{"id":"https://openalex.org/W7206214419","doi":"https://doi.org/10.48550/arxiv.2609.00694","title":"The Fermionic Cohomology Problem on the Full Fock Space Is $\\mathrm{QMA}_1$-Complete","display_name":"The Fermionic Cohomology Problem on the Full Fock Space Is $\\mathrm{QMA}_1$-Complete","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W7206214419","doi":"https://doi.org/10.48550/arxiv.2609.00694"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.00694","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.00694","pdf_url":"https://arxiv.org/pdf/2609.00694","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.00694","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5149279526","display_name":"Yibin Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I60134161","display_name":"Nagoya University","ror":"https://ror.org/04chrp450","country_code":"JP","type":"education","lineage":["https://openalex.org/I60134161"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Wang, Yibin","raw_affiliation_strings":["Graduate School of Mathematics , Nagoya University , Nagoya , 464-8601 , Aichi , Japan,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Mathematics , Nagoya University , Nagoya , 464-8601 , Aichi , Japan,","institution_ids":["https://openalex.org/I60134161"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5149279526"],"corresponding_institution_ids":["https://openalex.org/I60134161"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.8866999745368958,"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":0.8866999745368958,"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":0.06350000202655792,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.010900000110268593,"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/full-fock-space","display_name":"full Fock space","score":0.9470000267028809},{"id":"https://openalex.org/keywords/zero-energy-states","display_name":"zero-energy states","score":0.7990000247955322},{"id":"https://openalex.org/keywords/supersymmetric-hamiltonian","display_name":"supersymmetric Hamiltonian","score":0.9760000109672546},{"id":"https://openalex.org/keywords/quantum-verification","display_name":"quantum verification","score":0.3790000081062317}],"concepts":[{"id":"https://openalex.org/C114852677","wikidata":"https://www.wikidata.org/wiki/Q899044","display_name":"Fock space","level":2,"score":0.8597000241279602},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.6998999714851379},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6866000294685364},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6629999876022339},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.642799973487854},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41100001335144043},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38850000500679016},{"id":"https://openalex.org/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.38199999928474426},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38029998540878296},{"id":"https://openalex.org/C12891224","wikidata":"https://www.wikidata.org/wiki/Q678317","display_name":"Fock state","level":3,"score":0.35569998621940613},{"id":"https://openalex.org/C2777041388","wikidata":"https://www.wikidata.org/wiki/Q6664297","display_name":"Local cohomology","level":3,"score":0.30790001153945923},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2809000015258789},{"id":"https://openalex.org/C93067474","wikidata":"https://www.wikidata.org/wiki/Q1493952","display_name":"Sheaf cohomology","level":4,"score":0.26409998536109924},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25589999556541443},{"id":"https://openalex.org/C74196217","wikidata":"https://www.wikidata.org/wiki/Q1095535","display_name":"\u010cech cohomology","level":5,"score":0.25189998745918274},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.00694","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.00694","pdf_url":"https://arxiv.org/pdf/2609.00694","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.00694","doi":"https://doi.org/10.48550/arxiv.2609.00694","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.00694","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.00694","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.00694","pdf_url":"https://arxiv.org/pdf/2609.00694","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7206214419.pdf","grobid_xml":"https://content.openalex.org/works/W7206214419.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1534752942","https://openalex.org/W2084019889","https://openalex.org/W2100827027","https://openalex.org/W2111891221","https://openalex.org/W2153979649","https://openalex.org/W3173190396","https://openalex.org/W4404312875","https://openalex.org/W4404356316","https://openalex.org/W4404848713","https://openalex.org/W7172542560","https://openalex.org/W7204958348"],"related_works":["https://openalex.org/W3173190396","https://openalex.org/W7204958348","https://openalex.org/W7223559702","https://openalex.org/W3217385125","https://openalex.org/W1668036065","https://openalex.org/W6949616824","https://openalex.org/W4404356316","https://openalex.org/W4415729156","https://openalex.org/W3177795258","https://openalex.org/W4394669898"],"abstract_inverted_index":{"Fermionic":[0],"cohomology":[1,14,29],"detects":[2],"zero-energy":[3,42],"states":[4,43],"of":[5,87,109],"supersymmetric":[6],"Hamiltonians.":[7],"Previous":[8],"work":[9],"showed":[10],"that":[11,53,65],"deciding":[12],"nonzero":[13],"in":[15,44,48,106,148],"an":[16,63,84,149],"input-specified":[17,150],"particle-number":[18,151],"sector":[19,46,112],"is":[20,57,62,81],"$\\mathrm{QMA}_1$-hard":[21],"and":[22,47,71,159],"belongs":[23],"to":[24,73],"$\\mathrm{QMA}$.":[25],"We":[26,51,141],"study":[27],"total":[28],"on":[30,75,132],"the":[31,76,146],"unrestricted":[32],"full":[33,77],"Fock":[34,78],"space,":[35],"where":[36],"a":[37,107,127,161],"NO":[38],"instance":[39],"must":[40],"exclude":[41],"every":[45,133],"their":[49],"superpositions.":[50],"prove":[52,143],"this":[54,114],"global":[55],"problem":[56,147],"$\\mathrm{QMA}_1$-complete.":[58],"The":[59,97],"input":[60],"differential":[61],"operator":[64],"raises":[66],"fermion":[67,105],"number":[68],"by":[69,103],"one":[70,104],"squares":[72],"zero":[74],"space.":[79],"It":[80],"given":[82],"as":[83],"exact":[85,123],"list":[86],"local":[88],"fermionic":[89],"monomials,":[90],"each":[91,100],"involving":[92],"at":[93,119],"most":[94],"$41$":[95],"modes.":[96,110],"reduction":[98],"encodes":[99],"data":[101],"site":[102],"block":[108],"Every":[111],"violating":[113],"occupation":[115],"rule":[116],"has":[117],"energy":[118],"least":[120],"one.":[121],"An":[122],"quantum":[124],"verifier":[125],"accepts":[126],"suitable":[128],"witness":[129],"with":[130,138],"certainty":[131],"YES":[134],"instance,":[135],"establishing":[136],"containment":[137],"perfect":[139],"completeness.":[140],"also":[142],"$\\mathrm{QMA}_1$-completeness":[144],"for":[145],"sector.":[152],"Its":[153],"hard":[154],"instances":[155],"use":[156],"$30$-mode":[157],"terms":[158],"admit":[160],"one-dimensional":[162],"block-chain":[163],"realization.":[164]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-03T00:00:00"}
