{"id":"https://openalex.org/W2099170023","doi":"https://doi.org/10.4086/toc.2009.v005a005","title":"","display_name":"","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2099170023","doi":"https://doi.org/10.4086/toc.2009.v005a005","mag":"2099170023"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2009.v005a005","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2009.v005a005","pdf_url":"https://theoryofcomputing.org/articles/v005a005/v005a005.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v005a005/v005a005.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Andrew M. Childs","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andrew M. Childs","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Richard Cleve","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richard Cleve","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Stephen P. Jordan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stephen P. Jordan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"David Yonge-Mallo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David Yonge-Mallo","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.8728,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.96063038,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"5","issue":"1","first_page":"119","last_page":"123"},"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9987000226974487,"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":0.9962999820709229,"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/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5278000235557556},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.508899986743927},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4887000024318695},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.48510000109672546},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.3398999869823456},{"id":"https://openalex.org/keywords/running-time","display_name":"Running time","score":0.3271999955177307},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.3059000074863434}],"concepts":[{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5278000235557556},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.508899986743927},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49390000104904175},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4887000024318695},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.48510000109672546},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4372999966144562},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42980000376701355},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3578000068664551},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3458999991416931},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3398999869823456},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.3271999955177307},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.3059000074863434},{"id":"https://openalex.org/C124296912","wikidata":"https://www.wikidata.org/wiki/Q575178","display_name":"NAND gate","level":3,"score":0.30219998955726624},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.2590000033378601},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.25200000405311584}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.4086/toc.2009.v005a005","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2009.v005a005","pdf_url":"https://theoryofcomputing.org/articles/v005a005/v005a005.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:quant-ph/0702160","is_oa":true,"landing_page_url":"http://arxiv.org/abs/quant-ph/0702160","pdf_url":"https://arxiv.org/pdf/quant-ph/0702160","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":null,"raw_type":"text"},{"id":"pmh:oai:authors.library.caltech.edu:16421","is_oa":true,"landing_page_url":null,"pdf_url":"https://authors.library.caltech.edu/16421/","source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.4086/toc.2009.v005a005","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2009.v005a005","pdf_url":"https://theoryofcomputing.org/articles/v005a005/v005a005.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6636629706","display_name":"Institute for Quantum Information","funder_award_id":"0456720","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8998121839","display_name":null,"funder_award_id":"911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322675","display_name":"Mitacs","ror":"https://ror.org/00cjrc276"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2099170023.pdf","grobid_xml":"https://content.openalex.org/works/W2099170023.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1975528636","https://openalex.org/W1987152249","https://openalex.org/W2009353303","https://openalex.org/W2026325622","https://openalex.org/W2120560473","https://openalex.org/W2593070235","https://openalex.org/W3038086750","https://openalex.org/W3101636216"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2913765211","https://openalex.org/W4244379845","https://openalex.org/W2313400459","https://openalex.org/W2042127053","https://openalex.org/W2187256922","https://openalex.org/W2963510427","https://openalex.org/W1974891317","https://openalex.org/W2088929118"],"abstract_inverted_index":{"This":[0],"is":[1],"a":[2,32],"comment":[3],"on":[4],"the":[5,11,45,69],"article":[6],"\"A":[7],"Quantum":[8],"Algorithm":[9],"for":[10,35],"Hamiltonian":[12,46],"NAND":[13,37],"Tree\"":[14],"by":[15],"Edward":[16],"Farhi,":[17],"Jeffrey":[18],"Goldstone,":[19],"and":[20],"Sam":[21],"Gutmann,":[22],"Theory":[23],"of":[24],"Computing":[25],"4":[26],"(2008)":[27],"169-190.":[28],"That":[29],"paper":[30],"gave":[31],"quantum":[33,72],"algorithm":[34,57,63],"evaluating":[36],"trees":[38],"with":[39],"running":[40],"time":[41],"O(":[42],"N)":[43],"in":[44,68],"query":[47,73],"model.":[48,74],"In":[49],"this":[50],"note,":[51],"we":[52],"point":[53],"out":[54],"that":[55],"their":[56],"can":[58],"be":[59],"converted":[60],"into":[61],"an":[62],"using":[64],"N":[65],"1/2+o(1)":[66],"queries":[67],"conventional":[70],"(discrete)":[71]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2016-06-24T00:00:00"}
