{"id":"https://openalex.org/W3200790102","doi":"https://doi.org/10.4204/eptcs.343.7","title":"Diagrammatic Differentiation for Quantum Machine Learning","display_name":"Diagrammatic Differentiation for Quantum Machine Learning","publication_year":2021,"publication_date":"2021-09-09","ids":{"openalex":"https://openalex.org/W3200790102","doi":"https://doi.org/10.4204/eptcs.343.7","mag":"3200790102"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":null,"pdf_url":"https://arxiv.org/pdf/2103.07960","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":["Cornell University"],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://arxiv.org/pdf/2103.07960","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076217339","display_name":"Alexis Toumi","orcid":"https://orcid.org/0000-0002-7040-4532"},"institutions":[{"id":"https://openalex.org/I4210114455","display_name":"Cambridge Quantum Computing (United Kingdom)","ror":"https://ror.org/024779x77","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210114455"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alexis Toumi","raw_affiliation_strings":["Cambridge Quantum Computing Ltd.","University of Oxford"],"affiliations":[{"raw_affiliation_string":"Cambridge Quantum Computing Ltd.","institution_ids":["https://openalex.org/I4210114455"]},{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064240198","display_name":"Richie Yeung","orcid":"https://orcid.org/0000-0003-1953-8305"},"institutions":[{"id":"https://openalex.org/I4210114455","display_name":"Cambridge Quantum Computing (United Kingdom)","ror":"https://ror.org/024779x77","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210114455"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Richie Yeung","raw_affiliation_strings":["Cambridge Quantum Computing Ltd."],"affiliations":[{"raw_affiliation_string":"Cambridge Quantum Computing Ltd.","institution_ids":["https://openalex.org/I4210114455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082909966","display_name":"Giovanni de Felice","orcid":"https://orcid.org/0000-0002-8550-718X"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I4210114455","display_name":"Cambridge Quantum Computing (United Kingdom)","ror":"https://ror.org/024779x77","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210114455"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Giovanni de Felice","raw_affiliation_strings":["Cambridge Quantum Computing Ltd.","University of Oxford"],"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Cambridge Quantum Computing Ltd.","institution_ids":["https://openalex.org/I4210114455"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":0,"currency":"USD","value_usd":0,"provenance":"doaj"},"apc_paid":null,"fwci":1.711,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":5,"citation_normalized_percentile":{"value":0.999972,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":78,"max":81},"biblio":{"volume":"343","issue":null,"first_page":"132","last_page":"144"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9999,"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":0.9999,"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":0.9967,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9952,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/diagrammatic-reasoning","display_name":"Diagrammatic reasoning","score":0.95125717},{"id":"https://openalex.org/keywords/automatic-differentiation","display_name":"Automatic differentiation","score":0.4752726},{"id":"https://openalex.org/keywords/python","display_name":"Python","score":0.45666486}],"concepts":[{"id":"https://openalex.org/C106624574","wikidata":"https://www.wikidata.org/wiki/Q5270387","display_name":"Diagrammatic reasoning","level":2,"score":0.95125717},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.68464255},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5627231},{"id":"https://openalex.org/C169590947","wikidata":"https://www.wikidata.org/wiki/Q47506","display_name":"Compiler","level":2,"score":0.496147},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.48895824},{"id":"https://openalex.org/C133512626","wikidata":"https://www.wikidata.org/wiki/Q787371","display_name":"Automatic differentiation","level":3,"score":0.4752726},{"id":"https://openalex.org/C519991488","wikidata":"https://www.wikidata.org/wiki/Q28865","display_name":"Python (programming language)","level":2,"score":0.45666486},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4377383},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3991301},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31289017},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.277061},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23411393},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.17053485},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16446403},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1303066},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"is_oa":true,"landing_page_url":null,"pdf_url":"https://arxiv.org/pdf/2103.07960","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":["Cornell