{"id":"https://openalex.org/W3020839781","doi":"https://doi.org/10.22331/q-2021-01-12-380","title":"Exponentially faster implementations of Select(H) for fermionic Hamiltonians","display_name":"Exponentially faster implementations of Select(H) for fermionic Hamiltonians","publication_year":2021,"publication_date":"2021-01-12","ids":{"openalex":"https://openalex.org/W3020839781","doi":"https://doi.org/10.22331/q-2021-01-12-380","mag":"3020839781"},"language":"lv","primary_location":{"id":"doi:10.22331/q-2021-01-12-380","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-01-12-380","pdf_url":"https://quantum-journal.org/papers/q-2021-01-12-380/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2021-01-12-380/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009054815","display_name":"Kianna Wan","orcid":"https://orcid.org/0000-0002-1147-6528"},"institutions":[{"id":"https://openalex.org/I4210160795","display_name":"Praevium Research (United States)","ror":"https://ror.org/04t5n6k60","country_code":"US","type":"company","lineage":["https://openalex.org/I4210160795"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kianna Wan","raw_affiliation_strings":["PsiQuantum, Palo Alto, CA 94304, USA","Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305, USA"],"affiliations":[{"raw_affiliation_string":"PsiQuantum, Palo Alto, CA 94304, USA","institution_ids":["https://openalex.org/I4210160795"]},{"raw_affiliation_string":"Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009054815"],"corresponding_institution_ids":["https://openalex.org/I4210160795","https://openalex.org/I97018004"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":1.1199,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.81442682,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"5","issue":null,"first_page":"380","last_page":"380"},"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":0.9980999827384949,"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":0.9966999888420105,"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/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.7523819208145142},{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.585824191570282},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.5532316565513611},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5047813653945923},{"id":"https://openalex.org/keywords/atomic-orbital","display_name":"Atomic orbital","score":0.49409130215644836},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.48066389560699463},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.47053274512290955},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4662206470966339},{"id":"https://openalex.org/keywords/subroutine","display_name":"Subroutine","score":0.43030911684036255},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41873496770858765},{"id":"https://openalex.org/keywords/ground-state","display_name":"Ground state","score":0.41823577880859375},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40823253989219666},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.403829962015152},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.38756063580513},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37931710481643677},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13588368892669678},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1101691722869873}],"concepts":[{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.7523819208145142},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.585824191570282},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.5532316565513611},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5047813653945923},{"id":"https://openalex.org/C189394030","wikidata":"https://www.wikidata.org/wiki/Q53860","display_name":"Atomic orbital","level":3,"score":0.49409130215644836},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.48066389560699463},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.47053274512290955},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4662206470966339},{"id":"https://openalex.org/C96147967","wikidata":"https://www.wikidata.org/wiki/Q190686","display_name":"Subroutine","level":2,"score":0.43030911684036255},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41873496770858765},{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.41823577880859375},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40823253989219666},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.403829962015152},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.38756063580513},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37931710481643677},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13588368892669678},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1101691722869873},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2021-01-12-380","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-01-12-380","pdf_url":"https://quantum-journal.org/papers/q-2021-01-12-380/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2004.04170","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.04170","pdf_url":"https://arxiv.org/pdf/2004.04170","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:doaj.org/article:17feea618bdf467883bbcc84eb6096bd","is_oa":true,"landing_page_url":"https://doaj.org/article/17feea618bdf467883bbcc84eb6096bd","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 5, p 380 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2021-01-12-380","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-01-12-380","pdf_url":"https://quantum-journal.org/papers/q-2021-01-12-380/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3020839781.pdf","grobid_xml":"https://content.openalex.org/works/W3020839781.