{"id":"https://openalex.org/W4361761872","doi":"https://doi.org/10.1109/mbits.2023.3262219","title":"No $((n,K,d< 127))$ Code Can Violate the Quantum Hamming Bound","display_name":"No $((n,K,d< 127))$ Code Can Violate the Quantum Hamming Bound","publication_year":2022,"publication_date":"2022-12-01","ids":{"openalex":"https://openalex.org/W4361761872","doi":"https://doi.org/10.1109/mbits.2023.3262219"},"language":"en","primary_location":{"id":"doi:10.1109/mbits.2023.3262219","doi":"https://doi.org/10.1109/mbits.2023.3262219","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mbits.2023.3262219","pdf_url":null,"source":{"id":"https://openalex.org/S4210191909","display_name":"IEEE BITS the Information Theory Magazine","issn_l":"2692-4080","issn":["2692-4080","2692-4110"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","vabb-shw"],"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 BITS the Information Theory Magazine","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2208.11800","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002452938","display_name":"Emanuel Dallas","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Emanuel Dallas","raw_affiliation_strings":["Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014093102","display_name":"Faidon Andreadakis","orcid":"https://orcid.org/0000-0002-0372-2346","observed_orcids":["https://orcid.org/0000-0002-0372-2346"]},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Faidon Andreadakis","raw_affiliation_strings":["Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-0372-2346","affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083283029","display_name":"Daniel A. Lidar","orcid":"https://orcid.org/0000-0002-1671-1515","observed_orcids":["https://orcid.org/0000-0002-1671-1515"]},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Lidar","raw_affiliation_strings":["Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, CA, USA","Department of Chemistry, University of Southern California, Los Angeles, CA, USA","Department of Electrical & Computer Engineering, University of Southern California, Los Angeles, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-1671-1515","affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"Department of Chemistry, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":{"value":2995,"currency":"USD","value_usd":2995},"apc_paid":null,"fwci":0.1607,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.46093716,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":94},"biblio":{"volume":"2","issue":"3","first_page":"33","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9204000234603882,"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":0.9204000234603882,"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/T11130","display_name":"Coding theory and cryptography","score":0.06960000097751617,"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":0.004600000102072954,"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-error-correcting-codes","display_name":"quantum error-correcting codes","score":0.9179999828338623},{"id":"https://openalex.org/keywords/code-rate","display_name":"code rate","score":0.3880000114440918},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"minimum distance","score":0.671999990940094}],"concepts":[{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.7602460384368896},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.7334108352661133},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6400419473648071},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5744791626930237},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.551223874092102},{"id":"https://openalex.org/C112932734","wikidata":"https://www.wikidata.org/wiki/Q2322550","display_name":"Hamming(7,4)","level":5,"score":0.5185590386390686},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.48914673924446106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4725871980190277},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4427972137928009},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3948345184326172},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33278563618659973},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.310380756855011},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.27665162086486816},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27291572093963623},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.2327047884464264},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.053656160831451416},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/mbits.2023.3262219","doi":"https://doi.org/10.1109/mbits.2023.3262219","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mbits.2023.3262219","pdf_url":null,"source":{"id":"https://openalex.org/S4210191909","display_name":"IEEE BITS the Information Theory Magazine","issn_l":"2692-4080","issn":["2692-4080","2692-4110"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","vabb-shw"],"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 BITS the Information Theory Magazine","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2208.11800","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2208.11800","pdf_url":"https://arxiv.org/pdf/2208.11800","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,"listed_in":[],"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.2208.11800","doi":"https://doi.org/10.48550/arxiv.2208.11800","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2208.11800","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,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2208.11800","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2208.11800","pdf_url":"https://arxiv.org/pdf/2208.11800","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,"listed_in":[],"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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7833584438","display_name":null,"funder_award_id":"W911NF\u201020\u20101\u20100075","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1497498619","https://openalex.org/W1572877829","https://openalex.org/W1603424342","https://openalex.org/W1606480398","https://openalex.org/W1807170054","https://openalex.org/W1839785972","https://openalex.org/W1970302872","https://openalex.org/W1991443278","https://openalex.org/W1999706070","https://openalex.org/W2019024432","https://openalex.org/W2021404493","https://openalex.org/W2042474962","https://openalex.org/W2070290063","https://openalex.org/W2079362532","https://openalex.org/W2088324731","https://openalex.org/W2114207424","https://openalex.org/W2114999643","https://openalex.org/W2116059612","https://openalex.org/W2117002761","https://openalex.org/W2131370125","https://openalex.org/W2167413626","https://openalex.org/W2530658632","https://openalex.org/W2755418751","https://openalex.org/W2763302490","https://openalex.org/W2781738013","https://openalex.org/W3033912009","https://openalex.org/W3043792635","https://openalex.org/W3145257547","https://openalex.org/W3178633198","https://openalex.org/W3181660950","https://openalex.org/W3186940688","https://openalex.org/W4200634137","https://openalex.org/W4225797040","https://openalex.org/W4301287831","https://openalex.org/W4303188486","https://openalex.org/W4394672652","https://openalex.org/W6779290691"],"related_works":["https://openalex.org/W2008960744","https://openalex.org/W2371167013","https://openalex.org/W2105471374","https://openalex.org/W2740543340","https://openalex.org/W2014631828","https://openalex.org/W4302771537","https://openalex.org/W1964096323","https://openalex.org/W2119135810","https://openalex.org/W2951416090","https://openalex.org/W2743336384"],"abstract_inverted_index":{"It":[0],"is":[1],"well-known":[2],"that":[3,53,85],"non-degenerate":[4],"quantum":[5,14,62,91],"error":[6],"correcting":[7],"codes":[8,22,58],"(QECCs)":[9],"are":[10],"constrained":[11],"by":[12],"a":[13,26,30,43,54,75],"version":[15],"of":[16,39,45,56],"the":[17,37,61,90],"Hamming":[18,63,92],"bound.":[19,64,93],"Whether":[20],"degenerate":[21],"also":[23],"obey":[24,60],"such":[25],"bound,":[27],"however,":[28],"remains":[29],"long-standing":[31],"question":[32],"with":[33,74],"practical":[34],"implications":[35],"for":[36],"efficacy":[38],"QECCs.":[40],"We":[41],"employ":[42],"combination":[44],"previously":[46],"derived":[47],"bounds":[48],"on":[49],"QECCs":[50],"to":[51,72,79,83],"demonstrate":[52],"subset":[55],"all":[57],"must":[59],"Specifically,":[65],"we":[66],"combine":[67],"an":[68],"analytical":[69],"bound":[70,77],"due":[71,78],"Rains":[73],"numerical":[76],"Li":[80],"and":[81],"Xing":[82],"show":[84],"no$((n,K,d))$code":[86],"with$d<":[87],"127$can":[88],"violate":[89]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2023-04-04T00:00:00"}