{"id":"https://openalex.org/W4390702910","doi":"https://doi.org/10.22331/q-2024-01-10-1220","title":"Multivariate trace estimation in constant quantum depth","display_name":"Multivariate trace estimation in constant quantum depth","publication_year":2024,"publication_date":"2024-01-10","ids":{"openalex":"https://openalex.org/W4390702910","doi":"https://doi.org/10.22331/q-2024-01-10-1220"},"language":"en","primary_location":{"id":"doi:10.22331/q-2024-01-10-1220","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-01-10-1220","pdf_url":"https://quantum-journal.org/papers/q-2024-01-10-1220/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2024-01-10-1220/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077718480","display_name":"Yihui Quek","orcid":"https://orcid.org/0000-0002-1227-0804"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]},{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]},{"id":"https://openalex.org/I1743320","display_name":"Palo Alto University","ror":"https://ror.org/04f812k67","country_code":"US","type":"education","lineage":["https://openalex.org/I1743320"]}],"countries":["DE","US"],"is_corresponding":true,"raw_author_name":"Yihui Quek","raw_affiliation_strings":["Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany","Department of Mathematics, Massachusetts Institute of Technology, Cambridge MA 02139","Information Systems Laboratory, Stanford University, Palo Alto, CA 94305, USA"],"affiliations":[{"raw_affiliation_string":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]},{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology, Cambridge MA 02139","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Information Systems Laboratory, Stanford University, Palo Alto, CA 94305, USA","institution_ids":["https://openalex.org/I1743320","https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069916489","display_name":"Eneet Kaur","orcid":"https://orcid.org/0000-0003-3407-6284"},"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":"Eneet Kaur","raw_affiliation_strings":["Cisco Quantum Lab, Los Angeles, USA","Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1"],"affiliations":[{"raw_affiliation_string":"Cisco Quantum Lab, Los Angeles, USA","institution_ids":[]},{"raw_affiliation_string":"Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037632925","display_name":"Mark M. Wilde","orcid":"https://orcid.org/0000-0002-3916-4462"},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]},{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mark M. Wilde","raw_affiliation_strings":["Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA","School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14850, USA"],"affiliations":[{"raw_affiliation_string":"Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA","institution_ids":["https://openalex.org/I121820613"]},{"raw_affiliation_string":"School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14850, USA","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5077718480"],"corresponding_institution_ids":["https://openalex.org/I1743320","https://openalex.org/I63966007","https://openalex.org/I75951250","https://openalex.org/I97018004"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":9.5388,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.98306311,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"8","issue":null,"first_page":"1220","last_page":"1220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9991999864578247,"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/T11804","display_name":"Quantum many-body systems","score":0.9980000257492065,"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/algorithm","display_name":"Algorithm","score":0.6039076447486877},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5330542325973511},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.45151638984680176},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.41551294922828674},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.39931973814964294},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.26431459188461304},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18504735827445984},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.16817784309387207},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.09693670272827148}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6039076447486877},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5330542325973511},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.45151638984680176},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.41551294922828674},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39931973814964294},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.26431459188461304},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18504735827445984},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16817784309387207},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.09693670272827148},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.22331/q-2024-01-10-1220","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-01-10-1220","pdf_url":"https://quantum-journal.org/papers/q-2024-01-10-1220/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:doaj.org/article:29ff55ddc4fc465c87f1ff2bdfb7e2a6","is_oa":true,"landing_page_url":"https://doaj.org/article/29ff55ddc4fc465c87f1ff2bdfb7e2a6","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 