{"id":"https://openalex.org/W2035499096","doi":"https://doi.org/10.1007/s11128-012-0361-3","title":"Asymptotic distributions of quantum walks on the line with two entangled coins","display_name":"Asymptotic distributions of quantum walks on the line with two entangled coins","publication_year":2012,"publication_date":"2012-01-25","ids":{"openalex":"https://openalex.org/W2035499096","doi":"https://doi.org/10.1007/s11128-012-0361-3","mag":"2035499096"},"language":"en","primary_location":{"id":"doi:10.1007/s11128-012-0361-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11128-012-0361-3","pdf_url":null,"source":{"id":"https://openalex.org/S92819544","display_name":"Quantum Information Processing","issn_l":"1570-0755","issn":["1570-0755","1573-1332"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum Information Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004632038","display_name":"Chaobin Liu","orcid":"https://orcid.org/0000-0003-1827-6235"},"institutions":[{"id":"https://openalex.org/I324100","display_name":"Bowie State University","ror":"https://ror.org/0567w8j84","country_code":"US","type":"education","lineage":["https://openalex.org/I324100"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chaobin Liu","raw_affiliation_strings":["Department of Mathematics, Bowie State University, Bowie, MD, 20715, USA","Department of Mathematics, Bowie State University, Bowie, USA 20715#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bowie State University, Bowie, MD, 20715, USA","institution_ids":["https://openalex.org/I324100"]},{"raw_affiliation_string":"Department of Mathematics, Bowie State University, Bowie, USA 20715#TAB#","institution_ids":["https://openalex.org/I324100"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004632038"],"corresponding_institution_ids":["https://openalex.org/I324100"],"apc_list":{"value":2040,"currency":"EUR","value_usd":2690},"apc_paid":null,"fwci":2.652,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.90384062,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"11","issue":"5","first_page":"1193","last_page":"1205"},"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":0.9894999861717224,"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":0.9878000020980835,"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/quantum-walk","display_name":"Quantum walk","score":0.9817641973495483},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5191828012466431},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.4930257499217987},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.48717090487480164},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.48077553510665894},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4675435423851013},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4418213963508606},{"id":"https://openalex.org/keywords/quantum-state","display_name":"Quantum state","score":0.44103461503982544},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.43846723437309265},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.41892462968826294},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.39670297503471375},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3353678584098816},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12849083542823792},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08912250399589539}],"concepts":[{"id":"https://openalex.org/C140058369","wikidata":"https://www.wikidata.org/wiki/Q7269113","display_name":"Quantum walk","level":4,"score":0.9817641973495483},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5191828012466431},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.4930257499217987},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.48717090487480164},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.48077553510665894},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4675435423851013},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4418213963508606},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.44103461503982544},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.43846723437309265},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.41892462968826294},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.39670297503471375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3353678584098816},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12849083542823792},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08912250399589539},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11128-012-0361-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11128-012-0361-3","pdf_url":null,"source":{"id":"https://openalex.org/S92819544","display_name":"Quantum Information Processing","issn_l":"1570-0755","issn":["1570-0755","1573-1332"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum Information Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W581444746","https://openalex.org/W1510607640","https://openalex.org/W1519689626","https://openalex.org/W1571862096","https://openalex.org/W1770148716","https://openalex.org/W1853534046","https://openalex.org/W1966092221","https://openalex.org/W1972539665","https://openalex.org/W1973321785","https://openalex.org/W1975528636","https://openalex.org/W1998025305","https://openalex.org/W2010672697","https://openalex.org/W2015416844","https://openalex.org/W2022080729","https://openalex.org/W2050185359","https://openalex.org/W2054665888","https://openalex.org/W2056390378","https://openalex.org/W2067287259","https://openalex.org/W2076107645","https://openalex.org/W2077461478","https://openalex.org/W2080162480","https://openalex.org/W2101697221","https://openalex.org/W2156029098","https://openalex.org/W2160185408","https://openalex.org/W2163879306","https://openalex.org/W2964197561","https://openalex.org/W3106020145","https://openalex.org/W3106256965","https://openalex.org/W4210992804","https://openalex.org/W4211028461"],"related_works":["https://openalex.org/W2089342336","https://openalex.org/W2949694831","https://openalex.org/W3114654323","https://openalex.org/W1968287309","https://openalex.org/W2883913628","https://openalex.org/W2800432156","https://openalex.org/W1566596544","https://openalex.org/W638834885","https://openalex.org/W4320736706","https://openalex.org/W2025956887"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
