{"id":"https://openalex.org/W4396511690","doi":"https://doi.org/10.22331/q-2024-04-30-1321","title":"A family of permutationally invariant quantum codes","display_name":"A family of permutationally invariant quantum codes","publication_year":2024,"publication_date":"2024-04-30","ids":{"openalex":"https://openalex.org/W4396511690","doi":"https://doi.org/10.22331/q-2024-04-30-1321"},"language":"en","primary_location":{"id":"doi:10.22331/q-2024-04-30-1321","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-04-30-1321","pdf_url":"https://quantum-journal.org/papers/q-2024-04-30-1321/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-2024-04-30-1321/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113193663","display_name":"Arda Aydin","orcid":null},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Arda Aydin","raw_affiliation_strings":["Department of ECE and Institute for Systems Research, University of Maryland, College Park, MD 20742"],"affiliations":[{"raw_affiliation_string":"Department of ECE and Institute for Systems Research, University of Maryland, College Park, MD 20742","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012222528","display_name":"Max A. Alekseyev","orcid":"https://orcid.org/0000-0002-5140-8095"},"institutions":[{"id":"https://openalex.org/I193531525","display_name":"George Washington University","ror":"https://ror.org/00y4zzh67","country_code":"US","type":"education","lineage":["https://openalex.org/I193531525"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Max A. Alekseyev","raw_affiliation_strings":["Department of Mathematics, The George Washington University, Washington, DC 20052"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The George Washington University, Washington, DC 20052","institution_ids":["https://openalex.org/I193531525"]}]},{"author_position":"last","author":{"id":null,"display_name":"Alexander Barg","orcid":"https://orcid.org/0000-0003-1985-4623"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexander Barg","raw_affiliation_strings":["Department of ECE and Institute for Systems Research, University of Maryland, College Park, MD 20742"],"affiliations":[{"raw_affiliation_string":"Department of ECE and Institute for Systems Research, University of Maryland, College Park, MD 20742","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5113193663"],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":5.1226,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.95831009,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"8","issue":null,"first_page":"1321","last_page":"1321"},"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9994999766349792,"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":0.9983000159263611,"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/algorithm","display_name":"Algorithm","score":0.670280396938324},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.503513514995575},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45248040556907654},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.39373624324798584},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.29480624198913574},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.15918177366256714}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.670280396938324},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.503513514995575},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45248040556907654},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39373624324798584},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29480624198913574},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15918177366256714}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.22331/q-2024-04-30-1321","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-04-30-1321","pdf_url":"https://quantum-journal.org/papers/q-2024-04-30-1321/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:673be173a9314f2fb43bc1ce99fdcefb","is_oa":true,"landing_page_url":"https://doaj.org/article/673be173a9314f2fb43bc1ce99fdcefb","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 8, p 1321 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2024-04-30-1321","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-04-30-1321","pdf_url":"https://quantum-journal.org/papers/q-2024-04-30-1321/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/G4489091066","display_name":null,"funder_award_id":"CCF-2104489","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7809797728","display_name":null,"funder_award_id":"CCF-2110113 (NSF-BSF)","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8017156794","display_name":null,"funder_award_id":"CCF-2330909","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"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4396511690.pdf"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W186403072","https://openalex.org/W1647671624","https://openalex.org/W1972168844","https://openalex.org/W1982481617","https://openalex.org/W1999706070","https://openalex.org/W2017154611","https://openalex.org/W2039982965","https://openalex.org/W2045257197","https://openalex.org/W2106070508","https://openalex.org/W2115355654","https://openalex.org/W2116858786","https://openalex.org/W2295938918","https://openalex.org/W2607354129","https://openalex.org/W2763302490","https://openalex.org/W2892854173","https://openalex.org/W2931703646","https://openalex.org/W2990961515","https://openalex.org/W2991572977","https://openalex.org/W3001045379","https://openalex.org/W3014973523","https://openalex.org/W3026839285","https://openalex.org/W3030897411","https://openalex.org/W3081349881","https://openalex.org/W3125586885","https://openalex.org/W3126358592","https://openalex.org/W3141384256","https://openalex.org/W3197274543","https://openalex.org/W3197512744","https://openalex.org/W3215639374","https://openalex.org/W4225678544","https://openalex.org/W4297944615","https://openalex.org/W4388393516","https://openalex.org/W4389626312"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109"],"abstract_inverted_index":{"We":[0,19],"construct":[1,141],"a":[2,89,101],"new":[3,26,65,85,90,142],"family":[4,27,66,87],"of":[5,42,129,144],"permutationally":[6,46,75,109],"invariant":[7,47,76,110],"codes":[8,23,49,62,77,111,145],"that":[9,22],"correct":[10,28,113],"<mml:math":[11,17,91,114,124,133],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>t</mml:mi></mml:math>":[12,115],"Pauli":[13,79,116],"errors":[14,31,80,117],"for":[15,78,108,123],"any":[16,127],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>t</mml:mi><mml:mo>&amp;#x2265;</mml:mo><mml:mn>1</mml:mn></mml:math>.":[18],"also":[20,54],"show":[21],"in":[24,63],"the":[25,43,61,64,70,106,119],"quantum":[29,48],"deletion":[30],"as":[32,34,50],"well":[33],"spontaneous":[35],"decay":[36],"errors.":[37,130],"Our":[38],"construction":[39],"contains":[40],"some":[41],"previously":[44,72,120],"known":[45,73,121],"particular":[51],"cases,":[52,60],"which":[53],"admit":[55],"transversal":[56],"gates.":[57],"In":[58],"many":[59],"are":[67],"shorter":[68],"than":[69],"best":[71],"explicit":[74],"and":[81],"deletions.":[82],"Furthermore,":[83],"our":[84],"code":[86],"includes":[88],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mo":[92],"stretchy=\"false\">(</mml:mo><mml:mo":[93],"stretchy=\"false\">(</mml:mo><mml:mn>4</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo":[94],"stretchy=\"false\">)</mml:mo><mml:mo":[95],"stretchy=\"false\">)</mml:mo></mml:math>":[96],"optimal":[97],"single-deletion-correcting":[98],"code.":[99],"As":[100],"separate":[102],"result,":[103],"we":[104],"generalize":[105],"conditions":[107,136],"to":[112,126,140],"from":[118],"results":[122],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>":[125],"number":[128],"For":[131],"small":[132],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>t</mml:mi></mml:math>,":[134],"these":[135],"can":[137],"be":[138],"used":[139],"examples":[143],"by":[146],"computer.":[147]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":7}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
