{"id":"https://openalex.org/W2951503883","doi":"https://doi.org/10.22331/q-2020-03-26-248","title":"Variational Quantum Fidelity Estimation","display_name":"Variational Quantum Fidelity Estimation","publication_year":2020,"publication_date":"2020-03-26","ids":{"openalex":"https://openalex.org/W2951503883","doi":"https://doi.org/10.22331/q-2020-03-26-248","mag":"2951503883"},"language":"lv","primary_location":{"id":"doi:10.22331/q-2020-03-26-248","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-03-26-248","pdf_url":"https://quantum-journal.org/papers/q-2020-03-26-248/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-2020-03-26-248/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Marco Cerezo","orcid":"https://orcid.org/0000-0002-2757-3170"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Marco Cerezo","raw_affiliation_strings":["Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA","Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA"],"affiliations":[{"raw_affiliation_string":"Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA","institution_ids":["https://openalex.org/I1343871089"]},{"raw_affiliation_string":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Alexander Poremba","orcid":"https://orcid.org/0000-0002-7330-1539"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexander Poremba","raw_affiliation_strings":["Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA"],"affiliations":[{"raw_affiliation_string":"Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Lukasz Cincio","orcid":"https://orcid.org/0000-0002-6758-4376"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lukasz Cincio","raw_affiliation_strings":["Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA"],"affiliations":[{"raw_affiliation_string":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"last","author":{"id":null,"display_name":"Patrick J. Coles","orcid":"https://orcid.org/0000-0001-9879-8425"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Patrick J. Coles","raw_affiliation_strings":["Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA"],"affiliations":[{"raw_affiliation_string":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1343871089"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":10.4673,"has_fulltext":true,"cited_by_count":111,"citation_normalized_percentile":{"value":0.9861253,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"4","issue":null,"first_page":"248","last_page":"248"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.8894000053405762,"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":0.8894000053405762,"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":0.05469999834895134,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.015799999237060547,"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/quantum","display_name":"Quantum","score":0.6047999858856201},{"id":"https://openalex.org/keywords/fidelity","display_name":"Fidelity","score":0.5722000002861023},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.5372999906539917},{"id":"https://openalex.org/keywords/quantum-phase-estimation-algorithm","display_name":"Quantum phase estimation algorithm","score":0.5360999703407288},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4896000027656555},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.46459999680519104},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4523000121116638},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4357999861240387},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42410001158714294}],"concepts":[{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.6047999858856201},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.5722000002861023},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5372999906539917},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.5360999703407288},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4896000027656555},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.46459999680519104},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4523000121116638},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4401000142097473},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4357999861240387},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43470001220703125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4269999861717224},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42410001158714294},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.4000999927520752},{"id":"https://openalex.org/C113364801","wikidata":"https://www.wikidata.org/wiki/Q26674","display_name":"High fidelity","level":2,"score":0.3384000062942505},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.33059999346733093},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.321399986743927},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.31139999628067017},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.30379998683929443},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.3019999861717224},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.30169999599456787},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.3009999990463257},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.2865999937057495},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2554999887943268},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.25429999828338623},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2506999969482422},{"id":"https://openalex.org/C192353077","wikidata":"https://www.wikidata.org/wiki/Q4682635","display_name":"Adiabatic quantum computation","level":4,"score":0.25029999017715454}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.22331/q-2020-03-26-248","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-03-26-248","pdf_url":"https://quantum-journal.org/papers/q-2020-03-26-248/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:1906.09253","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1906.09253","pdf_url":"https://arxiv.org/pdf/1906.09253","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:102747","is_oa":true,"landing_page_url":"https://authors.library.caltech.edu/102747/","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:8eed981b53f541f788318a88a7741434","is_oa":true,"landing_page_url":"https://doaj.org/article/8eed981b53f541f788318a88a7741434","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 4, p 248 (2020)","raw_type":"article"},{"id":"pmh:oai:osti.gov:1659189","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1659189","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null}],"best_oa_location":{"id":"doi:10.22331/q-2020-03-26-248","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-03-26-248","pdf_url":"https://quantum-journal.org/papers/q-2020-03-26-248/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/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G2050599915","display_name":null,"funder_award_id":"PHY-173390","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G230078430","display_name":null,"funder_award_id":"FA9550-16","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G2403330605","display_name":null,"funder_award_id":"PHY-1733907","funder_id":"https://openalex.org/F4320334224","funder_display_name":"Institute for Quantum Information and Matter, California Institute of Technology"},{"id":"https://openalex.org/G3392305090","display_name":null,"funder_award_id":"-16-1-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3616359867","display_name":null,"funder_award_id":"FA9550-16-1","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G4533172783","display_name":null,"funder_award_id":"PHY-1733907","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G507237395","display_name":null,"funder_award_id":"1733907","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5175037542","display_name":null,"funder_award_id":"FA9550-16-1-0495","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5921281487","display_name":null,"funder_award_id":"number","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/F4320334224","display_name":"Institute for Quantum Information and Matter, California Institute of Technology","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338304","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2951503883.pdf","grobid_xml":"https://content.openalex.org/works/W2951503883.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W212428657","https://openalex.org/W391578156","https://openalex.org/W1492999010","https://openalex.org/W1612846254","https://openalex.org/W1621050367","https://openalex.org/W1623348669","https://openalex.org/W1770873769","https://openalex.org/W1910288008","https://openalex.org/W1970136394","https://openalex.org/W1971699777","https://openalex.org/W1988155384","https://openalex.org/W1989842989","https://openalex.org/W1994972076","https://openalex.org/W2000612921","https://openalex.org/W2008394317","https://openalex.org/W2012141099","https://openalex.org/W2016575268","https://openalex.org/W2023885784","https://openalex.org/W2045381264","https://openalex.org/W2060043187","https://openalex.org/W2082257352","https://openalex.org/W2155382668","https://openalex.org/W2161685427","https://openalex.org/W2166302514","https://openalex.org/W2168792807","https://openalex.org/W2257937122","https://openalex.org/W2605573827","https://openalex.org/W2799182930","https://openalex.org/W2810805621","https://openalex.org/W2811032035","https://openalex.org/W2895860665","https://openalex.org/W2897217696","https://openalex.org/W2907241261","https://openalex.org/W2922946882","https://openalex.org/W2949433943","https://openalex.org/W2990961515","https://openalex.org/W3098857864","https://openalex.org/W3100798923","https://openalex.org/W3100967482","https://openalex.org/W3101135395","https://openalex.org/W3101283594","https://openalex.org/W3101663526","https://openalex.org/W3101678819","https://openalex.org/W3101933006","https://openalex.org/W3103872322","https://openalex.org/W3105870134","https://openalex.org/W4232414979","https://openalex.org/W4238444343","https://openalex.org/W4297944615"],"related_works":[],"abstract_inverted_index":{"Computing":[0],"quantum":[1,15,150],"state":[2],"fidelity":[3,125],"will":[4],"be":[5,56],"important":[6],"to":[7,103],"verify":[8],"and":[9,24,97,127,153],"characterize":[10],"states":[11],"prepared":[12],"on":[13,33],"a":[14,44,70],"computer.":[16],"In":[17],"this":[18,137],"work,":[19],"we":[20,68,122,128,143],"propose":[21],"novel":[22],"lower":[23],"upper":[25],"bounds":[26,54,147,161],"for":[27,43,162],"the":[28,34,93,112],"fidelity<mml:math":[29],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>F</mml:mi><mml:mo":[30,37],"stretchy=\"false\">(</mml:mo><mml:mi>\u03c1</mml:mi><mml:mo>,</mml:mo><mml:mi>\u03c3</mml:mi><mml:mo":[31],"stretchy=\"false\">)</mml:mo></mml:math>based":[32],"``truncated":[35],"fidelity''<mml:math":[36],"stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>\u03c1</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi>\u03c3</mml:mi><mml:mo":[38],"stretchy=\"false\">)</mml:mo></mml:math>,":[39],"which":[40,121],"is":[41,109],"evaluated":[42],"state<mml:math":[45],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>\u03c1</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:math>obtained":[46],"by":[47],"projecting<mml:math":[48],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03c1</mml:mi></mml:math>onto":[49],"its<mml:math":[50],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>m</mml:mi></mml:math>-largest":[51],"eigenvalues.":[52],"Our":[53,107],"can":[55,134,148],"refined,":[57],"i.e.,":[58],"they":[59],"tighten":[60],"monotonically":[61],"with<mml:math":[62],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>m</mml:mi></mml:math>.":[63],"To":[64],"compute":[65,88,104],"our":[66,105,146],"bounds,":[67],"introduce":[69],"hybrid":[71],"quantum-classical":[72],"algorithm,":[73],"called":[74],"Variational":[75],"Quantum":[76],"Fidelity":[77],"Estimation,":[78],"that":[79,130,145],"involves":[80],"three":[81],"steps:":[82],"(1)":[83],"variationally":[84],"diagonalize<mml:math":[85],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03c1</mml:mi></mml:math>,":[86,96],"(2)":[87],"matrix":[89,101],"elements":[90,102],"of<mml:math":[91,95],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03c3</mml:mi></mml:math>in":[92],"eigenbasis":[94],"(3)":[98],"combine":[99],"these":[100],"bounds.":[106],"algorithm":[108,133],"aimed":[110],"at":[111],"case":[113],"where<mml:math":[114],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03c3</mml:mi></mml:math>is":[115],"arbitrary":[116],"and<mml:math":[117],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03c1</mml:mi></mml:math>is":[118],"low":[119],"rank,":[120],"call":[123],"low-rank":[124],"estimation,":[126],"prove":[129],"no":[131],"classical":[132],"efficiently":[135],"solve":[136],"problem":[138],"under":[139],"reasonable":[140],"assumptions.":[141],"Finally,":[142],"demonstrate":[144],"detect":[149],"phase":[151],"transitions":[152],"are":[154],"often":[155],"tighter":[156],"than":[157],"previously":[158],"known":[159],"computable":[160],"realistic":[163],"situations.":[164]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":24},{"year":2023,"cited_by_count":17},{"year":2022,"cited_by_count":32},{"year":2021,"cited_by_count":24},{"year":2020,"cited_by_count":4}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2019-06-27T00:00:00"}
