{"id":"https://openalex.org/W7214099559","doi":"https://doi.org/10.48550/arxiv.2609.26712","title":"A quantum lower bound for path finding in welded trees","display_name":"A quantum lower bound for path finding in welded trees","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214099559","doi":"https://doi.org/10.48550/arxiv.2609.26712"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.26712","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26712","pdf_url":"https://arxiv.org/pdf/2609.26712","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.26712","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070909635","display_name":"Joseph Carolan","orcid":"https://orcid.org/0000-0002-2891-9436","observed_orcids":["https://orcid.org/0000-0002-2891-9436"]},"institutions":[{"id":"https://openalex.org/I4210108409","display_name":"Joint Center for Quantum Information and Computer Science","ror":"https://ror.org/02048n894","country_code":"US","type":"facility","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065","https://openalex.org/I4210108409","https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Carolan, Joseph","raw_affiliation_strings":["Department of Computer Science , Institute for Advanced Computer Studies , and","Joint Center for Quantum Information and Computer Science , University of Maryland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , Institute for Advanced Computer Studies , and","institution_ids":[]},{"raw_affiliation_string":"Joint Center for Quantum Information and Computer Science , University of Maryland","institution_ids":["https://openalex.org/I4210108409"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018837979","display_name":"Andrew M. Childs","orcid":"https://orcid.org/0000-0002-9903-837X","observed_orcids":["https://orcid.org/0000-0002-9903-837X"]},"institutions":[{"id":"https://openalex.org/I4210108409","display_name":"Joint Center for Quantum Information and Computer Science","ror":"https://ror.org/02048n894","country_code":"US","type":"facility","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065","https://openalex.org/I4210108409","https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Childs, Andrew M.","raw_affiliation_strings":["Department of Computer Science , Institute for Advanced Computer Studies , and","Joint Center for Quantum Information and Computer Science , University of Maryland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , Institute for Advanced Computer Studies , and","institution_ids":[]},{"raw_affiliation_string":"Joint Center for Quantum Information and Computer Science , University of Maryland","institution_ids":["https://openalex.org/I4210108409"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026395918","display_name":"Matthew Coudron","orcid":"https://orcid.org/0000-0002-3296-4723","observed_orcids":["https://orcid.org/0000-0002-3296-4723"]},"institutions":[{"id":"https://openalex.org/I4210108409","display_name":"Joint Center for Quantum Information and Computer Science","ror":"https://ror.org/02048n894","country_code":"US","type":"facility","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065","https://openalex.org/I4210108409","https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Coudron, Matthew","raw_affiliation_strings":["Department of Computer Science , Institute for Advanced Computer Studies , and","Joint Center for Quantum Information and Computer Science , University of Maryland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , Institute for Advanced Computer Studies , and","institution_ids":[]},{"raw_affiliation_string":"Joint Center for Quantum Information and Computer Science , University of Maryland","institution_ids":["https://openalex.org/I4210108409"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018608700","display_name":"Amin Shiraz Gilani","orcid":"https://orcid.org/0000-0003-0859-7254","observed_orcids":["https://orcid.org/0000-0003-0859-7254"]},"institutions":[{"id":"https://openalex.org/I4210108409","display_name":"Joint Center for Quantum Information and Computer Science","ror":"https://ror.org/02048n894","country_code":"US","type":"facility","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065","https://openalex.org/I4210108409","https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gilani, Amin Shiraz","raw_affiliation_strings":["Department of Computer Science , Institute for Advanced Computer Studies , and","Joint Center for Quantum Information and Computer Science , University of Maryland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , Institute for Advanced Computer Studies , and","institution_ids":[]},{"raw_affiliation_string":"Joint Center for Quantum Information and Computer Science , University of Maryland","institution_ids":["https://openalex.org/I4210108409"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210108409"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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":0.9990000128746033,"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":0.9990000128746033,"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/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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.00019999999494757503,"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/quantum-lower-bounds","display_name":"quantum lower bounds","score":0.7419999837875366},{"id":"https://openalex.org/keywords/path-finding","display_name":"path finding","score":0.7210000157356262},{"id":"https://openalex.org/keywords/quantum-walks","display_name":"quantum walks","score":0.8040000200271606},{"id":"https://openalex.org/keywords/oracle-queries","display_name":"oracle queries","score":0.3970000147819519},{"id":"https://openalex.org/keywords/binary-trees","display_name":"binary trees","score":0.5120000243186951},{"id":"https://openalex.org/keywords/constructive-interference","display_name":"constructive