{"id":"https://openalex.org/W94834053","doi":null,"title":"Symmetry in quantum walks","display_name":"Symmetry in quantum walks","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W94834053","mag":"94834053"},"language":"en","primary_location":{"id":"mag:94834053","doi":null,"is_oa":false,"landing_page_url":"http://ui.adsabs.harvard.edu/abs/2007PhDT.......206K/abstract","pdf_url":null,"source":{"id":"https://openalex.org/S4306522422","display_name":"PhDT","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"PhDT","raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5061373590","display_name":"Todd A. Brun","orcid":"https://orcid.org/0000-0002-8807-3495","observed_orcids":["https://orcid.org/0000-0002-8807-3495"]},"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":false,"raw_author_name":"Todd A. Brun","raw_affiliation_strings":["University of Southern California"],"raw_orcid":"https://orcid.org/0000-0002-8807-3495","affiliations":[{"raw_affiliation_string":"University of Southern California","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070804288","display_name":"Hari Krovi","orcid":"https://orcid.org/0000-0001-9675-9959","observed_orcids":["https://orcid.org/0000-0001-9675-9959"]},"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":false,"raw_author_name":"Hari Krovi","raw_affiliation_strings":["University of Southern California"],"raw_orcid":"https://orcid.org/0000-0001-9675-9959","affiliations":[{"raw_affiliation_string":"University of Southern California","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":null,"apc_paid":null,"fwci":0.358,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.68896599,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":95},"biblio":{"volume":null,"issue":null,"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":0.9970999956130981,"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":0.9970999956130981,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.00039999998989515007,"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":0.0003000000142492354,"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/discrete-time-quantum-walks","display_name":"discrete-time quantum walks","score":0.9860000014305115},{"id":"https://openalex.org/keywords/first-passage-time","display_name":"first passage time","score":0.8330000042915344},{"id":"https://openalex.org/keywords/graph-automorphism-groups","display_name":"graph automorphism groups","score":0.7870000004768372},{"id":"https://openalex.org/keywords/graph-symmetry","display_name":"graph symmetry","score":0.7020000219345093},{"id":"https://openalex.org/keywords/quotient-graphs","display_name":"quotient graphs","score":0.7450000047683716},{"id":"https://openalex.org/keywords/irreducible-representations","display_name":"irreducible representations","score":0.8119999766349792},{"id":"https://openalex.org/keywords/superoperators","display_name":"superoperators","score":0.6069999933242798},{"id":"https://openalex.org/keywords/hypercube","display_name":"hypercube","score":0.8579999804496765},{"id":"https://openalex.org/keywords/quantum-advantage","display_name":"quantum advantage","score":0.6729999780654907},{"id":"https://openalex.org/keywords/decoherence-free-subspace","display_name":"decoherence-free subspace","score":0.9539999961853027},{"id":"https://openalex.org/keywords/coin-operator","display_name":"coin operator","score":0.5870000123977661},{"id":"https://openalex.org/keywords/decoherence-models","display_name":"decoherence models","score":0.6679999828338623}],"concepts":[{"id":"https://openalex.org/C140058369","wikidata":"https://www.wikidata.org/wiki/Q7269113","display_name":"Quantum walk","level":4,"score":0.9234439730644226},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7139739394187927},{"id":"https://openalex.org/C199277547","wikidata":"https://www.wikidata.org/wiki/Q5872687","display_name":"Hitting time","level":2,"score":0.579365074634552},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.4530692398548126},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4393211901187897},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4270429313182831},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.424391508102417},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.41077983379364014},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4063831567764282},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3986009955406189},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33271998167037964},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.31875142455101013},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.20753702521324158},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1369512677192688},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:94834053","doi":null,"is_oa":false,"landing_page_url":"http://ui.adsabs.harvard.edu/abs/2007PhDT.......206K/abstract","pdf_url":null,"source":{"id":"https