{"id":"https://openalex.org/W7140872877","doi":"https://doi.org/10.48550/arxiv.2603.24196","title":"Quantum Neural Physics: Solving Partial Differential Equations on Quantum Simulators using Quantum Convolutional Neural Networks","display_name":"Quantum Neural Physics: Solving Partial Differential Equations on Quantum Simulators using Quantum Convolutional Neural Networks","publication_year":2026,"publication_date":"2026-03-25","ids":{"openalex":"https://openalex.org/W7140872877","doi":"https://doi.org/10.48550/arxiv.2603.24196"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.24196","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24196","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.24196","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046645552","display_name":"Jucai Zhai","orcid":"https://orcid.org/0000-0002-7858-4873"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhai, Jucai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130690459","display_name":"Muhammad Abdullah","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abdullah, Muhammad","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130651432","display_name":"Boyang Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Boyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130711324","display_name":"Fazal Chaudry","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chaudry, Fazal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016499925","display_name":"Paul N. Smith","orcid":"https://orcid.org/0000-0001-6891-5694"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Smith, Paul N.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065979869","display_name":"Claire E. Heaney","orcid":"https://orcid.org/0000-0002-6555-1423"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Heaney, Claire E.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130700001","display_name":"Yanghua Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Yanghua","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077369272","display_name":"Jiansheng Xiang","orcid":"https://orcid.org/0000-0002-1343-3628"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiang, Jiansheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5130641258","display_name":"Christopher C. Pain","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pain, Christopher C.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.8253999948501587,"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":0.8253999948501587,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.05139999836683273,"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"}},{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.04259999841451645,"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/multigrid-method","display_name":"Multigrid method","score":0.6929000020027161},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.5442000031471252},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5245000123977661},{"id":"https://openalex.org/keywords/quantum-phase-estimation-algorithm","display_name":"Quantum phase estimation algorithm","score":0.5052000284194946},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5038999915122986},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5023000240325928},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.48510000109672546},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.4041999876499176},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.40220001339912415}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.6929000020027161},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5442000031471252},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.529699981212616},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5245000123977661},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.5052000284194946},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5038999915122986},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5023000240325928},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.48510000109672546},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4652999937534332},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41370001435279846},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.4041999876499176},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.40220001339912415},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.34459999203681946},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.33820000290870667},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.32249999046325684},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.3156999945640564},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3100000023841858},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.30959999561309814},{"id":"https://openalex.org/C161166931","wikidata":"https://www.wikidata.org/wiki/Q7269096","display_name":"Quantum simulator","level":4,"score":0.30649998784065247},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.302700012922287},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.3001999855041504},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.2757999897003174},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.27149999141693115},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.2632000148296356},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26249998807907104},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.24196","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24196","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.24196","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24196","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Neural":[0,54],"Physics":[1],"recasts":[2],"local":[3,75,121,193],"discretisations":[4],"of":[5,92,99,110,138,185],"partial":[6],"differential":[7],"equations":[8],"(PDEs)":[9],"as":[10,131],"fixed":[11],"convolutional":[12,77],"operators,":[13],"providing":[14],"a":[15,52,59,83],"physics-preserving":[16],"alternative":[17],"to":[18,32,41,74],"data-driven":[19],"surrogate":[20],"modelling":[21],"in":[22,188,205],"scientific":[23,93],"machine":[24],"learning.":[25],"However,":[26],"existing":[27],"realizations":[28],"remain":[29],"largely":[30],"confined":[31],"classical":[33,84],"AI":[34],"hardware":[35],"and":[36,57,79,113,156,166,198],"do":[37],"not":[38],"directly":[39],"connect":[40],"quantum":[42,76,122,175,207],"structured":[43],"operator":[44],"design.":[45],"To":[46],"bridge":[47],"this":[48],"gap,":[49],"we":[50],"introduce":[51],"\\emph{Quantum":[53],"Physics}":[55],"framework":[56],"develop":[58],"Hybrid":[60],"Quantum-Classical":[61],"CNN":[62],"Multigrid":[63],"Solver":[64],"(HQC-CNNMG).":[65],"The":[66],"proposed":[67],"method":[68],"maps":[69],"analytically":[70],"prescribed":[71],"stencil":[72],"operators":[73,123],"primitives":[78],"embeds":[80],"them":[81],"within":[82],"multilevel":[85,164],"W-cycle":[86],"architecture,":[87],"combining":[88],"the":[89,96,107,114,119,142,182],"operator-centric":[90],"view":[91],"ML":[94],"with":[95,106,127,173,200],"numerical":[97,161,196],"rigor":[98],"multigrid":[100],"solvers.":[101],"Using":[102],"amplitude":[103],"encoding":[104],"together":[105],"Linear":[108],"Combination":[109],"Unitaries":[111],"(LCU)":[112],"Quantum":[115],"Fourier":[116],"Transform":[117],"(QFT),":[118],"resulting":[120],"admit":[124],"logarithmic-depth":[125],"implementation,":[126],"circuit":[128,145,194],"depth":[129],"scaling":[130],"$\\mathcal{O}(\\log":[132],"K)$":[133],"for":[134],"an":[135],"encoded":[136],"block":[137],"size":[139],"$K$":[140],"under":[141],"idealized":[143],"parallel":[144],"model":[146],"considered":[147],"here.":[148],"Numerical":[149],"experiments":[150],"on":[151,169],"Poisson,":[152],"transient":[153],"diffusion,":[154],"convection--diffusion,":[155],"incompressible":[157],"Navier--Stokes":[158],"problems":[159],"demonstrate":[160],"consistency,":[162],"stable":[163],"behaviour,":[165],"workflow-level":[167],"feasibility":[168],"noiseless":[170],"simulators.":[171],"Comparisons":[172],"representative":[174],"linear":[176],"solver":[177],"paradigms":[178],"further":[179],"show":[180],"that":[181],"main":[183],"strength":[184],"HQC-CNNMG":[186],"lies":[187],"its":[189],"balanced":[190],"trade-off":[191],"among":[192],"depth,":[195],"robustness,":[197],"compatibility":[199],"PDE":[201],"structure,":[202],"rather":[203],"than":[204],"fully":[206],"global":[208],"inversion.":[209]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-27T00:00:00"}
