{"id":"https://openalex.org/W4390174748","doi":"https://doi.org/10.3390/quantum6010001","title":"The Quantum Amplitude Estimation Algorithms on Near-Term Devices: A Practical Guide","display_name":"The Quantum Amplitude Estimation Algorithms on Near-Term Devices: A Practical Guide","publication_year":2023,"publication_date":"2023-12-24","ids":{"openalex":"https://openalex.org/W4390174748","doi":"https://doi.org/10.3390/quantum6010001"},"language":"en","primary_location":{"id":"doi:10.3390/quantum6010001","doi":"https://doi.org/10.3390/quantum6010001","is_oa":true,"landing_page_url":"https://doi.org/10.3390/quantum6010001","pdf_url":"https://www.mdpi.com/2624-960X/6/1/1/pdf?version=1703404470","source":{"id":"https://openalex.org/S4210211996","display_name":"Quantum Reports","issn_l":"2624-960X","issn":["2624-960X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"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 Reports","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2624-960X/6/1/1/pdf?version=1703404470","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037335242","display_name":"Marco Maronese","orcid":"https://orcid.org/0000-0001-5548-5947","observed_orcids":["https://orcid.org/0000-0001-5548-5947"]},"institutions":[{"id":"https://openalex.org/I4210134310","display_name":"Istituto di Fotonica e Nanotecnologie","ror":"https://ror.org/049ebw417","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210134310","https://openalex.org/I4210155236"]},{"id":"https://openalex.org/I4210155236","display_name":"National Research Council","ror":"https://ror.org/04zaypm56","country_code":"IT","type":"nonprofit","lineage":["https://openalex.org/I4210155236"]},{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Maronese","raw_affiliation_strings":["Department of Pharmacy and Biotechnology, University of Bologna, Via Belmeloro 6, 40126 Bologna, Italy","Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Piazza Leonardo da Vinci 32, 20133 Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0001-5548-5947","affiliations":[{"raw_affiliation_string":"Department of Pharmacy and Biotechnology, University of Bologna, Via Belmeloro 6, 40126 Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]},{"raw_affiliation_string":"Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Piazza Leonardo da Vinci 32, 20133 Milano, Italy","institution_ids":["https://openalex.org/I4210134310","https://openalex.org/I4210155236"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052997153","display_name":"Massimiliano Incudini","orcid":"https://orcid.org/0000-0002-9389-5370","observed_orcids":["https://orcid.org/0000-0002-9389-5370"]},"institutions":[{"id":"https://openalex.org/I119439378","display_name":"University of Verona","ror":"https://ror.org/039bp8j42","country_code":"IT","type":"education","lineage":["https://openalex.org/I119439378"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Massimiliano Incudini","raw_affiliation_strings":["Data Reply s.r.l., Corso Francia, 110, 10143 Torino, Italy","Dipartimento di Informatica, Universita di Verona, Strada Le Grazie, 15, 37134 Verona, Italy"],"raw_orcid":"https://orcid.org/0000-0002-9389-5370","affiliations":[{"raw_affiliation_string":"Data Reply s.r.l., Corso Francia, 110, 10143 Torino, Italy","institution_ids":[]},{"raw_affiliation_string":"Dipartimento di Informatica, Universita di Verona, Strada Le Grazie, 15, 37134 Verona, Italy","institution_ids":["https://openalex.org/I119439378"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091423505","display_name":"Luca Asproni","orcid":"https://orcid.org/0000-0002-8383-0901","observed_orcids":["https://orcid.org/0000-0002-8383-0901"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luca Asproni","raw_affiliation_strings":["Data Reply s.r.l., Corso Francia, 110, 10143 Torino, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Data Reply s.r.l., Corso Francia, 110, 10143 Torino, Italy","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017727346","display_name":"Enrico Prati","orcid":"https://orcid.org/0000-0001-9839-202X","observed_orcids":["https://orcid.org/0000-0001-9839-202X"]},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]},{"id":"https://openalex.org/I4210099310","display_name":"Consorzio Nazionale Interuniversitario per le Telecomunicazioni","ror":"https://ror.org/0182a5n39","country_code":"IT","type":"funder","lineage":["https://openalex.org/I4210099310"]},{"id":"https://openalex.org/I4210134310","display_name":"Istituto di Fotonica e Nanotecnologie","ror":"https://ror.org/049ebw417","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210134310","https://openalex.org/I4210155236"]},{"id":"https://openalex.org/I4210155236","display_name":"National Research Council","ror":"https://ror.org/04zaypm56","country_code":"IT","type":"nonprofit","lineage":["https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Enrico Prati","raw_affiliation_strings":["Dipartimento di