{"id":"https://openalex.org/W4226053360","doi":"https://doi.org/10.1109/tit.2022.3170846","title":"Quantum Pin Codes","display_name":"Quantum Pin Codes","publication_year":2022,"publication_date":"2022-04-26","ids":{"openalex":"https://openalex.org/W4226053360","doi":"https://doi.org/10.1109/tit.2022.3170846"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3170846","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3170846","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research-information.bris.ac.uk/en/publications/418a8894-7cbb-406a-b137-464c2f118808","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070698248","display_name":"Christophe Vuillot","orcid":"https://orcid.org/0000-0002-3445-0179"},"institutions":[{"id":"https://openalex.org/I4210145640","display_name":"QuTech","ror":"https://ror.org/04wf30j82","country_code":"NL","type":"facility","lineage":["https://openalex.org/I148297040","https://openalex.org/I4210145640","https://openalex.org/I98358874"]},{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Christophe Vuillot","raw_affiliation_strings":["QuTech, TU Delft, Delft, The Netherlands","Faculty of Electrical Engineering, Mathematics and Computer Science [Delft] (Mekelweg 4, 2628 CD Delft - Netherlands)"],"raw_orcid":"https://orcid.org/0000-0002-3445-0179","affiliations":[{"raw_affiliation_string":"QuTech, TU Delft, Delft, The Netherlands","institution_ids":["https://openalex.org/I4210145640","https://openalex.org/I98358874"]},{"raw_affiliation_string":"Faculty of Electrical Engineering, Mathematics and Computer Science [Delft] (Mekelweg 4, 2628 CD Delft - Netherlands)","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019795211","display_name":"Nikolas P. Breuckmann","orcid":"https://orcid.org/0000-0002-7211-5515"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Nikolas P. Breuckmann","raw_affiliation_strings":["Department of Computer Science, University College London, London, U.K","Department of Physics and Astronomy [UCL London] (Gower Street, London WC1E 6BT, UK - United Kingdom)"],"raw_orcid":"https://orcid.org/0000-0002-7211-5515","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University College London, London, U.K","institution_ids":["https://openalex.org/I45129253"]},{"raw_affiliation_string":"Department of Physics and Astronomy [UCL London] (Gower Street, London WC1E 6BT, UK - United Kingdom)","institution_ids":["https://openalex.org/I45129253"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.31,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.82945913,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"68","issue":"9","first_page":"5955","last_page":"5974"},"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":0.9995999932289124,"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/notation","display_name":"Notation","score":0.5698828101158142},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5246708393096924},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.514674961566925},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.502879798412323},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4824734032154083},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4612736701965332},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3587217628955841},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33698129653930664},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25292912125587463},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.2383541464805603},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1625746488571167},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1266709864139557},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12428638339042664}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5698828101158142},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5246708393096924},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.514674961566925},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.502879798412323},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4824734032154083},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4612736701965332},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3587217628955841},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33698129653930664},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25292912125587463},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2383541464805603},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1625746488571167},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1266709864139557},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12428638339042664},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1109/tit.2022.3170846","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3170846","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"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire/418a8894-7cbb-406a-b137-464c2f118808","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/418a8894-7cbb-406a-b137-464c2f118808","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"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":"Vuillot, C & Breuckmann, N P 2022, 'Quantum Pin Codes', IEEE Transactions on Information Theory, vol. 68, no. 9, pp. 5955 - 5974. https://doi.org/10.1109/TIT.2022.3170846","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arXiv.org:1906.11394","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1906.11394","pdf_url":"https://arxiv.org/pdf/1906.11394","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:HAL:hal-02351417v2","is_oa":true,"landing_page_url":"https://hal.science/hal-02351417","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"IEEE Transactions on Information Theory, 