{"id":"https://openalex.org/W3027746348","doi":"https://doi.org/10.22331/q-2021-01-25-386","title":"Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule","display_name":"Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule","publication_year":2021,"publication_date":"2021-01-25","ids":{"openalex":"https://openalex.org/W3027746348","doi":"https://doi.org/10.22331/q-2021-01-25-386","mag":"3027746348"},"language":"en","primary_location":{"id":"doi:10.22331/q-2021-01-25-386","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-01-25-386","pdf_url":"https://quantum-journal.org/papers/q-2021-01-25-386/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-2021-01-25-386/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Leonardo Banchi","orcid":"https://orcid.org/0000-0002-6324-8754"},"institutions":[{"id":"https://openalex.org/I4210133295","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Firenze","ror":"https://ror.org/02vv5y108","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210133295"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Leonardo Banchi","raw_affiliation_strings":["Department of Physics and Astronomy, University of Florence, via G. Sansone 1, I-50019 Sesto Fiorentino (FI), Italy","INFN Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (FI), Italy"],"affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy, University of Florence, via G. Sansone 1, I-50019 Sesto Fiorentino (FI), Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"INFN Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (FI), Italy","institution_ids":["https://openalex.org/I4210133295"]}]},{"author_position":"last","author":{"id":null,"display_name":"Gavin E. Crooks","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gavin E. Crooks","raw_affiliation_strings":["Berkeley Institute for Theoretical Science, Berkeley, CA, USA","X, the moonshot factory (x.company), Mountain View, CA, USA"],"affiliations":[{"raw_affiliation_string":"Berkeley Institute for Theoretical Science, Berkeley, CA, USA","institution_ids":[]},{"raw_affiliation_string":"X, the moonshot factory (x.company), Mountain View, CA, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210133295","https://openalex.org/I45084792"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":8.9591,"has_fulltext":true,"cited_by_count":91,"citation_normalized_percentile":{"value":0.98188988,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"5","issue":null,"first_page":"386","last_page":"386"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.7469000220298767,"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":0.7469000220298767,"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":0.08780000358819962,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.02759999968111515,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6618000268936157},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.5698000192642212},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5485000014305115},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.5084999799728394},{"id":"https://openalex.org/keywords/quantum-phase-estimation-algorithm","display_name":"Quantum phase estimation algorithm","score":0.48660001158714294},{"id":"https://openalex.org/keywords/pauli-exclusion-principle","display_name":"Pauli exclusion principle","score":0.4519999921321869},{"id":"https://openalex.org/keywords/quantum-process","display_name":"Quantum process","score":0.45170000195503235},{"id":"https://openalex.org/keywords/quantum-operation","display_name":"Quantum operation","score":0.4392000138759613},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"Quantum error correction","score":0.42579999566078186}],"concepts":[{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6618000268936157},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5698000192642212},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5485000014305115},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.5084999799728394},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4925999939441681},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4925000071525574},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.48660001158714294},{"id":"https://openalex.org/C110340908","wikidata":"https://www.wikidata.org/wiki/Q131594","display_name":"Pauli exclusion principle","level":2,"score":0.4519999921321869},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.45170000195503235},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.4392000138759613},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.42579999566078186},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.38999998569488525},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.38760000467300415},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.3490000069141388},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.3393000066280365},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.33469998836517334},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.3059000074863434},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29670000076293945},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.29190000891685486},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29100000858306885},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.28929999470710754},{"id":"https://openalex.org/C179957908","wikidata":"https://www.wikidata.org/wiki/Q907206","display_name":"POVM","level":5,"score":0.28290000557899475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27630001306533813},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.2754000127315521},{"id":"https://openalex.org/C194975256","wikidata":"https://www.wikidata.org/wiki/Q7269039","display_name":"Quantum