{"id":"https://openalex.org/W85480495","doi":"https://doi.org/10.4086/toc.2010.v006a003","title":"","display_name":"","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W85480495","doi":"https://doi.org/10.4086/toc.2010.v006a003","mag":"85480495"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2010.v006a003","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2010.v006a003","pdf_url":"https://theoryofcomputing.org/articles/v006a003/v006a003.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v006a003/v006a003.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081761718","display_name":"Avraham Ben-Aroya","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Avraham Ben-Aroya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010957839","display_name":"Oded Schwartz","orcid":"https://orcid.org/0000-0003-1309-5566"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oded Schwartz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5051671028","display_name":"Amnon Ta\u2010Shma","orcid":"https://orcid.org/0000-0001-8186-3622"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Amnon Ta-Shma","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6736,"has_fulltext":true,"cited_by_count":61,"citation_normalized_percentile":{"value":0.92760147,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"6","issue":"1","first_page":"47","last_page":"79"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9696000218391418,"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":0.9696000218391418,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9423999786376953,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9412999749183655,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.694400429725647},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5369091033935547},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5075391530990601},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45365846157073975},{"id":"https://openalex.org/keywords/expander-graph","display_name":"Expander graph","score":0.4276978373527527},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.4145534932613373},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.18304350972175598},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.1451059877872467},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10962322354316711}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.694400429725647},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5369091033935547},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5075391530990601},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45365846157073975},{"id":"https://openalex.org/C154547637","wikidata":"https://www.wikidata.org/wiki/Q776602","display_name":"Expander graph","level":3,"score":0.4276978373527527},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4145534932613373},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.18304350972175598},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.1451059877872467},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10962322354316711}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2010.v006a003","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2010.v006a003","pdf_url":"https://theoryofcomputing.org/articles/v006a003/v006a003.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2010.v006a003","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2010.v006a003","pdf_url":"https://theoryofcomputing.org/articles/v006a003/v006a003.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5946206379","display_name":null,"funder_award_id":"015848","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322248","display_name":"Israel Academy of Sciences and Humanities","ror":"https://ror.org/03c6c9520"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W85480495.pdf","grobid_xml":"https://content.openalex.org/works/W85480495.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W200635132","https://openalex.org/W1596185498","https://openalex.org/W1597310767","https://openalex.org/W1631603072","https://openalex.org/W1880683812","https://openalex.org/W1950297283","https://openalex.org/W1966779504","https://openalex.org/W1971684380","https://openalex.org/W1973309660","https://openalex.org/W1987550746","https://openalex.org/W1993111701","https://openalex.org/W2018047324","https://openalex.org/W2032830293","https://openalex.org/W2036871172","https://openalex.org/W2036878392","https://openalex.org/W2045377861","https://openalex.org/W2047342855","https://openalex.org/W2048958388","https://openalex.org/W2057648657","https://openalex.org/W2093704631","https://openalex.org/W2116921087","https://openalex.org/W2120279343","https://openalex.org/W2136616826","https://openalex.org/W2148180254","https://openalex.org/W2320951892","https://openalex.org/W2578255341","https://openalex.org/W2610637368","https://openalex.org/W2764347725","https://openalex.org/W2950843936","https://openalex.org/W2952371212","https://openalex.org/W2953185906","https://openalex.org/W2963814814","https://openalex.org/W4235584939","https://openalex.org/W4235936977","https://openalex.org/W4240060697","https://openalex.org/W4246684182","https://openalex.org/W4301133941"],"related_works":["https://openalex.org/W49538288","https://openalex.org/W2920848012","https://openalex.org/W4289671387","https://openalex.org/W4234725236","https://openalex.org/W4380925380","https://openalex.org/W2185454958","https://openalex.org/W2050262222","https://openalex.org/W2122270497","https://openalex.org/W2004534915","https://openalex.org/W189296720"],"abstract_inverted_index":{"We":[0],"define":[1],"quantum":[2,13,58],"expanders":[3],"in":[4],"a":[5,57],"natural":[6],"way":[7],"and":[8,26,45,53,68,77],"give":[9],"two":[10],"constructions":[11,72],"of":[12,32,60,74],"expanders,":[14],"both":[15],"based":[16,28,55],"on":[17,29,56],"classical":[18],"expander":[19],"constructions.":[20],"The":[21,48],"first":[22],"construction":[23,31,50],"is":[24,27,51,54,81],"algebraic,":[25],"the":[30,37,61,78],"Cayley":[33],"Ramanujan":[34],"graphs":[35],"over":[36],"group":[38],"PGL(2,":[39],"q)":[40],"given":[41],"by":[42,65],"Lubotzky,":[43],"Phillips,":[44],"Sarnak":[46],"(1988).":[47],"second":[49,79],"combinatorial,":[52],"variant":[59],"Zig-Zag":[62],"product":[63],"introduced":[64],"Reingold,":[66],"Vadhan,":[67],"Wigderson":[69],"(2000).":[70],"Both":[71],"are":[73],"constant":[75],"degree,":[76],"one":[80],"explicit.":[82]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":34},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2025-12-17T22:08:43.090829","created_date":"2016-06-24T00:00:00"}