{"id":"https://openalex.org/W3110379352","doi":"https://doi.org/10.1007/s11128-021-03212-y","title":"An index theorem for one-dimensional gapless non-unitary quantum walks","display_name":"An index theorem for one-dimensional gapless non-unitary quantum walks","publication_year":2021,"publication_date":"2021-09-01","ids":{"openalex":"https://openalex.org/W3110379352","doi":"https://doi.org/10.1007/s11128-021-03212-y","mag":"3110379352"},"language":"en","primary_location":{"id":"doi:10.1007/s11128-021-03212-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11128-021-03212-y","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":true,"oa_status":"green","oa_url":"http://arxiv.org/abs/2011.12907","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042767517","display_name":"Keisuke Asahara","orcid":null},"institutions":[{"id":"https://openalex.org/I171494771","display_name":"Shiga University","ror":"https://ror.org/01vvhy971","country_code":"JP","type":"education","lineage":["https://openalex.org/I171494771"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Keisuke Asahara","raw_affiliation_strings":["The Center for Data Science Education and Research, Shiga University, Hikone, 522-8522, Japan","Shiga University#TAB#"],"affiliations":[{"raw_affiliation_string":"The Center for Data Science Education and Research, Shiga University, Hikone, 522-8522, Japan","institution_ids":["https://openalex.org/I171494771"]},{"raw_affiliation_string":"Shiga University#TAB#","institution_ids":["https://openalex.org/I171494771"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044824053","display_name":"Daiju Funakawa","orcid":"https://orcid.org/0000-0003-3991-8049"},"institutions":[{"id":"https://openalex.org/I91764395","display_name":"Hokkai Gakuen University","ror":"https://ror.org/05h9h0e34","country_code":"JP","type":"education","lineage":["https://openalex.org/I91764395"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Daiju Funakawa","raw_affiliation_strings":["Department of Electronics and Information Engineering, Hokkai-Gakuen University, Sapporo, 062-8605, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Electronics and Information Engineering, Hokkai-Gakuen University, Sapporo, 062-8605, Japan","institution_ids":["https://openalex.org/I91764395"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041491944","display_name":"Motoki Seki","orcid":"https://orcid.org/0000-0002-8374-6742"},"institutions":[{"id":"https://openalex.org/I205349734","display_name":"Hokkaido University","ror":"https://ror.org/02e16g702","country_code":"JP","type":"education","lineage":["https://openalex.org/I205349734"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Motoki Seki","raw_affiliation_strings":["Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan","*** Hokkaido University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan","institution_ids":["https://openalex.org/I205349734"]},{"raw_affiliation_string":"*** Hokkaido University","institution_ids":["https://openalex.org/I205349734"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015516695","display_name":"Yohei Tanaka","orcid":"https://orcid.org/0000-0001-6325-6976"},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]},{"id":"https://openalex.org/I4210162928","display_name":"\u014ctani University","ror":"https://ror.org/05b7rex33","country_code":"JP","type":"education","lineage":["https://openalex.org/I4210162928"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yohei Tanaka","raw_affiliation_strings":["Department of Science and Technology, Graduate School of Medicine, Science and Technology, Shinshu University, 4-17-1 Wakasato, Nagano, 380-8553, Japan","shinshu university"],"affiliations":[{"raw_affiliation_string":"Department of Science and Technology, Graduate School of Medicine, Science and Technology, Shinshu University, 4-17-1 Wakasato, Nagano, 380-8553, Japan","institution_ids":["https://openalex.org/I137975476"]},{"raw_affiliation_string":"shinshu university","institution_ids":["https://openalex.org/I4210162928"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5042767517"],"corresponding_institution_ids":["https://openalex.org/I171494771"],"apc_list":{"value":2040,"currency":"EUR","value_usd":2690},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01079818,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"9","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":1.0,"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":1.0,"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/T10382","display_name":"Quantum and electron transport phenomena","score":0.9995999932289124,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9991999864578247,"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/unitary-state","display_name":"Unitary state","score":0.7792111039161682},{"id":"https://openalex.org/keywords/quantum-walk","display_name":"Quantum walk","score":0.6751505732536316},{"id":"https://openalex.org/keywords/unitary-operator","display_name":"Unitary operator","score":0.4481375813484192},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.44730469584465027},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.42609304189682007},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.40663230419158936},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.3651104271411896},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3504650294780731},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34369638562202454},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.3294448256492615},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.3277788460254669},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.11551669239997864}],"concepts":[{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.7792111039161682},{"id":"https://openalex.org/C140058369","wikidata":"https://www.wikidata.org/wiki/Q7269113","display_name":"Quantum walk","level":4,"score":0.6751505732536316},{"id":"https://openalex.org/C188313703","wikidata":"https://www.wikidata.org/wiki/Q1972470","display_name":"Unitary operator","level":3,"score":0.4481375813484192},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.44730469584465027},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.42609304189682007},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.40663230419158936},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.3651104271411896},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3504650294780731},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34369638562202454},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3294448256492615},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3277788460254669},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.11551669239997864},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11128-021-03212-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11128-021-03212-y","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"},{"id":"mag:3110379352","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.12907","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:3110379352","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.12907","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G3312673305","display_name":null,"funder_award_id":"20J22684","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W1571862096","https://openalex.org/W1605376869","https://openalex.org/W1930898761","https://openalex.org/W1984066085","https://openalex.org/W1998942810","https://openalex.org/W2020750044","https://openalex.org/W2054665888","https://openalex.org/W2077461478","https://openalex.org/W2082600570","https://openalex.org/W2084652510","https://openalex.org/W2101697221","https://openalex.org/W2119006096","https://openalex.org/W2143496717","https://openalex.org/W2145841221","https://openalex.org/W2150979238","https://openalex.org/W2152074534","https://openalex.org/W2157417281","https://openalex.org/W2158797683","https://openalex.org/W2162328638","https://openalex.org/W2238068711","https://openalex.org/W2296505866","https://openalex.org/W2297550529","https://openalex.org/W2301204088","https://openalex.org/W2579770048","https://openalex.org/W2597006072","https://openalex.org/W2602672413","https://openalex.org/W2783696205","https://openalex.org/W2796609849","https://openalex.org/W2796930482","https://openalex.org/W2797914356","https://openalex.org/W2809823332","https://openalex.org/W2907786826","https://openalex.org/W2913627097","https://openalex.org/W2919781946","https://openalex.org/W2949509872","https://openalex.org/W2952108034","https://openalex.org/W2962981807","https://openalex.org/W2963351503","https://openalex.org/W2963486760","https://openalex.org/W2963497944","https://openalex.org/W2963927963","https://openalex.org/W2972669407","https://openalex.org/W2981537660","https://openalex.org/W2983677035","https://openalex.org/W3034151858","https://openalex.org/W3036736675","https://openalex.org/W3036853479","https://openalex.org/W3039704464","https://openalex.org/W3094798731","https://openalex.org/W3102259511","https://openalex.org/W3103714698","https://openalex.org/W3105403009","https://openalex.org/W3106418682","https://openalex.org/W3108407801","https://openalex.org/W3118886727","https://openalex.org/W3213089405","https://openalex.org/W4205692735","https://openalex.org/W4244341722"],"related_works":["https://openalex.org/W28780544","https://openalex.org/W21981753","https://openalex.org/W9332776","https://openalex.org/W8697828","https://openalex.org/W853042","https://openalex.org/W19569559","https://openalex.org/W14700008","https://openalex.org/W1591543","https://openalex.org/W17791918","https://openalex.org/W8867144"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
