{"id":"https://openalex.org/W2972341748","doi":"https://doi.org/10.22331/q-2021-04-15-431","title":"Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations","display_name":"Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations","publication_year":2021,"publication_date":"2021-04-15","ids":{"openalex":"https://openalex.org/W2972341748","doi":"https://doi.org/10.22331/q-2021-04-15-431","mag":"2972341748"},"language":"en","primary_location":{"id":"doi:10.22331/q-2021-04-15-431","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-04-15-431","pdf_url":"https://quantum-journal.org/papers/q-2021-04-15-431/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-2021-04-15-431/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033237621","display_name":"Juan Jos\u00e9 Garc\u00eda\u2010Ripoll","orcid":"https://orcid.org/0000-0001-8993-4624"},"institutions":[{"id":"https://openalex.org/I4210095385","display_name":"Instituto de F\u00edsica Fundamental","ror":"https://ror.org/009wseg80","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210095385"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Juan Jos\u00e9 Garc\u00eda-Ripoll","raw_affiliation_strings":["Institute of Fundamental Physics, Calle Serrano 113b, 28006 Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Institute of Fundamental Physics, Calle Serrano 113b, 28006 Madrid, Spain","institution_ids":["https://openalex.org/I4210095385"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033237621"],"corresponding_institution_ids":["https://openalex.org/I4210095385"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":5.8796,"has_fulltext":true,"cited_by_count":62,"citation_normalized_percentile":{"value":0.96693354,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"5","issue":null,"first_page":"431","last_page":"431"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9997000098228455,"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":0.9997000098228455,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.9977999925613403,"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-phase-estimation-algorithm","display_name":"Quantum phase estimation algorithm","score":0.7331951856613159},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.6542771458625793},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5987860560417175},{"id":"https://openalex.org/keywords/quantum-fourier-transform","display_name":"Quantum Fourier transform","score":0.5464438796043396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48428505659103394},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37574562430381775},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"Quantum error correction","score":0.37299418449401855},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3331153988838196},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.3329264521598816},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13574635982513428},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09723111987113953}],"concepts":[{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.7331951856613159},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.6542771458625793},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5987860560417175},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.5464438796043396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48428505659103394},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37574562430381775},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.37299418449401855},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3331153988838196},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3329264521598816},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13574635982513428},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09723111987113953}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.22331/q-2021-04-15-431","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-04-15-431","pdf_url":"https://quantum-journal.org/papers/q-2021-04-15-431/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:1909.06619","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.06619","pdf_url":"https://arxiv.org/pdf/1909.06619","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:digital.csic.es:10261/213953","is_oa":false,"landing_page_url":"http://hdl.handle.net/10261/213953","pdf_url":null,"source":{"id":"https://openalex.org/S4306400616","display_name":"DIGITAL.CSIC (Spanish National Research Council (CSIC))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I134820265","host_organization_name":"Consejo Superior de Investigaciones Cient\u00edficas","host_organization_lineage":["https://openalex.org/I134820265"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"comunicaci\u00f3n de congreso"},{"id":"pmh:oai:digital.csic.es:10261/258230","is_oa":false,"landing_page_url":"http://hdl.handle.net/10261/258230","pdf_url":null,"source":{"id":"https://openalex.org/S4306400616","display_name":"DIGITAL.CSIC (Spanish National Research Council (CSIC))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I134820265","host_organization_name":"Consejo Superior de Investigaciones