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W22923443","https://openalex.org/W1495478173","https://openalex.org/W1508413598","https://openalex.org/W1629113622","https://openalex.org/W1645422644","https://openalex.org/W1663839511","https://openalex.org/W1975451401","https://openalex.org/W2023789062","https://openalex.org/W2027003240","https://openalex.org/W2037118799","https://openalex.org/W2037354050","https://openalex.org/W2079692740","https://openalex.org/W2097174474","https://openalex.org/W2102008187","https://openalex.org/W2109741106","https://openalex.org/W2114600892","https://openalex.org/W2415656260","https://openalex.org/W2499071604","https://openalex.org/W2535738892","https://openalex.org/W2580426609","https://openalex.org/W2613212126","https://openalex.org/W2770585428","https://openalex.org/W2775106578","https://openalex.org/W2775563604","https://openalex.org/W2791899439","https://openalex.org/W2798836793","https://openalex.org/W2799222224","https://openalex.org/W2801305581","https://openalex.org/W2805699655","https://openalex.org/W2889126882","https://openalex.org/W2902431979","https://openalex.org/W2906538035","https://openalex.org/W2962738101","https://openalex.org/W2963652075","https://openalex.org/W2999629616","https://openalex.org/W3008208642","https://openalex.org/W3015378848","https://openalex.org/W3094595762","https://openalex.org/W3097997666","https://openalex.org/W3099200606","https://openalex.org/W3100831540","https://openalex.org/W3101824094","https://openalex.org/W3106120343","https://openalex.org/W3113113368","https://openalex.org/W3215460652","https://openalex.org/W4297662785"],"related_works":["https://openalex.org/W2391861012","https://openalex.org/W2488336788","https://openalex.org/W4285469493","https://openalex.org/W1593224248","https://openalex.org/W2375766869","https://openalex.org/W2080384954","https://openalex.org/W4382519933","https://openalex.org/W1546864018","https://openalex.org/W2951363717","https://openalex.org/W2134613344"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,78],"simple":[3],"but":[4],"general":[5],"framework":[6],"for":[7,58,93,107],"constructing":[8],"quantum":[9,53,97],"circuits":[10],"that":[11],"implement":[12],"the":[13,32,48,65,82,91,94,105,139,153,183],"multiply-controlled":[14],"unitary":[15],"<mml:math":[16,29,41,71,75,87,109,119,129,144,154,158],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mtext>Select</mml:mtext><mml:mo":[17,42,120],"stretchy=\"false\">(</mml:mo><mml:mi>H</mml:mi><mml:mo":[18,43,121],"stretchy=\"false\">)</mml:mo><mml:mo>:=</mml:mo><mml:munder><mml:mo>\u2211</mml:mo><mml:mi>\u2113</mml:mi></mml:munder><mml:mrow":[19],"class=\"MJX-TeXAtom-ORD\"><mml:mo":[20,26],"stretchy=\"false\">|</mml:mo></mml:mrow><mml:mi>\u2113</mml:mi><mml:mo":[21],"fence=\"false\"":[22,24],"stretchy=\"false\">\u27e9</mml:mo><mml:mo":[23],"stretchy=\"false\">\u27e8</mml:mo><mml:mi>\u2113</mml:mi><mml:mrow":[25],"stretchy=\"false\">|</mml:mo></mml:mrow><mml:mo>\u2297</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mi>\u2113</mml:mi></mml:msub></mml:math>,":[27],"where":[28],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>H</mml:mi><mml:mo>=</mml:mo><mml:munder><mml:mo>\u2211</mml:mo><mml:mi>\u2113</mml:mi></mml:munder><mml:msub><mml:mi>H</mml:mi><mml:mi>\u2113</mml:mi></mml:msub></mml:math>":[30],"is":[31,45,77,90,111],"Jordan-Wigner":[33],"transform":[34],"of":[35,47,51,81,85,96,118,185],"an":[36,165],"arbitrary":[37],"second-quantised":[38,66],"fermionic":[39],"Hamiltonian.":[40],"stretchy=\"false\">)</mml:mo></mml:math>":[44,122,135,150,161],"one":[46],"main":[49],"subroutines":[50],"several":[52],"algorithms,":[54],"including":[55],"state-of-the-art":[56],"techniques":[57],"Hamiltonian":[59,67],"simulation.":[60],"If":[61],"each":[62],"term":[63],"in":[64,104,143,157,168],"involves":[68],"at":[69],"most":[70],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>":[72,76,110],"spin-orbitals":[73,86],"and":[74,99,127,152,171,181],"constant":[79],"independent":[80],"total":[83],"number":[84,184],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>n</mml:mi></mml:math>":[88],"(as":[89],"case":[92],"majority":[95],"chemistry":[98],"condensed":[100],"matter":[101],"models":[102],"considered":[103],"literature,":[106],"which":[108],"typically":[112],"2":[113],"or":[114],"4),":[115],"our":[116],"implementation":[117],"requires":[123],"no":[124],"ancilla":[125],"qubits":[126],"uses":[128],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow":[130,145],"class=\"MJX-TeXAtom-ORD\"><mml:mi":[131,146],"class=\"MJX-tex-caligraphic\"":[132,147],"mathvariant=\"script\">O</mml:mi></mml:mrow><mml:mo":[133,148],"stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo":[134],"Clifford+T":[136],"gates,":[137],"with":[138],"Clifford":[140],"gates":[141,156],"applied":[142],"stretchy=\"false\">(</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msup><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mi>n</mml:mi><mml:mo":[149],"layers":[151],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>T</mml:mi></mml:math>":[155],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>O</mml:mi><mml:mo":[159],"stretchy=\"false\">(</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi><mml:mo":[160],"layers.":[162],"This":[163],"achieves":[164],"exponential":[166],"improvement":[167],"both":[169],"Clifford-":[170],"T-depth":[172],"over":[173],"previous":[174],"work,":[175],"while":[176],"maintaining":[177],"linear":[178],"gate":[179],"count":[180],"reducing":[182],"ancillae":[186],"to":[187],"zero.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2020-05-13T00:00:00"}