Fisica, Universita di Milano, Via Celoria 16, 20133 Milano, Italy","Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Piazza Leonardo da Vinci 32, 20133 Milano, Italy","National Inter-University Consortium for Telecommunications (CNIT), Viale G.P. Usberti, 181/A Pal.3, 43124 Parma, Italy"],"raw_orcid":"https://orcid.org/0000-0001-9839-202X","affiliations":[{"raw_affiliation_string":"Dipartimento di Fisica, Universita di Milano, Via Celoria 16, 20133 Milano, Italy","institution_ids":["https://openalex.org/I189158943"]},{"raw_affiliation_string":"Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Piazza Leonardo da Vinci 32, 20133 Milano, Italy","institution_ids":["https://openalex.org/I4210134310","https://openalex.org/I4210155236"]},{"raw_affiliation_string":"National Inter-University Consortium for Telecommunications (CNIT), Viale G.P. Usberti, 181/A Pal.3, 43124 Parma, Italy","institution_ids":["https://openalex.org/I4210099310"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5017727346"],"corresponding_institution_ids":["https://openalex.org/I189158943","https://openalex.org/I4210099310","https://openalex.org/I4210134310","https://openalex.org/I4210155236"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1557},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1557},"fwci":0.658,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.69445641,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"6","issue":"1","first_page":"1","last_page":"13"},"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":0.0,"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/T11804","display_name":"Quantum many-body systems","score":0.0,"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-amplitude-estimation","display_name":"quantum amplitude estimation","score":0.984000027179718},{"id":"https://openalex.org/keywords/nisq-devices","display_name":"NISQ devices","score":0.8629999756813049},{"id":"https://openalex.org/keywords/integral-evaluation","display_name":"integral evaluation","score":0.5789999961853027},{"id":"https://openalex.org/keywords/monte-carlo-simulation-comparison","display_name":"Monte Carlo comparison","score":0.6909999847412109},{"id":"https://openalex.org/keywords/metropolis-hastings-algorithm","display_name":"Metropolis-Hastings algorithm","score":0.9629999995231628},{"id":"https://openalex.org/keywords/maximum-likelihood-estimation","display_name":"maximum likelihood estimation","score":0.890999972820282},{"id":"https://openalex.org/keywords/phase-estimation","display_name":"phase estimation","score":0.7960000038146973},{"id":"https://openalex.org/keywords/trapped-ion-quantum-computer","display_name":"trapped-ion quantum computer","score":0.8230000138282776},{"id":"https://openalex.org/keywords/noisy-quantum-circuits","display_name":"noisy quantum circuits","score":0.6480000019073486},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"numerical integration","score":0.4429999887943268}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7239012718200684},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.6520869731903076},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.6331347227096558},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6061107516288757},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.603533923625946},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5844981670379639},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.5632498860359192},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5626813173294067},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.47237828373908997},{"id":"https://openalex.org/C16016025","wikidata":"https://www.wikidata.org/wiki/Q3861408","display_name":"Quantum Monte Carlo","level":3,"score":0.4238263964653015},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25688299536705017},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.2560800313949585},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.199695885181427},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08785784244537354},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08780133724212646},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/quantum6010001","doi":"https://doi.org/10.3390/quantum6010001","is_oa":true,"landing_page_url":"https://doi.org/10.3390/quantum6010001","pdf_url":"https://www.mdpi.com/2624-960X/6/1/1/pdf?version=1703404470","source":{"id":"https://openalex.org/S4210211996","display_name":"Quantum Reports","issn_l":"2624-960X","issn":["2624-960X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"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 Reports","raw_type":"journal-article"},{"id":"pmh:oai:air.unimi.it:2434/1251501","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/2434/1251501","pdf_url":"https://air.unimi.it/bitstream/2434/1251501/2/quantumrep-06-00001-v2-1.pdf","source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:eb20aee64e1f42edafaa6e11b737006f","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/eb20aee64e1f42edafaa6e11b737006f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"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 