","ror":"https://ror.org/026er9r08"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W175185051","https://openalex.org/W987035227","https://openalex.org/W1479964525","https://openalex.org/W1515518740","https://openalex.org/W1527197079","https://openalex.org/W1546596972","https://openalex.org/W1551363121","https://openalex.org/W1556443961","https://openalex.org/W1564918482","https://openalex.org/W1594652978","https://openalex.org/W1608621648","https://openalex.org/W1631356911","https://openalex.org/W1839785972","https://openalex.org/W1850344377","https://openalex.org/W1873948376","https://openalex.org/W1971261557","https://openalex.org/W1975650268","https://openalex.org/W1982050833","https://openalex.org/W1995875735","https://openalex.org/W1999706070","https://openalex.org/W2004118225","https://openalex.org/W2026129786","https://openalex.org/W2035929826","https://openalex.org/W2045873381","https://openalex.org/W2071522897","https://openalex.org/W2074237359","https://openalex.org/W2085970623","https://openalex.org/W2091331782","https://openalex.org/W2092897641","https://openalex.org/W2103532256","https://openalex.org/W2107453273","https://openalex.org/W2109785828","https://openalex.org/W2111319461","https://openalex.org/W2115826669","https://openalex.org/W2119314900","https://openalex.org/W2123809589","https://openalex.org/W2135273380","https://openalex.org/W2137407595","https://openalex.org/W2144045978","https://openalex.org/W2147590609","https://openalex.org/W2148912087","https://openalex.org/W2559868876","https://openalex.org/W2595142274","https://openalex.org/W2616493737","https://openalex.org/W2764347725","https://openalex.org/W3101716590","https://openalex.org/W3102818703","https://openalex.org/W3123590924","https://openalex.org/W4298227433","https://openalex.org/W4299329567","https://openalex.org/W4394672652","https://openalex.org/W6630973447","https://openalex.org/W6632783170","https://openalex.org/W6633075062","https://openalex.org/W6633785146","https://openalex.org/W6638801799","https://openalex.org/W6638938434","https://openalex.org/W6639286488","https://openalex.org/W6645658036","https://openalex.org/W6948220965"],"related_works":["https://openalex.org/W2385322349","https://openalex.org/W2369600518","https://openalex.org/W2370284973","https://openalex.org/W2028976748","https://openalex.org/W2050784748","https://openalex.org/W2383267581","https://openalex.org/W2102627024","https://openalex.org/W2182594114","https://openalex.org/W2085052822","https://openalex.org/W2135388054"],"abstract_inverted_index":{"In":[0],"this":[1,73],"paper,":[2],"we":[3,103],"address":[4],"the":[5,34,40,45,80,96,100],"computational":[6],"hardness":[7],"of":[8,38,108,125],"optimally":[9],"decoding":[10,35,61,74,107,124],"a":[11,59],"quantum":[12,64,81],"stabilizer":[13,109],"code.":[14,101],"Much":[15],"like":[16],"classical":[17,49,126],"linear":[18,127],"codes,":[19,128],"errors":[20,93],"are":[21,57],"detected":[22],"by":[23],"measuring":[24],"certain":[25],"check":[26],"operators":[27],"which":[28,90],"yield":[29],"an":[30],"error":[31,88],"syndrome,":[32],"and":[33,56],"problem":[36,50,62],"consists":[37],"determining":[39],"most":[41],"likely":[42],"recovery":[43],"given":[44],"syndrome.":[46],"The":[47],"corresponding":[48],"is":[51,66,76,116,130],"known":[52,68,112],"to":[53,69,94,113],"be":[54,70,114],"NP-complete,":[55],"appropriate":[58],"similar":[60],"for":[63],"codes":[65,110],"also":[67],"NP-complete.":[71],"However,":[72],"strategy":[75],"not":[77,86],"optimal":[78,106,123],"in":[79,117],"setting":[82],"as":[83],"it":[84,129],"does":[85],"consider":[87],"degeneracy,":[89],"causes":[91],"distinct":[92],"have":[95],"same":[97],"effect":[98],"on":[99],"Here,":[102],"show":[104],"that":[105],"(previously":[111],"NP-hard)":[115],"fact":[118],"computationally":[119],"much":[120],"harder":[121],"than":[122],"#P-complete.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":22},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
