{"id":"https://openalex.org/W3205751967","doi":"https://doi.org/10.22331/q-2022-04-21-693","title":"Boundaries for the Honeycomb Code","display_name":"Boundaries for the Honeycomb Code","publication_year":2022,"publication_date":"2022-04-21","ids":{"openalex":"https://openalex.org/W3205751967","doi":"https://doi.org/10.22331/q-2022-04-21-693","mag":"3205751967"},"language":"en","primary_location":{"id":"doi:10.22331/q-2022-04-21-693","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-21-693","pdf_url":"https://quantum-journal.org/papers/q-2022-04-21-693/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":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2022-04-21-693/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036464616","display_name":"Jeongwan Haah","orcid":"https://orcid.org/0000-0002-1087-6853"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jeongwan Haah","raw_affiliation_strings":["Microsoft Quantum and Microsoft Research, Redmond, WA 98052, USA"],"affiliations":[{"raw_affiliation_string":"Microsoft Quantum and Microsoft Research, Redmond, WA 98052, USA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112441815","display_name":"Matthew B. Hastings","orcid":null},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew B. Hastings","raw_affiliation_strings":["Microsoft Quantum and Microsoft Research, Redmond, WA 98052, USA","Station Q, Microsoft Quantum, Santa Barbara, CA 93106-6105, USA"],"affiliations":[{"raw_affiliation_string":"Microsoft Quantum and Microsoft Research, Redmond, WA 98052, USA","institution_ids":["https://openalex.org/I1290206253"]},{"raw_affiliation_string":"Station Q, Microsoft Quantum, Santa Barbara, CA 93106-6105, USA","institution_ids":["https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036464616"],"corresponding_institution_ids":["https://openalex.org/I1290206253"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":6.8353,"has_fulltext":true,"cited_by_count":52,"citation_normalized_percentile":{"value":0.97743091,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"6","issue":null,"first_page":"693","last_page":"693"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11682","display_name":"Advanced Condensed Matter Physics","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12588","display_name":"Electronic and Structural Properties of Oxides","score":0.9638000130653381,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/parallelogram","display_name":"Parallelogram","score":0.7417768239974976},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.6996267437934875},{"id":"https://openalex.org/keywords/honeycomb","display_name":"Honeycomb","score":0.6985489726066589},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6067178249359131},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.598168671131134},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5603271126747131},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5590737462043762},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5310172438621521},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3655714988708496},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3432731628417969},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2860541343688965},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.27451467514038086},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12177598476409912},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11851897835731506}],"concepts":[{"id":"https://openalex.org/C53118041","wikidata":"https://www.wikidata.org/wiki/Q45867","display_name":"Parallelogram","level":3,"score":0.7417768239974976},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.6996267437934875},{"id":"https://openalex.org/C145665481","wikidata":"https://www.wikidata.org/wiki/Q123339","display_name":"Honeycomb","level":2,"score":0.6985489726066589},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6067178249359131},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.598168671131134},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5603271126747131},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5590737462043762},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5310172438621521},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3655714988708496},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3432731628417969},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2860541343688965},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27451467514038086},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12177598476409912},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11851897835731506},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2022-04-21-693","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-21-693","pdf_url":"https://quantum-journal.org/papers/q-2022-04-21-693/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:arXiv.org:2110.09545","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2110.09545","pdf_url":"https://arxiv.org/pdf/2110.09545","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:doaj.org/article:7b6e01d250d44a82a89043860cd4a93a","is_oa":true,"landing_page_url":"https://doaj.org/article/7b6e01d250d44a82a89043860cd4a93a","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 6, p 693 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2022-04-21-693","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-21-693","pdf_url":"https://quantum-journal.org/papers/q-2022-04-21-693/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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3205751967.pdf","grobid_xml":"https://content.openalex.org/works/W3205751967.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1521207535","https://openalex.org/W2013754283","https://openalex.org/W2026181396","https://openalex.org/W2045342516","https://openalex.org/W2045873381","https://openalex.org/W2088636071","https://openalex.org/W2141708961","https://openalex.org/W2157276712","https://openalex.org/W3038590673","https://openalex.org/W3097500892","https://openalex.org/W3100736866","https://openalex.org/W3103321606","https://openalex.org/W3105874174","https://openalex.org/W3181439919","https://openalex.org/W3194025247","https://openalex.org/W3206668458","https://openalex.org/W3207451214","https://openalex.org/W4295987789","https://openalex.org/W4302774904"],"related_works":["https://openalex.org/W4298181155","https://openalex.org/W4210985719","https://openalex.org/W2127261674","https://openalex.org/W78786167","https://openalex.org/W2949507605","https://openalex.org/W4249323188","https://openalex.org/W2387120636","https://openalex.org/W2055676168","https://openalex.org/W2350170215","https://openalex.org/W2026896861"],"abstract_inverted_index":{"We":[0,31],"introduce":[1],"a":[2],"simple":[3],"construction":[4],"of":[5,25,35],"boundary":[6],"conditions":[7],"for":[8],"the":[9,23,27,36],"honeycomb":[10],"code":[11],"\\cite{honeycomb}":[12],"that":[13],"uses":[14],"only":[15],"pairwise":[16],"checks":[17],"and":[18],"allows":[19],"parallelogram":[20],"geometries":[21],"at":[22],"cost":[24],"modifying":[26],"bulk":[28],"measurement":[29],"sequence.":[30],"discuss":[32],"small":[33],"instances":[34],"code.":[37]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":19},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":8}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}