Reports, Vol 6, Iss 1, Pp 1-13 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/quantum6010001","doi":"https://doi.org/10.3390/quantum6010001","is_oa":true,"landing_page_url":"https://doi.org/10.3390/quantum6010001","pdf_url":"https://www.mdpi.com/2624-960X/6/1/1/pdf?version=1703404470","source":{"id":"https://openalex.org/S4210211996","display_name":"Quantum Reports","issn_l":"2624-960X","issn":["2624-960X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"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 Reports","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310598","display_name":"Amazon Web Services","ror":"https://ror.org/04mv4n011"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4390174748.pdf","grobid_xml":"https://content.openalex.org/works/W4390174748.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1602773783","https://openalex.org/W1639600422","https://openalex.org/W2121981260","https://openalex.org/W2164248509","https://openalex.org/W2771783640","https://openalex.org/W2781738013","https://openalex.org/W2798745146","https://openalex.org/W2809024202","https://openalex.org/W2903542250","https://openalex.org/W2924182316","https://openalex.org/W2943869291","https://openalex.org/W2949253647","https://openalex.org/W2995849402","https://openalex.org/W2998842053","https://openalex.org/W3008500221","https://openalex.org/W3009929844","https://openalex.org/W3014386333","https://openalex.org/W3035899097","https://openalex.org/W3043514756","https://openalex.org/W3095846505","https://openalex.org/W3096261668","https://openalex.org/W3110682311","https://openalex.org/W3111561052","https://openalex.org/W3113052911","https://openalex.org/W3138943493","https://openalex.org/W3168728763","https://openalex.org/W3197536459","https://openalex.org/W3207510357","https://openalex.org/W4205990238","https://openalex.org/W4211066527","https://openalex.org/W4220718195","https://openalex.org/W4221159795","https://openalex.org/W4251436587","https://openalex.org/W4285257569","https://openalex.org/W4290935155","https://openalex.org/W4321438611","https://openalex.org/W4324094513","https://openalex.org/W4378191399","https://openalex.org/W4386715627"],"related_works":["https://openalex.org/W4389168145","https://openalex.org/W3024421942","https://openalex.org/W3080702103","https://openalex.org/W3038106692","https://openalex.org/W2995849402","https://openalex.org/W4390957244","https://openalex.org/W2998842053","https://openalex.org/W7133536350","https://openalex.org/W3201010747","https://openalex.org/W3009929844"],"abstract_inverted_index":{"The":[0,80,111],"Quantum":[1,59],"Amplitude":[2],"Estimation":[3],"(QAE)":[4],"algorithm":[5,10,54],"is":[6,21,148],"a":[7,14,65,77,91,135],"major":[8],"quantum":[9,19,104,124,172],"designed":[11],"to":[12,39,128,152,186],"achieve":[13],"quadratic":[15],"speed-up.":[16],"Until":[17],"fault-tolerant":[18],"computing":[20],"achieved,":[22],"being":[23],"competitive":[24],"over":[25],"classical":[26,78],"Monte":[27,71],"Carlo":[28,72],"(MC)":[29],"remains":[30],"elusive.":[31],"Alternative":[32],"methods":[33],"have":[34],"been":[35],"developed":[36],"so":[37],"as":[38,76,90,181,183],"require":[40],"fewer":[41],"resources":[42],"while":[43],"maintaining":[44],"an":[45,121,145],"advantageous":[46],"theoretical":[47],"scaling.":[48],"We":[49,142],"compared":[50],"the":[51,70,87,94,103,108,114,138,154,159,164,168,171,175,178],"standard":[52],"QAE":[53,63,116],"with":[55,69,150],"two":[56,115],"Noisy":[57],"Intermediate-Scale":[58],"(NISQ)-friendly":[60],"versions":[61],"of":[62,74,86,93,96,102,113,170],"on":[64,120],"numerical":[66],"integration":[67],"task,":[68],"technique":[73],"Metropolis\u2013Hastings":[75],"benchmark.":[79],"algorithms":[81],"were":[82],"evaluated":[83],"in":[84,126,137,177],"terms":[85],"estimation":[88,140,156,162],"error":[89],"function":[92],"number":[95],"samples,":[97],"computational":[98],"time,":[99],"and":[100,174],"length":[101,169],"circuits":[105,173],"required":[106],"by":[107],"solutions,":[109],"respectively.":[110],"effectiveness":[112],"alternatives":[117],"was":[118],"tested":[119],"11-qubit":[122],"trapped-ion":[123],"computer":[125],"order":[127],"verify":[129],"which":[130],"solution":[131],"can":[132],"first":[133],"provide":[134],"speed-up":[136],"integral":[139,179],"problems.":[141],"concluded":[143],"that":[144],"alternative":[146],"approach":[147],"preferable":[149],"respect":[151],"employing":[153],"phase":[155],"routine.":[157],"Indeed,":[158],"Maximum":[160],"Likelihood":[161],"guaranteed":[163],"best":[165],"trade-off":[166],"between":[167],"precision":[176],"estimation,":[180],"well":[182],"greater":[184],"resistance":[185],"noise.":[187]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2023-12-25T00:00:00"}
