{"id":"https://openalex.org/W4297109183","doi":"https://doi.org/10.26421/qic22.13-14-2","title":"Of shadows and gaps in spatial search","display_name":"Of shadows and gaps in spatial search","publication_year":2022,"publication_date":"2022-09-01","ids":{"openalex":"https://openalex.org/W4297109183","doi":"https://doi.org/10.26421/qic22.13-14-2"},"language":"en","primary_location":{"id":"doi:10.26421/qic22.13-14-2","is_oa":false,"landing_page_url":"https://doi.org/10.26421/qic22.13-14-2","pdf_url":null,"source":{"id":"https://openalex.org/S41034432","display_name":"Quantum Information and Computation","issn_l":"1533-7146","issn":["1533-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310322612","host_organization_name":"Rinton Press","host_organization_lineage":["https://openalex.org/P4310322612"],"host_organization_lineage_names":["Rinton Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum Information and Computation","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/A5008696931","display_name":"Ada Chan","orcid":"https://orcid.org/0000-0001-9310-034X"},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Ada Chan","raw_affiliation_strings":["Department of Mathematics and Statistics, York University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, York University","institution_ids":["https://openalex.org/I192455969"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079662904","display_name":"Chris Godsil","orcid":"https://orcid.org/0000-0001-6110-5752"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Chris Godsil","raw_affiliation_strings":["Department of Combinatorics and Optimization, University of Waterloo"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089437859","display_name":"Christino Tamon","orcid":"https://orcid.org/0000-0003-4955-5253"},"institutions":[{"id":"https://openalex.org/I16944753","display_name":"Clarkson University","ror":"https://ror.org/03rwgpn18","country_code":"US","type":"education","lineage":["https://openalex.org/I16944753"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christino Tamon","raw_affiliation_strings":["Department of Computer Science, Clarkson University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Clarkson University","institution_ids":["https://openalex.org/I16944753"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020740605","display_name":"Weichen Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I16944753","display_name":"Clarkson University","ror":"https://ror.org/03rwgpn18","country_code":"US","type":"education","lineage":["https://openalex.org/I16944753"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Weichen Xie","raw_affiliation_strings":["Department of Mathematics, Clarkson University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Clarkson University","institution_ids":["https://openalex.org/I16944753"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4162,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.6859118,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"22","issue":"13&14","first_page":"1110","last_page":"1131"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9980000257492065,"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":0.9980000257492065,"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/T12288","display_name":"Optimization and Search Problems","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9524000287055969,"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/mathematics","display_name":"Mathematics","score":0.702960729598999},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.6829949021339417},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5539247989654541},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5194534659385681},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4996652603149414},{"id":"https://openalex.org/keywords/hamming-graph","display_name":"Hamming graph","score":0.4122542142868042},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3850695490837097},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.333804726600647},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22984349727630615},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.1954898238182068},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.15792763233184814}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.702960729598999},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.6829949021339417},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5539247989654541},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5194534659385681},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4996652603149414},{"id":"https://openalex.org/C29696283","wikidata":"https://www.wikidata.org/wiki/Q369440","display_name":"Hamming graph","level":5,"score":0.4122542142868042},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3850695490837097},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.333804726600647},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22984349727630615},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.1954898238182068},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.15792763233184814},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.26421/qic22.13-14-2","is_oa":false,"landing_page_url":"https://doi.org/10.26421/qic22.13-14-2","pdf_url":null,"source":{"id":"https://openalex.org/S41034432","display_name":"Quantum Information and Computation","issn_l":"1533-7146","issn":["1533-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310322612","host_organization_name":"Rinton Press","host_organization_lineage":["https://openalex.org/P4310322612"],"host_organization_lineage_names":["Rinton Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum Information and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1561344775","https://openalex.org/W1839255271","https://openalex.org/W1987962147","https://openalex.org/W2026110478","https://openalex.org/W2040927484","https://openalex.org/W2058286540","https://openalex.org/W2222710443","https://openalex.org/W2284228492","https://openalex.org/W2620195106","https://openalex.org/W2764347725","https://openalex.org/W3192868571"],"related_works":["https://openalex.org/W3110471371","https://openalex.org/W3009392694","https://openalex.org/W4287829431","https://openalex.org/W1996010389","https://openalex.org/W2887981140","https://openalex.org/W2083881167","https://openalex.org/W1573315184","https://openalex.org/W2374778222","https://openalex.org/W1963961477","https://openalex.org/W38971153"],"abstract_inverted_index":{"Spatial":[0],"search":[1,57,140],"occurs":[2,65],"in":[3,70],"a":[4,8,22,48,86,100,132,146],"connected":[5],"graph":[6,37],"if":[7,63],"continuous-time":[9,50],"quantum":[10],"walk":[11],"on":[12,81,108,136],"the":[13,17,32,36,39,43,75,78,82],"adjacency":[14],"matrix":[15],"of":[16,35,42,52,77,88,103,116],"graph,":[18],"suitably":[19],"scaled,":[20],"plus":[21],"rank-one":[23],"perturbation":[24],"induced":[25],"by":[26],"any":[27],"vertex":[28,80],"will":[29],"unitarily":[30],"map":[31],"principal":[33,83],"eigenvector":[34],"to":[38,60,74,149],"characteristic":[40],"vector":[41],"vertex.":[44],"This":[45],"phenomenon":[46],"is":[47,58],"natural":[49],"analogue":[51],"Grover":[53],"search.":[54,106,128],"The":[55],"spatial":[56,105,127,139],"said":[59],"be":[61],"optimal":[62,104,126],"it":[64],"with":[66,141],"constant":[67,142],"fidelity":[68],"and":[69,122,151,166],"time":[71,137],"inversely":[72],"proportional":[73],"shadow":[76],"target":[79],"eigenvector.":[84],"Extending":[85],"result":[87],"Chakraborty":[89],"\\etal":[90],"({\\em":[91],"Physical":[92],"Review":[93],"A},":[94],"{\\bf":[95],"102}:032214,":[96],"2020),":[97],"we":[98,111],"prove":[99],"simpler":[101],"characterization":[102],"Based":[107],"this":[109],"characterization,":[110],"observe":[112],"that":[113],"some":[114],"families":[115],"distance-regular":[117],"graphs,":[118,124],"such":[119,162],"as":[120,163],"Hamming":[121],"Grassmann":[123],"have":[125],"We":[129],"also":[130],"show":[131],"matching":[133],"lower":[134],"bound":[135,147],"for":[138,153],"fidelity,":[143],"which":[144],"extends":[145],"due":[148],"Farhi":[150],"Gutmann":[152],"perfect":[154],"fidelity.":[155],"Our":[156],"elementary":[157],"proofs":[158],"employ":[159],"standard":[160],"tools,":[161],"Weyl":[164],"inequalities":[165],"Cauchy":[167],"determinant":[168],"formula.":[169]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
