{"id":"https://openalex.org/W7164029542","doi":"https://doi.org/10.48550/arxiv.2606.08053","title":"Numerical solution of the nonlinear Dirac equation by a splitting variational quantum algorithm","display_name":"Numerical solution of the nonlinear Dirac equation by a splitting variational quantum algorithm","publication_year":2026,"publication_date":"2026-06-06","ids":{"openalex":"https://openalex.org/W7164029542","doi":"https://doi.org/10.48550/arxiv.2606.08053"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.08053","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.08053","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":null,"license_id":null,"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.2606.08053","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138209112","display_name":"Qian Zuo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zuo, Qian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138278609","display_name":"Ying He","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"He, Ying","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138263765","display_name":"Xiaofei Zhao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao, Xiaofei","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":0.539900004863739,"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":0.539900004863739,"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":0.262800008058548,"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/T10566","display_name":"Laser-Matter Interactions and Applications","score":0.029600000008940697,"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/dirac","display_name":"Dirac (video compression format)","score":0.6108999848365784},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5745000243186951},{"id":"https://openalex.org/keywords/dirac-equation","display_name":"Dirac equation","score":0.5062000155448914},{"id":"https://openalex.org/keywords/spinor","display_name":"Spinor","score":0.44519999623298645},{"id":"https://openalex.org/keywords/relativistic-wave-equations","display_name":"Relativistic wave equations","score":0.3790000081062317},{"id":"https://openalex.org/keywords/dirac-spinor","display_name":"Dirac spinor","score":0.3785000145435333},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.3474000096321106},{"id":"https://openalex.org/keywords/propagator","display_name":"Propagator","score":0.3172000050544739}],"concepts":[{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.6108999848365784},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5745000243186951},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.5062000155448914},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4756999909877777},{"id":"https://openalex.org/C43506125","wikidata":"https://www.wikidata.org/wiki/Q604907","display_name":"Spinor","level":2,"score":0.44519999623298645},{"id":"https://openalex.org/C140673361","wikidata":"https://www.wikidata.org/wiki/Q7310838","display_name":"Relativistic wave equations","level":3,"score":0.3790000081062317},{"id":"https://openalex.org/C156785651","wikidata":"https://www.wikidata.org/wiki/Q688945","display_name":"Dirac spinor","level":4,"score":0.3785000145435333},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3474000096321106},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.33820000290870667},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33250001072883606},{"id":"https://openalex.org/C104416048","wikidata":"https://www.wikidata.org/wiki/Q302518","display_name":"Propagator","level":2,"score":0.3172000050544739},{"id":"https://openalex.org/C30005106","wikidata":"https://www.wikidata.org/wiki/Q7858689","display_name":"Two-body Dirac equations","level":3,"score":0.3147999942302704},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.3084999918937683},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.30469998717308044},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.2969000041484833},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.27480000257492065},{"id":"https://openalex.org/C64618476","wikidata":"https://www.wikidata.org/wiki/Q164296","display_name":"Variational method","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2678000032901764},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.26669999957084656},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.265500009059906},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.26179999113082886},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C125867301","wikidata":"https://www.wikidata.org/wiki/Q18205881","display_name":"Causal fermion system","level":5,"score":0.2535000145435333}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.08053","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.08053","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.08053","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.08053","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":null,"license_id":null,"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":{"In":[0],"this":[1,52],"work,":[2],"we":[3,54],"propose":[4],"an":[5],"operator-splitting":[6,174],"variational":[7,68,105,175],"quantum":[8,121,176],"algorithm,":[9],"termed":[10],"Dirac-sVQA,":[11],"for":[12,170,178],"simulating":[13],"the":[14,24,34,56,86,94,119,142,146,171],"nonlinear":[15,26,67,98,134,179],"Dirac":[16,63,78,95],"equation":[17],"(NLDE).":[18],"The":[19,70,97],"main":[20],"difficulty":[21],"arises":[22],"from":[23],"state-dependent":[25],"interaction,":[27],"its":[28],"time-discrete":[29],"update":[30,106],"depends":[31],"explicitly":[32],"on":[33,80],"intermediate":[35],"spinor":[36,148],"state":[37],"and,":[38],"in":[39,132],"general,":[40],"cannot":[41],"be":[42],"implemented":[43,74],"as":[44,102],"a":[45,60,66,76,81,103,108],"fixed":[46],"state-independent":[47],"unitary":[48],"circuit.":[49],"To":[50],"address":[51],"difficulty,":[53],"decompose":[55],"NLDE":[57],"evolution":[58,92],"into":[59],"structured":[61],"linear":[62,71],"substep":[64,72],"and":[65,89,114,123,127,145,158],"correction.":[69],"is":[73,100],"by":[75],"spinor-Fourier":[77],"propagator":[79],"joint":[82],"position-spin":[83],"register,":[84],"preserving":[85],"spin-momentum":[87],"coupling":[88],"mass-induced":[90],"spin":[91],"of":[93,111,173],"operator.":[96],"correction":[99],"reformulated":[101],"measurement-based":[104],"through":[107],"small":[109],"set":[110],"overlap,":[112],"self-channel,":[113],"cross-channel":[115],"observables.":[116],"We":[117],"provide":[118,167],"corresponding":[120],"circuits":[122],"derive":[124],"measurement-aware":[125],"resource":[126],"complexity":[128],"estimates.":[129],"Numerical":[130],"experiments":[131],"several":[133],"regimes":[135],"show":[136],"that":[137],"Dirac-sVQA":[138],"accurately":[139],"captures":[140],"both":[141],"total":[143],"density":[144],"componentwise":[147],"dynamics,":[149],"agrees":[150],"well":[151],"with":[152],"classical":[153],"Fourier":[154],"pseudospectral":[155],"splitting":[156],"solutions,":[157],"exhibits":[159],"stable":[160],"error":[161],"behavior":[162],"over":[163],"time.":[164],"These":[165],"results":[166],"numerical":[168],"evidence":[169],"feasibility":[172],"simulation":[177],"relativistic":[180],"wave":[181],"equations.":[182]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-10T00:00:00"}