8, p 1220 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2024-01-10-1220","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-01-10-1220","pdf_url":"https://quantum-journal.org/papers/q-2024-01-10-1220/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":[{"id":"https://openalex.org/G3685167319","display_name":null,"funder_award_id":"1714215","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6894402473","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","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/F4320310395","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4390702910.pdf"},"referenced_works_count":67,"referenced_works":["https://openalex.org/W190201242","https://openalex.org/W1492999010","https://openalex.org/W1675244148","https://openalex.org/W1922629554","https://openalex.org/W1980118425","https://openalex.org/W1981162221","https://openalex.org/W1988369744","https://openalex.org/W1989151402","https://openalex.org/W2004057278","https://openalex.org/W2004980778","https://openalex.org/W2007159481","https://openalex.org/W2055519393","https://openalex.org/W2068064413","https://openalex.org/W2071937582","https://openalex.org/W2074786363","https://openalex.org/W2077040005","https://openalex.org/W2082257352","https://openalex.org/W2090161225","https://openalex.org/W2120083314","https://openalex.org/W2148719904","https://openalex.org/W2164248509","https://openalex.org/W2167927798","https://openalex.org/W2397593486","https://openalex.org/W2490964415","https://openalex.org/W2625656753","https://openalex.org/W2738165287","https://openalex.org/W2756071920","https://openalex.org/W2782044500","https://openalex.org/W2803839275","https://openalex.org/W2805612073","https://openalex.org/W2807819165","https://openalex.org/W2811032035","https://openalex.org/W2949433943","https://openalex.org/W2949766140","https://openalex.org/W2952456716","https://openalex.org/W2963608890","https://openalex.org/W2963720577","https://openalex.org/W2963970827","https://openalex.org/W2968611999","https://openalex.org/W2982169647","https://openalex.org/W3003478940","https://openalex.org/W3006823398","https://openalex.org/W3037687232","https://openalex.org/W3039791778","https://openalex.org/W3048692662","https://openalex.org/W3081216242","https://openalex.org/W3091884911","https://openalex.org/W3098317871","https://openalex.org/W3099556192","https://openalex.org/W3101119256","https://openalex.org/W3101678819","https://openalex.org/W3103715576","https://openalex.org/W3103753699","https://openalex.org/W3103870741","https://openalex.org/W3104433882","https://openalex.org/W3113052911","https://openalex.org/W3139255692","https://openalex.org/W3177757055","https://openalex.org/W3194069509","https://openalex.org/W3213289548","https://openalex.org/W4205346544","https://openalex.org/W4205803100","https://openalex.org/W4206502013","https://openalex.org/W4221119529","https://openalex.org/W4238472918","https://openalex.org/W4313991536","https://openalex.org/W4365509315"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2131958170"],"abstract_inverted_index":{"There":[0],"is":[1,14,49],"a":[2,6,29,32,54,77,89,131],"folkloric":[3],"belief":[4,48],"that":[5,46,98],"depth-<mml:math":[7],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi":[8],"mathvariant=\"normal\">&amp;#x0398;</mml:mi><mml:mo":[9],"stretchy=\"false\">(</mml:mo><mml:mi>m</mml:mi><mml:mo":[10],"stretchy=\"false\">)</mml:mo></mml:math>":[11],"quantum":[12,41,123,138],"circuit":[13,57,71,80],"needed":[15],"to":[16,35,85,97,118],"estimate":[17],"the":[18,21,59,63,110,119,127],"trace":[19,115],"of":[20,23,65,99,113,121,137],"product":[22],"<mml:math":[24,101],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>m</mml:mi></mml:math>":[25],"density":[26],"matrices":[27],"(i.e.,":[28],"multivariate":[30,114],"trace),":[31],"subroutine":[33],"crucial":[34],"applications":[36],"in":[37,76,88],"condensed":[38],"matter":[39],"and":[40],"information":[42],"science.":[43],"We":[44,125],"prove":[45],"this":[47],"overly":[50],"conservative":[51],"by":[52,62],"constructing":[53],"constant":[55],"quantum-depth":[56],"for":[58],"task,":[60],"inspired":[61],"method":[64],"Shor":[66],"error":[67],"correction.":[68],"Furthermore,":[69],"our":[70,107],"demands":[72],"only":[73],"local":[74],"gates":[75],"two":[78],"dimensional":[79],"\u2013":[81],"we":[82],"show":[83],"how":[84],"implement":[86],"it":[87],"highly":[90],"parallelized":[91],"way":[92],"on":[93,133],"an":[94],"architecture":[95],"similar":[96],"Google's":[100],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>S</mml:mi><mml:mi>y</mml:mi><mml:mi>c</mml:mi><mml:mi>a</mml:mi><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:math>":[102],"processor.":[103],"With":[104],"these":[105],"features,":[106],"algorithm":[108],"brings":[109],"central":[111],"task":[112],"estimation":[116],"closer":[117],"capabilities":[120],"near-term":[122],"processors.":[124],"instantiate":[126],"latter":[128],"application":[129],"with":[130,140],"theorem":[132],"estimating":[134],"nonlinear":[135],"functions":[136],"states":[139],"\"well-behaved\"":[141],"polynomial":[142],"approximations.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":18},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}