dissipation","level":3,"score":0.27489998936653137},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.265500009059906},{"id":"https://openalex.org/C50150098","wikidata":"https://www.wikidata.org/wiki/Q2607127","display_name":"Weak measurement","level":3,"score":0.25519999861717224},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.2542000114917755},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.22331/q-2021-01-25-386","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-01-25-386","pdf_url":"https://quantum-journal.org/papers/q-2021-01-25-386/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:2005.10299","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.10299","pdf_url":"https://arxiv.org/pdf/2005.10299","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:3a8672fe4fa643ceb40865fc6cf6760a","is_oa":true,"landing_page_url":"https://doaj.org/article/3a8672fe4fa643ceb40865fc6cf6760a","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 386 (2021)","raw_type":"article"},{"id":"pmh:oai:flore.unifi.it:2158/1227060","is_oa":true,"landing_page_url":"https://hdl.handle.net/2158/1227060","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.22331/q-2021-01-25-386","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-01-25-386","pdf_url":"https://quantum-journal.org/papers/q-2021-01-25-386/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/W3027746348.pdf","grobid_xml":"https://content.openalex.org/works/W3027746348.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1578322733","https://openalex.org/W1967883933","https://openalex.org/W1978533437","https://openalex.org/W1984167858","https://openalex.org/W2040792108","https://openalex.org/W2071461214","https://openalex.org/W2092479209","https://openalex.org/W2124289529","https://openalex.org/W2126511900","https://openalex.org/W2161685427","https://openalex.org/W2174510006","https://openalex.org/W2262683142","https://openalex.org/W2558921197","https://openalex.org/W2562234976","https://openalex.org/W2578080479","https://openalex.org/W2781738013","https://openalex.org/W2790388700","https://openalex.org/W2793072493","https://openalex.org/W2794444783","https://openalex.org/W2796293949","https://openalex.org/W2810721533","https://openalex.org/W2888774813","https://openalex.org/W2903221501","https://openalex.org/W2903627855","https://openalex.org/W2907242142","https://openalex.org/W2963239445","https://openalex.org/W2963652075","https://openalex.org/W2972032089","https://openalex.org/W2978899725","https://openalex.org/W2980446414","https://openalex.org/W2996682177","https://openalex.org/W3106269494","https://openalex.org/W4206742934","https://openalex.org/W6912284476"],"related_works":[],"abstract_inverted_index":{"Hybrid":[0],"quantum-classical":[1],"optimization":[2],"algorithms":[3,17],"represent":[4],"one":[5],"of":[6,46,50,90,99,105,126],"the":[7,18,38,44,48,51,67,71,88,97,103,115,124,127,133,147,157,160],"most":[8],"promising":[9],"application":[10],"for":[11,86,153],"near-term":[12],"quantum":[13,39,58,94,149,161],"computers.":[14],"In":[15],"these":[16],"goal":[19],"is":[20,112],"to":[21,28,53,138,156],"optimize":[22],"an":[23,164],"observable":[24],"quantity":[25],"with":[26,141],"respect":[27],"some":[29,63,142],"classical":[30],"parameters,":[31],"using":[32],"feedback":[33],"from":[34,57],"measurements":[35],"performed":[36],"on":[37,132],"device.":[40],"Here":[41],"we":[42],"study":[43],"problem":[45],"estimating":[47,87],"gradient":[49,89,110],"function":[52],"be":[54],"optimized":[55],"directly":[56],"measurements,":[59],"generalizing":[60],"and":[61,163],"simplifying":[62],"approaches":[64],"present":[65],"in":[66,123],"literature,":[68],"such":[69],"as":[70],"so-called":[72],"parameter-shift":[73],"rule.":[74],"We":[75],"derive":[76],"a":[77,83],"mathematically":[78],"exact":[79],"formula":[80],"that":[81],"provides":[82],"stochastic":[84],"algorithm":[85,136],"any":[91],"multi-qubit":[92],"parametric":[93],"evolution,":[95],"without":[96],"introduction":[98],"ancillary":[100],"qubits":[101],"or":[102],"use":[104],"Hamiltonian":[106,128],"simulation":[107],"techniques.":[108],"The":[109],"measurement":[111],"possible":[113],"when":[114,145],"underlying":[116],"device":[117,162],"can":[118],"realize":[119],"all":[120,146],"Pauli":[121],"rotations":[122],"expansion":[125],"whose":[129],"coefficients":[130],"depend":[131],"parameter.":[134],"Our":[135],"continues":[137],"work,":[139],"although":[140],"approximations,":[143],"even":[144],"available":[148],"gates":[150],"are":[151],"noisy,":[152],"instance":[154],"due":[155],"coupling":[158],"between":[159],"unknown":[165],"environment.":[166]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":22},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":17},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":11}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2020-05-29T00:00:00"}