2022, &#x27E8;10.1109/TIT.2022.3170846&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/37e2403e-a00f-499b-9c7f-d34ce2022933","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/37e2403e-a00f-499b-9c7f-d34ce2022933","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:research-information.bris.ac.uk:publications/418a8894-7cbb-406a-b137-464c2f118808","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=85129641178&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:tudelft.nl:uuid:ce5f451c-336e-4346-856c-42e26ac55d5e","is_oa":false,"landing_page_url":"http://resolver.tudelft.nl/uuid:ce5f451c-336e-4346-856c-42e26ac55d5e","pdf_url":null,"source":{"id":"https://openalex.org/S4306400906","display_name":"Research Repository (Delft University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98358874","host_organization_name":"Delft University of Technology","host_organization_lineage":["https://openalex.org/I98358874"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"}],"best_oa_location":{"id":"pmh:oai:research-information.bris.ac.uk:openaire/418a8894-7cbb-406a-b137-464c2f118808","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/418a8894-7cbb-406a-b137-464c2f118808","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"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":"Vuillot, C & Breuckmann, N P 2022, 'Quantum Pin Codes', IEEE Transactions on Information Theory, vol. 68, no. 9, pp. 5955 - 5974. https://doi.org/10.1109/TIT.2022.3170846","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7735421842","display_name":null,"funder_award_id":"682726","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320320286","display_name":"University College London","ror":"https://ror.org/02jx3x895"},{"id":"https://openalex.org/F4320330828","display_name":"QuantERA","ror":null},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":78,"referenced_works":["https://openalex.org/W51037165","https://openalex.org/W66887941","https://openalex.org/W142413548","https://openalex.org/W280079156","https://openalex.org/W1533024485","https://openalex.org/W1542530597","https://openalex.org/W1542689491","https://openalex.org/W1841286492","https://openalex.org/W1929354142","https://openalex.org/W1956864028","https://openalex.org/W1971516277","https://openalex.org/W1989420631","https://openalex.org/W1999770545","https://openalex.org/W2005868823","https://openalex.org/W2009067556","https://openalex.org/W2013754283","https://openalex.org/W2017925055","https://openalex.org/W2019836938","https://openalex.org/W2040103735","https://openalex.org/W2044066793","https://openalex.org/W2045873381","https://openalex.org/W2046753312","https://openalex.org/W2060532199","https://openalex.org/W2079294297","https://openalex.org/W2095025840","https://openalex.org/W2107817077","https://openalex.org/W2114207424","https://openalex.org/W2128765501","https://openalex.org/W2131690084","https://openalex.org/W2135273380","https://openalex.org/W2145801399","https://openalex.org/W2162963911","https://openalex.org/W2167413626","https://openalex.org/W2272435756","https://openalex.org/W2273531969","https://openalex.org/W2410139980","https://openalex.org/W2410653068","https://openalex.org/W2414800610","https://openalex.org/W2512564998","https://openalex.org/W2605394516","https://openalex.org/W2616493737","https://openalex.org/W2750348520","https://openalex.org/W2755290849","https://openalex.org/W2755418751","https://openalex.org/W2755575243","https://openalex.org/W2804113880","https://openalex.org/W2807081011","https://openalex.org/W2894935780","https://openalex.org/W2952077272","https://openalex.org/W2962721054","https://openalex.org/W2963091690","https://openalex.org/W2963760674","https://openalex.org/W2980742961","https://openalex.org/W3046642801","https://openalex.org/W3098541391","https://openalex.org/W3100500243","https://openalex.org/W3100704244","https://openalex.org/W3101551690","https://openalex.org/W3102019613","https://openalex.org/W3102685293","https://openalex.org/W3102818703","https://openalex.org/W3103161377","https://openalex.org/W3103222061","https://openalex.org/W3104757600","https://openalex.org/W3105835575","https://openalex.org/W3106097399","https://openalex.org/W3197075912","https://openalex.org/W4210453336","https://openalex.org/W4297782786","https://openalex.org/W4300188436","https://openalex.org/W4311105358","https://openalex.org/W4394672652","https://openalex.org/W6631693528","https://openalex.org/W6632392208","https://openalex.org/W6634900687","https://openalex.org/W6638801799","https://openalex.org/W6762335758","https://openalex.org/W6800376655"],"related_works":["https://openalex.org/W2504004674","https://openalex.org/W1987679298","https://openalex.org/W2963177394","https://openalex.org/W4313359513","https://openalex.org/W2498744856","https://openalex.org/W4390482104","https://openalex.org/W322408318","https://openalex.org/W149041114","https://openalex.org/W1965815883","https://openalex.org/W763418848"],"abstract_inverted_index":{"We":[0,91],"introduce":[1],"quantum":[2,8,18],"pin":[3,12],"codes:":[4],"a":[5,15,26],"class":[6],"of":[7,17,28,94],"CSS":[9],"codes.":[10],"Quantum":[11],"codes":[13,20,23,34,96],"are":[14],"generalization":[16],"color":[19],"and":[21,24,31,41,97],"Reed-Muller":[22],"share":[25],"lot":[27],"their":[29,42,98],"structure":[30],"properties.":[32,99],"Pin":[33],"have":[35],"gauge":[36],"operators,":[37],"an":[38],"unfolding":[39],"procedure":[40],"stabilizers":[43],"form":[44],"so-called":[45],"<inline-formula":[46,62],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[47,63],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[48,64],"<tex-math":[49,65],"notation=\"LaTeX\">$\\ell":[50,66],"$":[51,67],"</tex-math></inline-formula>":[52,68],"-orthogonal":[53],"spaces":[54],"meaning":[55],"that":[56],"the":[57],"joint":[58],"overlap":[59],"between":[60],"any":[61],"stabilizer":[69],"elements":[70],"is":[71],"always":[72],"even.":[73],"This":[74],"last":[75],"feature":[76],"makes":[77],"them":[78],"interesting":[79],"for":[80,85],"devising":[81],"magic-state":[82],"distillation":[83],"protocols,":[84],"instance":[86],"by":[87],"using":[88],"puncturing":[89],"techniques.":[90],"study":[92],"examples":[93],"these":[95]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2022-05-05T00:00:00"}