interference","score":0.4959999918937683},{"id":"https://openalex.org/keywords/superposition","display_name":"superposition","score":0.4399999976158142}],"concepts":[{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.5875999927520752},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5831000208854675},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5318999886512756},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5242000222206116},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5213000178337097},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5092999935150146},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5048999786376953},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48579999804496765},{"id":"https://openalex.org/C140058369","wikidata":"https://www.wikidata.org/wiki/Q7269113","display_name":"Quantum walk","level":4,"score":0.4302000105381012},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42080000042915344},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.4187999963760376},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.3982999920845032},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.38530001044273376},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.36340001225471497},{"id":"https://openalex.org/C70501317","wikidata":"https://www.wikidata.org/wiki/Q462095","display_name":"Tree decomposition","level":5,"score":0.3603000044822693},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3544999957084656},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.3538999855518341},{"id":"https://openalex.org/C188032258","wikidata":"https://www.wikidata.org/wiki/Q1128371","display_name":"Constructive solid geometry","level":2,"score":0.34060001373291016},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.337799996137619},{"id":"https://openalex.org/C207024777","wikidata":"https://www.wikidata.org/wiki/Q621673","display_name":"Search tree","level":3,"score":0.3366999924182892},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32190001010894775},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.32030001282691956},{"id":"https://openalex.org/C62641251","wikidata":"https://www.wikidata.org/wiki/Q7269097","display_name":"Quantum sort","level":5,"score":0.3118000030517578},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.31040000915527344},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3034000098705292},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.29750001430511475},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C129045301","wikidata":"https://www.wikidata.org/wiki/Q7144654","display_name":"Path length","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2759999930858612},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2581999897956848},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.2533000111579895}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.26712","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26712","pdf_url":"https://arxiv.org/pdf/2609.26712","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.26712","doi":"https://doi.org/10.48550/arxiv.2609.26712","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.26712","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.26712","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26712","pdf_url":"https://arxiv.org/pdf/2609.26712","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3403804132","display_name":null,"funder_award_id":"DE-SC0020264","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320337506","display_name":"Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214099559.pdf","grobid_xml":"https://content.openalex.org/works/W7214099559.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1966934456","https://openalex.org/W2009948449","https://openalex.org/W2040792108","https://openalex.org/W3023478445","https://openalex.org/W3036045522","https://openalex.org/W3098715942","https://openalex.org/W3200803425","https://openalex.org/W4319050956","https://openalex.org/W4406055292","https://openalex.org/W4407889719","https://openalex.org/W4410119152","https://openalex.org/W6929523933","https://openalex.org/W7160958040","https://openalex.org/W7213602205"],"related_works":["https://openalex.org/W7213602205","https://openalex.org/W4402338177","https://openalex.org/W6922271085","https://openalex.org/W4407889719","https://openalex.org/W4403135068","https://openalex.org/W4390575968","https://openalex.org/W4396600721","https://openalex.org/W4376639497","https://openalex.org/W2750670778","https://openalex.org/W7097720941"],"abstract_inverted_index":{"In":[0],"the":[1,20,53,57,64,84,138,147,152,168,171],"welded":[2,90],"tree":[3,91,192],"problem,":[4],"an":[5,87,95],"algorithm":[6,74,111,143,172],"is":[7,70,122],"tasked":[8],"with":[9,173,193],"navigating":[10],"a":[11,23,50,81,98,101,141,159,187,190],"graph":[12],"formed":[13],"from":[14,33],"two":[15],"binary":[16],"trees":[17],"joined":[18],"at":[19],"leaves":[21],"through":[22],"``weld''":[24],"of":[25,86,97,140,170],"connecting":[26],"edges.":[27],"A":[28],"quantum":[29,46,73,102,142],"walk":[30],"can":[31,104],"navigate":[32],"root":[34,36],"to":[35,79,125,136,158,185],"exponentially":[37,76,106,114],"faster":[38,107],"than":[39,108],"any":[40,72,109,127],"classical":[41,110],"algorithm.":[42],"However,":[43],"known":[44],"efficient":[45],"algorithms":[47],"cannot":[48],"find":[49,80,126,186],"path":[51,58,82,188],"between":[52,83],"roots,":[54],"as":[55,144],"recording":[56],"destroys":[59],"constructive":[60],"interference":[61],"and":[62,166],"thus":[63],"speedup.":[65],"We":[66,149],"prove":[67],"that":[68,100,151,180],"this":[69],"inherent:":[71],"needs":[75],"many":[77,115],"queries":[78,146,182],"roots":[85],"independently":[88],"matched":[89],"graph.":[92,148],"This":[93],"provides":[94],"example":[96],"problem":[99],"computer":[103],"solve":[105],"by":[112],"exploring":[113],"paths":[116],"in":[117,189],"superposition,":[118],"but":[119],"where":[120],"it":[121,145],"provably":[123],"intractable":[124],"such":[128,164],"path.":[129],"The":[130],"proof":[131],"uses":[132],"compressed":[133,153,175],"permutation":[134],"oracles":[135],"record":[137],"progress":[139,169],"show":[150,179],"database":[154],"remains":[155],"path-free":[156],"up":[157],"small":[160],"error.":[161],"By":[162],"controlling":[163],"errors":[165],"bounding":[167],"each":[174],"oracle":[176],"query,":[177],"we":[178],"$\u03a9(2^{n/12})$":[181],"are":[183],"required":[184],"height-$n$":[191],"constant":[194],"success":[195],"probability.":[196]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-09-24T00:00:00"}