{"id":"https://openalex.org/W2978899725","doi":"https://doi.org/10.22331/q-2020-08-31-314","title":"Stochastic gradient descent for hybrid quantum-classical optimization","display_name":"Stochastic gradient descent for hybrid quantum-classical optimization","publication_year":2020,"publication_date":"2020-08-31","ids":{"openalex":"https://openalex.org/W2978899725","doi":"https://doi.org/10.22331/q-2020-08-31-314","mag":"2978899725"},"language":"en","primary_location":{"id":"doi:10.22331/q-2020-08-31-314","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-08-31-314","pdf_url":"https://quantum-journal.org/papers/q-2020-08-31-314/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-2020-08-31-314/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ryan Sweke","orcid":"https://orcid.org/0000-0002-6202-8864"},"institutions":[{"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"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ryan Sweke","raw_affiliation_strings":["Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-6202-8864","affiliations":[{"raw_affiliation_string":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Frederik Wilde","orcid":"https://orcid.org/0000-0002-6224-1964"},"institutions":[{"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"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Frederik Wilde","raw_affiliation_strings":["Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-6224-1964","affiliations":[{"raw_affiliation_string":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Johannes Meyer","orcid":"https://orcid.org/0000-0003-1533-8015"},"institutions":[{"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"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Johannes Meyer","raw_affiliation_strings":["Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0003-1533-8015","affiliations":[{"raw_affiliation_string":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Maria Schuld","orcid":"https://orcid.org/0000-0001-8626-168X"},"institutions":[{"id":"https://openalex.org/I4210150097","display_name":"Xanadu Quantum Technologies (Canada)","ror":"https://ror.org/05qj0n416","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210150097"]},{"id":"https://openalex.org/I95023434","display_name":"University of KwaZulu-Natal","ror":"https://ror.org/04qzfn040","country_code":"ZA","type":"education","lineage":["https://openalex.org/I95023434"]}],"countries":["CA","ZA"],"is_corresponding":false,"raw_author_name":"Maria Schuld","raw_affiliation_strings":["Quantum Research Group, University of KwaZulu-Natal, 4000 Durban, South Africa","Xanadu, 777 Bay Street, Toronto, Ontario, Canada"],"raw_orcid":"https://orcid.org/0000-0001-8626-168X","affiliations":[{"raw_affiliation_string":"Quantum Research Group, University of KwaZulu-Natal, 4000 Durban, South Africa","institution_ids":["https://openalex.org/I95023434"]},{"raw_affiliation_string":"Xanadu, 777 Bay Street, Toronto, Ontario, Canada","institution_ids":["https://openalex.org/I4210150097"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Paul K. Faehrmann","orcid":"https://orcid.org/0000-0002-8706-1732"},"institutions":[{"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"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Paul K. Faehrmann","raw_affiliation_strings":["Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-8706-1732","affiliations":[{"raw_affiliation_string":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Barth\u00e9l\u00e9my Meynard-Piganeau","orcid":null},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Barth\u00e9l\u00e9my Meynard-Piganeau","raw_affiliation_strings":["Department of Physics, Ecole Polytechnique, Palaiseau, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Ecole Polytechnique, Palaiseau, France","institution_ids":["https://openalex.org/I142476485"]}]},{"author_position":"last","author":{"id":null,"display_name":"Jens Eisert","orcid":"https://orcid.org/0000-0003-3033-1292"},"institutions":[{"id":"https://openalex.org/I2800795503","display_name":"Helmholtz-Zentrum Berlin f\u00fcr Materialien und Energie","ror":"https://ror.org/02aj13c28","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2800795503"]},{"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"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jens Eisert","raw_affiliation_strings":["Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany","Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, D-14195 Berlin","Helmholtz Center Berlin, 14109 Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0003-3033-1292","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 and Computer Science, Freie Universit\u00e4t Berlin, D-14195 Berlin","institution_ids":["https://openalex.org/I75951250"]},{"raw_affiliation_string":"Helmholtz Center Berlin, 14109 