{"id":"https://openalex.org/W3038590673","doi":"https://doi.org/10.22331/q-2020-10-28-352","title":"Optimization of the surface code design for Majorana-based qubits","display_name":"Optimization of the surface code design for Majorana-based qubits","publication_year":2020,"publication_date":"2020-10-28","ids":{"openalex":"https://openalex.org/W3038590673","doi":"https://doi.org/10.22331/q-2020-10-28-352","mag":"3038590673"},"language":"en","primary_location":{"id":"doi:10.22331/q-2020-10-28-352","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-10-28-352","pdf_url":"https://quantum-journal.org/papers/q-2020-10-28-352/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-2020-10-28-352/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073243450","display_name":"Rui Chao","orcid":"https://orcid.org/0000-0002-2570-2426"},"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":true,"raw_author_name":"Rui Chao","raw_affiliation_strings":["University of Southern California, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055526635","display_name":"Michael E. Beverland","orcid":"https://orcid.org/0000-0003-0954-4509"},"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":"Michael E. Beverland","raw_affiliation_strings":["Microsoft Quantum and Microsoft Research, Redmond, WA, USA"],"affiliations":[{"raw_affiliation_string":"Microsoft Quantum and Microsoft Research, Redmond, WA, USA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034652805","display_name":"Nicolas Delfosse","orcid":"https://orcid.org/0000-0002-3949-981X"},"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":"Nicolas Delfosse","raw_affiliation_strings":["Microsoft Quantum and Microsoft Research, Redmond, WA, USA"],"affiliations":[{"raw_affiliation_string":"Microsoft Quantum and Microsoft Research, Redmond, WA, USA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","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":false,"raw_author_name":"Jeongwan Haah","raw_affiliation_strings":["Microsoft Quantum and Microsoft Research, Redmond, WA, USA"],"affiliations":[{"raw_affiliation_string":"Microsoft Quantum and Microsoft Research, Redmond, WA, USA","institution_ids":["https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5073243450"],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":2.8547,"has_fulltext":true,"cited_by_count":33,"citation_normalized_percentile":{"value":0.92517081,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"4","issue":null,"first_page":"352","last_page":"352"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998000264167786,"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":0.9998000264167786,"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/T10657","display_name":"Topological Materials and Phenomena","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10382","display_name":"Quantum and electron transport phenomena","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.8264293670654297},{"id":"https://openalex.org/keywords/controlled-not-gate","display_name":"Controlled NOT gate","score":0.547784686088562},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.5340802669525146},{"id":"https://openalex.org/keywords/pauli-exclusion-principle","display_name":"Pauli exclusion principle","score":0.5290830731391907},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4877951443195343},{"id":"https://openalex.org/keywords/error-detection-and-correction","display_name":"Error detection and correction","score":0.46505293250083923},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4530555307865143},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45173463225364685},{"id":"https://openalex.org/keywords/fault-tolerance","display_name":"Fault tolerance","score":0.426738440990448},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4144544303417206},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"Quantum error correction","score":0.38276422023773193},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3180824816226959},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.27333131432533264},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.26684248447418213},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.10422557592391968},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09940066933631897}],"concepts":[{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.8264293670654297},{"id":"https://openalex.org/C182953411","wikidata":"https://www.wikidata.org/wiki/Q917713","display_name":"Controlled NOT gate","level":5,"score":0.547784686088562},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.5340802669525146},{"id":"https://openalex.org/C110340908","wikidata":"https://www.wikidata.org/wiki/Q131594","display_name":"Pauli exclusion principle","level":2,"score":0.5290830731391907},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4877951443195343},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.46505293250083923},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4530555307865143},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45173463225364685},{"id":"https://openalex.org/C63540848","wikidata":"https://www.wikidata.org/wiki/Q3140932","display_name":"Fault