{"id":"https://openalex.org/W7204958348","doi":"https://doi.org/10.48550/arxiv.2608.29333","title":"Zero-Energy Problems for Supersymmetric Hamiltonians on a Chain Are $\\mathrm{QMA}_1$-Complete","display_name":"Zero-Energy Problems for Supersymmetric Hamiltonians on a Chain Are $\\mathrm{QMA}_1$-Complete","publication_year":2026,"publication_date":"2026-08-29","ids":{"openalex":"https://openalex.org/W7204958348","doi":"https://doi.org/10.48550/arxiv.2608.29333"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29333","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29333","pdf_url":"https://arxiv.org/pdf/2608.29333","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/2608.29333","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148894313","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/A5148894313"],"corresponding_institution_ids":["https://openalex.org/I60134161"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.9096999764442444,"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":0.9096999764442444,"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":0.04129999876022339,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.009700000286102295,"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/one-dimensional-chains","display_name":"one-dimensional chains","score":0.7329999804496765},{"id":"https://openalex.org/keywords/quantum-satisfiability","display_name":"quantum satisfiability","score":0.8930000066757202},{"id":"https://openalex.org/keywords/supercharges","display_name":"supercharges","score":0.7559999823570251}],"concepts":[{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.7077999711036682},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6743000149726868},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5403000116348267},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5309000015258789},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.4966999888420105},{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.46790000796318054},{"id":"https://openalex.org/C53104380","wikidata":"https://www.wikidata.org/wiki/Q4327971","display_name":"Zero-point energy","level":2,"score":0.413100004196167},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4047999978065491},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.3968000113964081},{"id":"https://openalex.org/C116674579","wikidata":"https://www.wikidata.org/wiki/Q193442","display_name":"Supersymmetry","level":2,"score":0.3790999948978424},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.37770000100135803},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.375},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.35589998960494995},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3109000027179718},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.29269999265670776},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28130000829696655},{"id":"https://openalex.org/C174084160","wikidata":"https://www.wikidata.org/wiki/Q908049","display_name":"Bound state","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27079999446868896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2694000005722046},{"id":"https://openalex.org/C174038435","wikidata":"https://www.wikidata.org/wiki/Q232431","display_name":"Quantum number","level":2,"score":0.26919999718666077},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.26170000433921814},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.260699987411499},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29333","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29333","pdf_url":"https://arxiv.org/pdf/2608.29333","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.2608.29333","doi":"https://doi.org/10.48550/arxiv.2608.29333","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29333","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:2608.29333","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29333","pdf_url":"https://arxiv.org/pdf/2608.29333","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204958348.pdf","grobid_xml":"https://content.openalex.org/works/W7204958348.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1534752942","https://openalex.org/W1549606184","https://openalex.org/W2019692968","https://openalex.org/W2033430067","https://openalex.org/W2072381205","https://openalex.org/W2078081035","https://openalex.org/W2084019889","https://openalex.org/W2100827027","https://openalex.org/W2111891221","https://openalex.org/W2153979649","https://openalex.org/W3173190396","https://openalex.org/W4404356316"],"related_works":["https://openalex.org/W7206214419","https://openalex.org/W7097395705","https://openalex.org/W7100118397","https://openalex.org/W7095715034","https://openalex.org/W2034763770","https://openalex.org/W3177795258","https://openalex.org/W7223559702","https://openalex.org/W3099163724","https://openalex.org/W3106202032","https://openalex.org/W4409527659"],"abstract_inverted_index":{"We":[0,21],"determine":[1],"the":[2,38,42,46,52,55,64],"computational":[3],"complexity":[4],"of":[5,31],"deciding":[6],"whether":[7],"a":[8,13,17,73],"supersymmetric":[9],"quantum":[10,70],"system":[11],"on":[12,51,72],"one-dimensional":[14],"chain":[15,74],"has":[16],"zero-energy":[18],"ground":[19],"state.":[20],"prove":[22],"$\\mathrm{QMA}_1$-completeness":[23],"for":[24,86],"two":[25],"input":[26],"models,":[27],"formulated":[28],"in":[29,54,95],"terms":[30,44],"Hermitian":[32,39],"and":[33,45,79],"nilpotent":[34,56],"supercharges,":[35],"respectively.":[36],"In":[37],"model,":[40,57],"both":[41],"supercharge":[43,101],"Hamiltonian":[47],"have":[48],"bounded":[49],"range":[50],"chain;":[53],"this":[58],"geometric":[59],"restriction":[60],"applies":[61],"only":[62],"to":[63],"Hamiltonian.":[65],"The":[66],"hardness":[67],"reduction":[68],"from":[69],"satisfiability":[71],"preserves":[75],"exact":[76],"zero":[77],"energy":[78],"gives":[80],"an":[81],"inverse-polynomial":[82],"ground-energy":[83],"lower":[84],"bound":[85],"negative":[87],"instances.":[88],"A":[89],"common":[90],"verification":[91],"method":[92],"establishes":[93],"membership":[94],"$\\mathrm{QMA}_1$":[96],"while":[97],"allowing":[98],"cancellations":[99],"between":[100],"terms.":[102]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-02T00:00:00"}