Berlin, Germany","institution_ids":["https://openalex.org/I2800795503"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":16.5203,"has_fulltext":true,"cited_by_count":206,"citation_normalized_percentile":{"value":0.99314964,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"4","issue":null,"first_page":"314","last_page":"314"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9332000017166138,"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":0.9332000017166138,"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":0.012299999594688416,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.0035000001080334187,"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/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.7333999872207642},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6353999972343445},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6193000078201294},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.604200005531311},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5879999995231628},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5852000117301941},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.47369998693466187},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.41850000619888306},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.41620001196861267}],"concepts":[{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.7333999872207642},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6353999972343445},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6193000078201294},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.604200005531311},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5879999995231628},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5852000117301941},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5662999749183655},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5390999913215637},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.47369998693466187},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4505999982357025},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44279998540878296},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.41850000619888306},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.36410000920295715},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.3603000044822693},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3546999990940094},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3517000079154968},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3052999973297119},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.30390000343322754},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.28119999170303345},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.2542000114917755},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.2524000108242035},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2500999867916107}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2020-08-31-314","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-08-31-314","pdf_url":"https://quantum-journal.org/papers/q-2020-08-31-314/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:1910.01155","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.01155","pdf_url":"https://arxiv.org/pdf/1910.01155","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:cb8b58b168e94cdda835675b3fd77378","is_oa":true,"landing_page_url":"https://doaj.org/article/cb8b58b168e94cdda835675b3fd77378","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,"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, Vol 4, p 314 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2020-08-31-314","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-08-31-314","pdf_url":"https://quantum-journal.org/papers/q-2020-08-31-314/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/G1372115314","display_name":null,"funder_award_id":"EXC-2046","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2117824717","display_name":null,"funder_award_id":"project ID: 390685689","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3017080660","display_name":null,"funder_award_id":"project ID: 390685689","funder_id":"https://openalex.org/F4320324521","funder_display_name":"Freie Universit\u00e4t Berlin"},{"id":"https://openalex.org/G3842438689","display_name":null,"funder_award_id":"EI 519/14-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7168488674","display_name":null,"funder_award_id":"EI 519/15-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7194386616","display_name":null,"funder_award_id":"CRC 183","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7354608348","display_name":null,"funder_award_id":"EXC-2046/1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7578079922","display_name":null,"funder_award_id":"/14-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7604888570","display_name":null,"funder_award_id":"EXC-2046/1","funder_id":"https://openalex.org/F4320324521","funder_display_name":"Freie Universit\u00e4t Berlin"},{"id":"https://openalex.org/G7725451807","display_name":null,"funder_award_id":"390685689","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G846074939","display_name":null,"funder_award_id":"817482","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320306193","display_name":"John