tolerance","level":2,"score":0.426738440990448},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4144544303417206},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.38276422023773193},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3180824816226959},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.27333131432533264},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26684248447418213},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.10422557592391968},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09940066933631897},{"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},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2020-10-28-352","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-10-28-352","pdf_url":"https://quantum-journal.org/papers/q-2020-10-28-352/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:2007.00307","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.00307","pdf_url":"https://arxiv.org/pdf/2007.00307","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:f6c1dbca9e9d4c2db941a385571403c7","is_oa":true,"landing_page_url":"https://doaj.org/article/f6c1dbca9e9d4c2db941a385571403c7","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 4, p 352 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2020-10-28-352","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-10-28-352","pdf_url":"https://quantum-journal.org/papers/q-2020-10-28-352/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/G2898000730","display_name":"CAREER: Fundamental principles of computation and physics","funder_award_id":"1254119","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3297071621","display_name":null,"funder_award_id":"FA9550-18-1-016","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G5233406010","display_name":null,"funder_award_id":"CCF-1254119","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"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/G8015857005","display_name":null,"funder_award_id":"W911NF-12-1-0541","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8163048266","display_name":null,"funder_award_id":"FA9550-18-1-0161","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G8337768007","display_name":null,"funder_award_id":"W911NF-12-1-0541","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8998121839","display_name":null,"funder_award_id":"911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3038590673.pdf","grobid_xml":"https://content.openalex.org/works/W3038590673.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W2016171150","https://openalex.org/W2030867075","https://openalex.org/W2032684234","https://openalex.org/W2040009340","https://openalex.org/W2056281570","https://openalex.org/W2088636071","https://openalex.org/W2134210354","https://openalex.org/W2135273380","https://openalex.org/W2300444825","https://openalex.org/W2469757275","https://openalex.org/W2534820175","https://openalex.org/W2606182139","https://openalex.org/W2806754346","https://openalex.org/W2962953030","https://openalex.org/W2976542453","https://openalex.org/W2990607893","https://openalex.org/W3015998597","https://openalex.org/W3041260181","https://openalex.org/W3098177648","https://openalex.org/W3098722073","https://openalex.org/W3100736866","https://openalex.org/W3102159806","https://openalex.org/W3121376493","https://openalex.org/W6607609142"],"related_works":["https://openalex.org/W2009848941","https://openalex.org/W2045473016","https://openalex.org/W2066640878","https://openalex.org/W2808177279","https://openalex.org/W2057468308","https://openalex.org/W2584669118","https://openalex.org/W1981408427","https://openalex.org/W3081235969","https://openalex.org/W3092615945","https://openalex.org/W4389168214"],"abstract_inverted_index":{"The":[0],"surface":[1,21,44],"code":[2,8,22,45],"is":[3],"a":[4,26],"prominent":[5],"topological":[6],"error-correcting":[7],"exhibiting":[9],"high":[10],"fault-tolerance":[11,100],"accuracy":[12],"thresholds.":[13],"Conventional":[14],"schemes":[15,47],"for":[16,90],"error":[17,96],"correction":[18],"with":[19,38,109],"the":[20,35,127],"place":[23],"qubits":[24,37,58,107],"on":[25,56,60],"planar":[27],"grid":[28],"and":[29,59,81,98,113],"assume":[30],"native":[31,128],"CNOT":[32,124],"gates":[33,125],"between":[34,76],"data":[36],"nearest-neighbor":[39,63],"ancilla":[40],"qubits.Here,":[41],"we":[42,67],"present":[43],"error-correction":[46],"using":[48],"<mml:math":[49],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow":[50],"class=\"MJX-TeXAtom-ORD\"><mml:mtext":[51],"class=\"MJX-tex-mathit\"":[52],"mathvariant=\"italic\">only</mml:mtext></mml:mrow></mml:math>":[53],"Pauli":[54,120],"measurements":[55,121],"single":[57],"pairs":[61],"of":[62],"qubits.":[64],"In":[65],"particular,":[66],"provide":[68],"several":[69],"qubit":[70,77],"layouts":[71],"that":[72],"offer":[73],"favorable":[74],"trade-offs":[75],"overhead,":[78],"circuit":[79],"depth":[80],"connectivity":[82],"degree.":[83],"We":[84],"also":[85],"develop":[86],"minimized":[87],"measurement":[88],"sequences":[89],"syndrome":[91],"extraction,":[92],"enabling":[93],"reduced":[94],"logical":[95],"rates":[97],"improved":[99],"thresholds.Our":[101],"work":[102],"applies":[103],"to":[104,114],"topologically":[105],"protected":[106],"realized":[108],"Majorana":[110],"zero":[111],"modes":[112],"similar":[115],"systems":[116],"in":[117],"which":[118],"multi-qubit":[119],"rather":[122],"than":[123],"are":[126],"operations.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":5}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}