University"],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.07960","pdf_url":"http://arxiv.org/pdf/2103.07960","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://api.datacite.org/dois/10.48550/arxiv.2103.07960","pdf_url":null,"source":{"id":"https://openalex.org/S4393179698","display_name":"DataCite API","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210145204","host_organization_name":"DataCite","host_organization_lineage":["https://openalex.org/I4210145204"],"host_organization_lineage_names":["DataCite"],"type":"metadata"},"license":null,"license_id":null,"version":null}],"best_oa_location":{"is_oa":true,"landing_page_url":null,"pdf_url":"https://arxiv.org/pdf/2103.07960","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":["Cornell University"],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":["https://openalex.org/W3136786421","https://openalex.org/W3200790102"],"referenced_works_count":49,"referenced_works":["https://openalex.org/W1491396042","https://openalex.org/W1501547546","https://openalex.org/W1583784885","https://openalex.org/W1617295181","https://openalex.org/W1789645782","https://openalex.org/W1973799895","https://openalex.org/W2008699979","https://openalex.org/W2040040776","https://openalex.org/W2119180894","https://openalex.org/W2134207475","https://openalex.org/W2146292423","https://openalex.org/W2318411205","https://openalex.org/W2417863416","https://openalex.org/W2559582198","https://openalex.org/W2598985404","https://openalex.org/W2792699004","https://openalex.org/W2798434869","https://openalex.org/W2798910219","https://openalex.org/W2903221501","https://openalex.org/W2913248536","https://openalex.org/W2918135161","https://openalex.org/W2922906818","https://openalex.org/W2945477927","https://openalex.org/W2963619589","https://openalex.org/W2964268018","https://openalex.org/W2980693978","https://openalex.org/W3009801593","https://openalex.org/W3015643100","https://openalex.org/W3016020519","https://openalex.org/W3023127812","https://openalex.org/W3044460193","https://openalex.org/W3049052537","https://openalex.org/W3083868759","https://openalex.org/W3098041393","https://openalex.org/W3101122608","https://openalex.org/W3103164351","https://openalex.org/W3104914200","https://openalex.org/W3105463217","https://openalex.org/W3109084083","https://openalex.org/W3122563667","https://openalex.org/W3124268591","https://openalex.org/W3134406394","https://openalex.org/W3169377977","https://openalex.org/W3198049459","https://openalex.org/W4287556403","https://openalex.org/W4287711460","https://openalex.org/W4287815573","https://openalex.org/W4288349717","https://openalex.org/W4382132565"],"related_works":["https://openalex.org/W4288417689","https://openalex.org/W4233209174","https://openalex.org/W3090641240","https://openalex.org/W3083799684","https://openalex.org/W3003518673","https://openalex.org/W2933723564","https://openalex.org/W2768092088","https://openalex.org/W2243494072","https://openalex.org/W1588273335","https://openalex.org/W1582653816"],"abstract_inverted_index":{"We":[0,61],"introduce":[1],"diagrammatic":[2,84],"differentiation":[3,85],"for":[4,96],"tensor":[5],"calculus":[6],"by":[7],"generalising":[8],"the":[9,29,49,54,67,93,109,118,123,131,137],"dual":[10],"number":[11],"construction":[12],"from":[13],"rigs":[14],"to":[15,20,26,37,66,78,125],"monoidal":[16,97],"categories.":[17,98],"Applying":[18],"this":[19],"ZX":[21],"diagrams,":[22],"we":[23,47],"show":[24],"how":[25],"calculate":[27],"diagrammatically":[28],"gradient":[30],"of":[31,43,56,70,101,133,140],"a":[32,38],"linear":[33],"map":[34],"with":[35,76,87],"respect":[36],"phase":[39],"parameter.":[40],"For":[41],"diagrams":[42,75,135],"parametrised":[44],"quantum":[45,59,115,141],"circuits,":[46,73],"get":[48],"well-known":[50],"parameter-shift":[51],"rule":[52],"at":[53],"basis":[55],"many":[57,126],"variational":[58],"algorithms.":[60],"then":[62,105],"extend":[63],"our":[64],"method":[65],"automatic":[68],"differentation":[69],"hybrid":[71],"classical-quantum":[72,102],"using":[74,108],"bubbles":[77],"encode":[79],"arbitrary":[80],"non-linear":[81],"operators.":[82],"Moreover,":[83],"comes":[86],"an":[88],"open-source":[89],"implementation":[90],"in":[91],"DisCoPy,":[92],"Python":[94],"library":[95,111],"Diagrammatic":[99],"gradients":[100],"circuits":[103],"can":[104],"be":[106],"simplified":[107],"PyZX":[110],"and":[112,136],"executed":[113],"on":[114],"hardware":[116],"via":[117],"tket":[119],"compiler.":[120],"This":[121],"opens":[122],"door":[124],"practical":[127],"applications":[128],"harnessing":[129],"both":[130],"structure":[132],"string":[134],"computational":[138],"power":[139],"machine":[142],"learning.":[143]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3200790102","counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":3}],"updated_date":"2025-01-09T10:31:55.587402","created_date":"2021-09-27"}