Templeton Foundation","ror":"https://ror.org/035tnyy05"},{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320324521","display_name":"Freie Universit\u00e4t Berlin","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W114517082","https://openalex.org/W1557310162","https://openalex.org/W1590419653","https://openalex.org/W1993292204","https://openalex.org/W2054381333","https://openalex.org/W2073977329","https://openalex.org/W2138243089","https://openalex.org/W2145763471","https://openalex.org/W2161685427","https://openalex.org/W2257937122","https://openalex.org/W2517871044","https://openalex.org/W2573736728","https://openalex.org/W2735457220","https://openalex.org/W2744305830","https://openalex.org/W2749114779","https://openalex.org/W2755255888","https://openalex.org/W2758259983","https://openalex.org/W2766294686","https://openalex.org/W2781738013","https://openalex.org/W2788945937","https://openalex.org/W2790388700","https://openalex.org/W2796293949","https://openalex.org/W2798434869","https://openalex.org/W2804993962","https://openalex.org/W2811066766","https://openalex.org/W2888774813","https://openalex.org/W2901677314","https://openalex.org/W2901859177","https://openalex.org/W2903058119","https://openalex.org/W2903221501","https://openalex.org/W2945544467","https://openalex.org/W2963248893","https://openalex.org/W2965189647","https://openalex.org/W2974883009","https://openalex.org/W2980446414","https://openalex.org/W2980456669","https://openalex.org/W2982169647","https://openalex.org/W3028642772","https://openalex.org/W4236362309","https://openalex.org/W4251618665","https://openalex.org/W6684249991","https://openalex.org/W6730267373"],"related_works":[],"abstract_inverted_index":{"Within":[0],"the":[1,13,21,32,35,106,117,171,192,199,224],"context":[2,200],"of":[3,15,23,34,40,108,126,138,170,194,201],"hybrid":[4],"quantum-classical":[5],"optimization,":[6],"gradient":[7,178],"descent":[8,52,179],"based":[9],"optimizers":[10],"typically":[11],"require":[12],"evaluation":[14],"expectation":[16,76,109,127,160],"values":[17,77,110,128],"with":[18,166,233],"respect":[19],"to":[20,61,174],"outcome":[22],"parameterized":[24],"quantum":[25,44,73,203],"circuits.":[26],"In":[27,98],"this":[28,56],"work,":[29],"we":[30,153,184,206],"explore":[31,207],"consequences":[33],"prior":[36],"observation":[37],"that":[38,63,155,222],"estimation":[39,107,162],"these":[41,157,209],"quantities":[42],"on":[43,211],"hardware":[45],"results":[46,81,197,232],"in":[47,64,82,114,156,198],"a":[48,133,139,141,146,189],"form":[49],"of<mml:math":[50,96],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>s</mml:mi><mml:mi>t</mml:mi><mml:mi>o</mml:mi><mml:mi>c</mml:mi><mml:mi>h</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>c</mml:mi></mml:math>gradient":[51],"optimization.":[53],"We":[54],"formalize":[55],"notion,":[57],"which":[58],"allows":[59,229],"us":[60],"show":[62,154,221],"many":[65,115],"relevant":[66],"cases,":[67],"including":[68],"VQE,":[69,213],"QAOA":[70,214],"and":[71,152,215,220,238],"certain":[72],"classifiers,":[74],"estimating":[75],"with<mml:math":[78],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>measurement":[79],"outcomes":[80,104],"optimization":[83,196],"algorithms":[84,183],"whose":[85],"convergence":[86,186],"properties":[87],"can":[88,120,163],"be":[89,121,164],"rigorously":[90],"well":[91],"understood,":[92],"for":[93,105,191,230],"any":[94],"value":[95,161],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>.":[97],"fact,":[99],"even":[100],"using":[101],"single":[102],"measurement":[103],"is":[111],"sufficient.":[112],"Moreover,":[113],"settings":[116,226],"required":[118],"gradients":[119],"expressed":[122],"as":[123,227],"linear":[124,172],"combinations":[125],"--":[129,151],"originating,":[130],"e.g.,":[131],"from":[132],"sum":[134,147],"over":[135,148,168],"local":[136],"terms":[137,169],"Hamiltonian,":[140],"parameter":[142],"shift":[143],"rule,":[144],"or":[145],"data-set":[149],"instances":[150],"cases<mml:math":[158],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>-shot":[159],"combined":[165],"sampling":[167],"combination,":[173],"obtain":[175],"``doubly":[176],"stochastic''":[177],"optimizers.":[180],"For":[181],"all":[182],"prove":[185],"guarantees,":[187],"providing":[188],"framework":[190],"derivation":[193],"rigorous":[195],"near-term":[202],"devices.":[204],"Additionally,":[205],"numerically":[208],"methods":[210],"benchmark":[212],"quantum-enhanced":[216],"machine":[217],"learning":[218],"tasks":[219],"treating":[223],"stochastic":[225],"hyper-parameters":[228],"state-of-the-art":[231],"significantly":[234],"fewer":[235],"circuit":[236],"executions":[237],"measurements.":[239]},"counts_by_year":[{"year":2026,"cited_by_count":15},{"year":2025,"cited_by_count":32},{"year":2024,"cited_by_count":37},{"year":2023,"cited_by_count":36},{"year":2022,"cited_by_count":46},{"year":2021,"cited_by_count":35},{"year":2020,"cited_by_count":5}],"updated_date":"2026-06-16T09:24:06.705377","created_date":"2019-10-10T00:00:00"}
