{"id":"https://openalex.org/W4416874037","doi":"https://doi.org/10.1109/qce65121.2025.00185","title":"Partitioned Hybrid Quantum Fourier Neural Operators for Scientific Quantum Machine Learning","display_name":"Partitioned Hybrid Quantum Fourier Neural Operators for Scientific Quantum Machine Learning","publication_year":2025,"publication_date":"2025-08-30","ids":{"openalex":"https://openalex.org/W4416874037","doi":"https://doi.org/10.1109/qce65121.2025.00185"},"language":"en","primary_location":{"id":"doi:10.1109/qce65121.2025.00185","is_oa":false,"landing_page_url":"https://doi.org/10.1109/qce65121.2025.00185","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE International Conference on Quantum Computing and Engineering (QCE)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107644489","display_name":"Paolo Marcandelli","orcid":null},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Paolo Marcandelli","raw_affiliation_strings":["Politecnico di Milano,Department of Civil and Environmental Engineering,Milan,Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Politecnico di Milano,Department of Civil and Environmental Engineering,Milan,Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091809505","display_name":"Yuanrong He","orcid":"https://orcid.org/0000-0003-0783-9733"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Yuanchun He","raw_affiliation_strings":["School of Electrical Engineering and Computer Science KTH Royal Institute of technology,Stockholm,Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Computer Science KTH Royal Institute of technology,Stockholm,Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040750841","display_name":"Stefano Mariani","orcid":"https://orcid.org/0000-0001-7027-3117"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Stefano Mariani","raw_affiliation_strings":["Politecnico di Milano,Department of Civil and Environmental Engineering,Milan,Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Politecnico di Milano,Department of Civil and Environmental Engineering,Milan,Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102996684","display_name":"Martina Siena","orcid":"https://orcid.org/0000-0001-9094-4731"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Martina Siena","raw_affiliation_strings":["Politecnico di Milano,Department of Civil and Environmental Engineering,Milan,Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Politecnico di Milano,Department of Civil and Environmental Engineering,Milan,Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070572735","display_name":"Stefano Markidis","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Stefano Markidis","raw_affiliation_strings":["School of Electrical Engineering and Computer Science KTH Royal Institute of technology,Stockholm,Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Computer Science KTH Royal Institute of technology,Stockholm,Sweden","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1676","last_page":"1687"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9646000266075134,"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":0.9646000266075134,"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":0.008899999782443047,"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"}},{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.0035000001080334187,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-fourier-transform","display_name":"Quantum Fourier transform","score":0.7675999999046326},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5824000239372253},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5612000226974487},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.5324000120162964},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5242999792098999},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.49390000104904175},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.460999995470047},{"id":"https://openalex.org/keywords/quantum-machine-learning","display_name":"Quantum machine learning","score":0.4447999894618988},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.41920000314712524}],"concepts":[{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.7675999999046326},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5824000239372253},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5612000226974487},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5324000120162964},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5242999792098999},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.49390000104904175},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.460999995470047},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45170000195503235},{"id":"https://openalex.org/C2779094486","wikidata":"https://www.wikidata.org/wiki/Q18811578","display_name":"Quantum machine learning","level":4,"score":0.4447999894618988},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42820000648498535},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.41920000314712524},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.39089998602867126},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3749000132083893},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35920000076293945},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.34139999747276306},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.32749998569488525},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.3075999915599823},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.2890999913215637},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.27790001034736633},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.2761000096797943},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.27250000834465027},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26919999718666077},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2644999921321869},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.2597000002861023},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.25929999351501465},{"id":"https://openalex.org/C181543814","wikidata":"https://www.wikidata.org/wiki/Q44746","display_name":"Uncertainty principle","level":3,"score":0.2554999887943268},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.25279998779296875}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/qce65121.2025.00185","is_oa":false,"landing_page_url":"https://doi.org/10.1109/qce65121.2025.00185","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE International Conference on Quantum Computing and Engineering (QCE)","raw_type":"proceedings-article"},{"id":"pmh:oai:re.public.polimi.it:11311/1308486","is_oa":false,"landing_page_url":"https://hdl.handle.net/11311/1308486","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"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":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310077","display_name":"National Research Centre","ror":"https://ror.org/02n85j827"},{"id":"https://openalex.org/F7311471023","display_name":"NextGenerationEU","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1492999010","https://openalex.org/W1990486890","https://openalex.org/W1990514347","https://openalex.org/W2781738013","https://openalex.org/W2808979145","https://openalex.org/W2898401615","https://openalex.org/W2899283552","https://openalex.org/W2945680873","https://openalex.org/W2981748719","https://openalex.org/W2990961515","https://openalex.org/W3108818881","https://openalex.org/W3111162498","https://openalex.org/W3132743969","https://openalex.org/W3164436820","https://openalex.org/W3168508484","https://openalex.org/W3189829096","https://openalex.org/W3206451759","https://openalex.org/W3213910114","https://openalex.org/W4246367117","https://openalex.org/W4307872100","https://openalex.org/W4312189222","https://openalex.org/W4320032187","https://openalex.org/W4322760659","https://openalex.org/W4366594995","https://openalex.org/W4382683505","https://openalex.org/W4396814960","https://openalex.org/W4400224458","https://openalex.org/W4404465609","https://openalex.org/W4405926070","https://openalex.org/W4411026638"],"related_works":[],"abstract_inverted_index":{"We":[0,84,103],"introduce":[1],"the":[2,13,25],"Partitioned":[3],"Hybrid":[4],"Quantum":[5,14],"Fourier":[6,15,26],"Neural":[7,16],"Operator":[8,17],"(PH-QFNO),":[9],"a":[10,55,81,125],"generalization":[11],"of":[12,134],"(QFNO)":[18],"for":[19],"scientific":[20],"machine":[21],"learning.":[22],"PH-QFNO":[23,86,106,114,135],"partitions":[24],"operator":[27],"computation":[28],"across":[29,41,61],"classical":[30,44,108,120,137],"and":[31,38,43,53,74,92,99],"quantum":[32,42,69,75],"resources,":[33],"enabling":[34],"tunable":[35],"quantum-classical":[36],"hybridization":[37],"distributed":[39],"execution":[40],"devices.":[45],"The":[46],"method":[47],"extends":[48],"QFNOs":[49],"to":[50,58],"higher":[51,116],"dimensions":[52],"incorporates":[54],"message-passing":[56],"framework":[57],"distribute":[59],"data":[60,65],"different":[62],"partitions.":[63],"Input":[64],"are":[66,78],"encoded":[67],"into":[68],"states":[70],"using":[71,80,87],"unary":[72],"encoding,":[73],"circuit":[76],"parameters":[77],"optimized":[79],"variational":[82],"scheme.":[83],"implement":[85],"PennyLane":[88],"with":[89],"PyTorch":[90],"integration":[91],"evaluate":[93],"it":[94],"on":[95],"Burgers'":[96],"equation,":[97],"incompressible":[98,112],"compressible":[100],"Navier-Stokes":[101],"equations.":[102],"show":[104],"that":[105],"recovers":[107],"FNO":[109],"accuracy.":[110],"On":[111],"Navier-Stokes,":[113],"achieves":[115],"accuracy":[117],"than":[118],"its":[119],"counterparts.":[121],"Finally,":[122],"we":[123],"perform":[124],"sensitivity":[126],"analysis":[127],"under":[128],"input":[129],"noise,":[130],"confirming":[131],"improved":[132],"stability":[133],"over":[136],"baselines.":[138]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-12-01T00:00:00"}