Cient\u00edficas","host_organization_lineage":["https://openalex.org/I134820265"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"art\u00edculo"},{"id":"pmh:oai:doaj.org/article:99f53db927c14b99a1b0377cdb6fb668","is_oa":true,"landing_page_url":"https://doaj.org/article/99f53db927c14b99a1b0377cdb6fb668","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 431 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2021-04-15-431","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-04-15-431","pdf_url":"https://quantum-journal.org/papers/q-2021-04-15-431/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/G228440392","display_name":null,"funder_award_id":"FA2386-18-1-4019","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6700992506","display_name":null,"funder_award_id":"PGC2018-094792-B-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2972341748.pdf","grobid_xml":"https://content.openalex.org/works/W2972341748.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W1550516781","https://openalex.org/W1563049925","https://openalex.org/W1624621931","https://openalex.org/W1966702987","https://openalex.org/W1967077133","https://openalex.org/W1972140872","https://openalex.org/W1973584065","https://openalex.org/W2008634363","https://openalex.org/W2019177023","https://openalex.org/W2022419246","https://openalex.org/W2033368244","https://openalex.org/W2036604884","https://openalex.org/W2037772232","https://openalex.org/W2054381333","https://openalex.org/W2082946462","https://openalex.org/W2086731084","https://openalex.org/W2096391265","https://openalex.org/W2105472443","https://openalex.org/W2106818257","https://openalex.org/W2154815292","https://openalex.org/W2156190205","https://openalex.org/W2164248509","https://openalex.org/W2170120409","https://openalex.org/W2343408237","https://openalex.org/W2609950881","https://openalex.org/W2770725152","https://openalex.org/W2796128092","https://openalex.org/W2798745146","https://openalex.org/W2809024202","https://openalex.org/W2841500134","https://openalex.org/W2890217530","https://openalex.org/W2931020703","https://openalex.org/W2943575154","https://openalex.org/W2943869291","https://openalex.org/W2955315321","https://openalex.org/W2962820207","https://openalex.org/W2963198496","https://openalex.org/W2963223228","https://openalex.org/W2963963042","https://openalex.org/W2964200210","https://openalex.org/W2971636091","https://openalex.org/W3098477102","https://openalex.org/W3099497510","https://openalex.org/W3100806676","https://openalex.org/W3102193956","https://openalex.org/W3103800805","https://openalex.org/W3104703121","https://openalex.org/W3105221311","https://openalex.org/W3113785444","https://openalex.org/W3123136496","https://openalex.org/W6893631272","https://openalex.org/W6912738804"],"related_works":["https://openalex.org/W3136237069","https://openalex.org/W2138874081","https://openalex.org/W2566913519","https://openalex.org/W2891491794","https://openalex.org/W4311689615","https://openalex.org/W1980834277","https://openalex.org/W3203856319","https://openalex.org/W2013727936","https://openalex.org/W2362057230","https://openalex.org/W3117026029"],"abstract_inverted_index":{"In":[0],"this":[1,64],"work":[2],"we":[3,66],"study":[4],"the":[5,36,96,108],"encoding":[6,98],"of":[7,27,35,81,99,147],"smooth,":[8],"differentiable":[9],"multivariate":[10],"functions":[11],"in":[12,45],"quantum":[13,16,37,47,100,156],"registers,":[14,101],"using":[15,58],"computers":[17],"or":[18],"tensor-network":[19],"representations.":[20],"We":[21],"show":[22],"that":[23,73],"a":[24,46,155,160],"large":[25],"family":[26],"distributions":[28],"can":[29,41,150],"be":[30,42,151],"encoded":[31],"as":[32,107,131],"low-entanglement":[33],"states":[34,40],"register.":[38],"These":[39,85],"efficiently":[43,53],"created":[44],"computer,":[48],"but":[49],"they":[50,121,144],"are":[51],"also":[52],"stored,":[54],"manipulated":[55],"and":[56,79,102,136],"probed":[57],"Matrix-Product":[59],"States":[60],"techniques.":[61],"Inspired":[62],"by":[63],"idea,":[65],"present":[67],"eight":[68],"quantum-inspired":[69],"numerical":[70],"analysis":[71],"algorithms,":[72,105,129],"include":[74],"Fourier":[75,110,138],"sampling,":[76],"interpolation,":[77],"differentiation":[78],"integration":[80],"partial":[82],"derivative":[83],"equations.":[84],"algorithms":[86,149],"combine":[87],"classical":[88,128],"ideas":[89],"\u2013":[90,94],"finite-differences,":[91],"spectral":[92],"methods":[93,119],"with":[95],"efficient":[97],"well":[103],"known":[104],"such":[106,130],"Quantum":[109],"Transform.":[111],"<mml:math":[112],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow":[113],"class=\"MJX-TeXAtom-ORD\"><mml:mtext":[114],"class=\"MJX-tex-mathit\"":[115],"mathvariant=\"italic\">When":[116],"these":[117,148],"heuristic":[118],"work</mml:mtext></mml:mrow></mml:math>,":[120],"provide":[122],"an":[123],"exponential":[124],"speed-up":[125],"over":[126],"other":[127],"Monte":[132],"Carlo":[133],"integration,":[134],"finite-difference":[135],"fast":[137],"transforms":[139],"(FFT).":[140],"But":[141],"even":[142],"when":[143],"don't,":[145],"some":[146],"translated":[152],"back":[153],"to":[154,158],"computer":[157],"implement":[159],"similar":[161],"task.":[162]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}