://openalex.org/S4306522422","display_name":"PhDT","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"PhDT","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W71890215","https://openalex.org/W126362881","https://openalex.org/W1502176956","https://openalex.org/W1503154552","https://openalex.org/W1520302490","https://openalex.org/W1558273801","https://openalex.org/W1596185498","https://openalex.org/W1616736674","https://openalex.org/W1631356911","https://openalex.org/W1640526923","https://openalex.org/W1770148716","https://openalex.org/W1973321785","https://openalex.org/W1978553093","https://openalex.org/W1999462261","https://openalex.org/W2005268019","https://openalex.org/W2009948449","https://openalex.org/W2010245486","https://openalex.org/W2015179126","https://openalex.org/W2020750044","https://openalex.org/W2022914085","https://openalex.org/W2025956887","https://openalex.org/W2028528561","https://openalex.org/W2040927484","https://openalex.org/W2050334794","https://openalex.org/W2059041305","https://openalex.org/W2059551605","https://openalex.org/W2074348237","https://openalex.org/W2084652510","https://openalex.org/W2101088258","https://openalex.org/W2121124751","https://openalex.org/W2127608358","https://openalex.org/W2137005141","https://openalex.org/W2147228721","https://openalex.org/W2148132004","https://openalex.org/W2154773309","https://openalex.org/W2160185408","https://openalex.org/W2179731956","https://openalex.org/W2295428206","https://openalex.org/W2964137917","https://openalex.org/W3133726852"],"related_works":["https://openalex.org/W2074348237","https://openalex.org/W2022914085","https://openalex.org/W3178845911","https://openalex.org/W2068842305","https://openalex.org/W1779869318","https://openalex.org/W1013904132","https://openalex.org/W1977392168","https://openalex.org/W1609008923","https://openalex.org/W7047358039","https://openalex.org/W2950944671"],"abstract_inverted_index":{"A":[0],"discrete-time":[1],"quantum":[2,28,89,126,194,234,251,323],"walk":[3,38,58,75,108,213,235,252,319],"on":[4,30,59,76,109,197,253],"a":[5,12,17,72,77,106,110,119,153,167,219,233,249,254,307,318,322,345],"graph":[6,79,111,160,199,266,280,287,310,343],"is":[7,128,150,315,344],"the":[8,22,37,57,60,130,133,139,142,156,159,178,182,186,212,222,238,264,272,278,285,289,294,304,330,338,341,349],"repeated":[9],"application":[10],"of":[11,132,141,146,155,158,166,185,221,263,271,277,306,332,340,348],"unitary":[13],"evolution":[14,134,179],"operator":[15,135],"to":[16,21,103,214,218,237,241,298,320,335],"Hilbert":[18,224],"space":[19,225],"corresponding":[20,240],"graph.":[23,143,257],"Hitting":[24],"times":[25,95,149,204,314],"for":[26,47,56,62,71,96,123,205,226,267,317],"discrete":[27,124],"walks":[29,90,127,195],"graphs":[31],"give":[32,259],"an":[33,40,45,260],"average":[34],"time":[35,49,70,125],"before":[36],"reaches":[39],"ending":[41],"condition.":[42],"We":[43,84,100,230,258,301],"derive":[44,190],"expression":[46],"hitting":[48,69,94,115,148,203,313],"using":[50],"superoperators,":[51],"and":[52,65,117,161,329],"numerically":[53],"evaluate":[54],"it":[55],"hypercube":[61],"various":[63],"coins":[64],"decoherence":[66],"models.":[67],"The":[68,144,275],"classical":[73],"random":[74],"connected":[78],"will":[80,112],"always":[81],"be":[82,136,175,216,246],"finite.":[83],"show":[85,231],"that,":[86],"by":[87,170,177],"contrast,":[88],"can":[91,174,210,245],"have":[92,113,201],"infinite":[93,114,147,202],"some":[97,206],"initial":[98,207,228],"states.":[99,208,229],"seek":[101],"criteria":[102],"determine":[104,336],"if":[105],"given":[107,169],"times,":[116],"find":[118],"sufficient":[120],"condition,":[121],"which":[122,281],"that":[129,193,232,303],"degeneracy":[131],"greater":[137],"than":[138],"degree":[140],"phenomenon":[145],"in":[151],"general":[152],"consequence":[154],"symmetry":[157,243,328],"its":[162,171],"automorphism":[163,172,187,273,291],"group.":[164,274],"\r\nSymmetries":[165],"graph,":[168],"group,":[173,188],"inherited":[176,283],"operator.":[180],"Using":[181],"irreducible":[183],"representations":[184],"we":[189,326],"conditions":[191],"such":[192],"defined":[196],"this":[198,242],"must":[200],"Symmetry":[209],"cause":[211],"also":[215],"confined":[217,236],"subspace":[220,239,339,347],"original":[223,286,290],"cartain":[227],"group":[244,292],"seen":[247],"as":[248],"different":[250],"smaller":[255],"quotient":[256,265,279,309,342],"explicit":[261],"construction":[262],"any":[268],"subgroup":[269,295],"H":[270,296],"automorphisms":[276],"are":[282,288],"from":[284],"modulo":[293],"used":[297],"construct":[299],"it.":[300],"conjecture":[302],"existence":[305],"small":[308],"with":[311],"finite":[312],"necessary":[316],"exhibit":[321],"speed-up.":[324],"Finally,":[325],"use":[327],"theory":[331],"decoherence-free":[333,346],"subspaces":[334],"when":[337],"dynamics.":[350]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}