{"id":"https://openalex.org/W7225155290","doi":"https://doi.org/10.48550/arxiv.2611.02819","title":"unitaryQIP = unitaryPSPACE","display_name":"unitaryQIP = unitaryPSPACE","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225155290","doi":"https://doi.org/10.48550/arxiv.2611.02819"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2611.02819","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.02819","pdf_url":"https://arxiv.org/pdf/2611.02819","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/2611.02819","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5094178982","display_name":"Entong He","orcid":"https://orcid.org/0009-0001-3911-0966","observed_orcids":["https://orcid.org/0009-0001-3911-0966"]},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"He, Entong","raw_affiliation_strings":["QICI Quantum Information and Computation Initiative , School of Computing and Data Science , The University of Hong Kong , Pokfulam Road , Hong Kong SAR , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"QICI Quantum Information and Computation Initiative , School of Computing and Data Science , The University of Hong Kong , Pokfulam Road , Hong Kong SAR , China","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093356446","display_name":"Fengning Ou","orcid":"https://orcid.org/0009-0008-0871-3095","observed_orcids":["https://orcid.org/0009-0008-0871-3095"]},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ou, Fengning","raw_affiliation_strings":["State Key Laboratory for Novel Software Technology , Nanjing University , Nanjing 210023 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory for Novel Software Technology , Nanjing University , Nanjing 210023 , China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102557723","display_name":"Mingnan Zhao","orcid":"https://orcid.org/0009-0006-9623-9703","observed_orcids":["https://orcid.org/0009-0006-9623-9703"]},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhao, Mingnan","raw_affiliation_strings":["State Key Laboratory for Novel Software Technology , Nanjing University , Nanjing 210023 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory for Novel Software Technology , Nanjing University , Nanjing 210023 , China","institution_ids":["https://openalex.org/I881766915"]}]}],"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":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":0.9574999809265137,"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":0.9574999809265137,"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":0.024399999529123306,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.009600000455975533,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/interactive-proof-systems","display_name":"interactive proofs","score":0.8949999809265137},{"id":"https://openalex.org/keywords/polynomial-spaces","display_name":"polynomial spaces","score":0.6320000290870667},{"id":"https://openalex.org/keywords/quantum-interactive-proofs","display_name":"quantum interactive proofs","score":0.5870000123977661}],"concepts":[{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.8343999981880188},{"id":"https://openalex.org/C159718280","wikidata":"https://www.wikidata.org/wiki/Q5526353","display_name":"Gas meter prover","level":3,"score":0.7504000067710876},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6843000054359436},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6202999949455261},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.555400013923645},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5403000116348267},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.44679999351501465},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4456999897956848},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.41449999809265137},{"id":"https://openalex.org/C188313703","wikidata":"https://www.wikidata.org/wiki/Q1972470","display_name":"Unitary operator","level":3,"score":0.40639999508857727},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.38999998569488525},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3779999911785126},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.350600004196167},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.33090001344680786},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.3285999894142151},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3131999969482422},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.303600013256073},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.3005000054836273},{"id":"https://openalex.org/C92043244","wikidata":"https://www.wikidata.org/wiki/Q7269023","display_name":"Quantum complexity theory","level":4,"score":0.29679998755455017},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2881999909877777},{"id":"https://openalex.org/C99072794","wikidata":"https://www.wikidata.org/wiki/Q1500617","display_name":"Unitary group","level":3,"score":0.2770000100135803},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2611.02819","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.02819","pdf_url":"https://arxiv.org/pdf/2611.02819","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.2611.02819","doi":"https://doi.org/10.48550/arxiv.2611.02819","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.02819","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:2611.02819","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.02819","pdf_url":"https://arxiv.org/pdf/2611.02819","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":[{"id":"https://openalex.org/G1573799692","display_name":null,"funder_award_id":"B26023","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G1668631657","display_name":null,"funder_award_id":"2026300376","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G1997119393","display_name":null,"funder_award_id":"2021ZD0302901","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2659216395","display_name":null,"funder_award_id":"62332009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2948017901","display_name":null,"funder_award_id":"JYB2025XDXM118","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G4647107926","display_name":null,"funder_award_id":"BK20243060","funder_id":"https://openalex.org/F4320324852","funder_display_name":"Nanjing University"},{"id":"https://openalex.org/G5414997189","display_name":null,"funder_award_id":"BK20243060","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G5528670684","display_name":null,"funder_award_id":"12347104","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6712651544","display_name":null,"funder_award_id":"B26023","funder_id":"https://openalex.org/F4320336698","funder_display_name":"Overseas Expertise Introduction Center for Discipline Innovation of Food Nutrition and Human Health (111 Center)"},{"id":"https://openalex.org/G7347053913","display_name":null,"funder_award_id":"2021ZD0302901","funder_id":"https://openalex.org/F4320329860","funder_display_name":"National Science and Technology Major Project"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321106","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324852","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760"},{"id":"https://openalex.org/F4320329860","display_name":"National Science and Technology Major Project","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null},{"id":"https://openalex.org/F4320336698","display_name":"Overseas Expertise Introduction Center for Discipline Innovation of Food Nutrition and Human Health (111 Center)","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225155290.pdf","grobid_xml":"https://content.openalex.org/works/W7225155290.grobid-xml"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W171105080","https://openalex.org/W1506342804","https://openalex.org/W1624621931","https://openalex.org/W1964089073","https://openalex.org/W1985671429","https://openalex.org/W1993661095","https://openalex.org/W2028406173","https://openalex.org/W2033216491","https://openalex.org/W2040792108","https://openalex.org/W2060887031","https://openalex.org/W2066229005","https://openalex.org/W2080505327","https://openalex.org/W2081444194","https://openalex.org/W2084019889","https://openalex.org/W2084040475","https://openalex.org/W2086187371","https://openalex.org/W2100061495","https://openalex.org/W2104590612","https://openalex.org/W2107411554","https://openalex.org/W2109741106","https://openalex.org/W2119964170","https://openalex.org/W2121981260","https://openalex.org/W2134984950","https://openalex.org/W2193371463","https://openalex.org/W2197788506","https://openalex.org/W2295995314","https://openalex.org/W2476440251","https://openalex.org/W2535738892","https://openalex.org/W2804172638","https://openalex.org/W2805612073","https://openalex.org/W2951680627","https://openalex.org/W3091983754","https://openalex.org/W3138196689","https://openalex.org/W3195430465","https://openalex.org/W4211106290","https://openalex.org/W4211192810","https://openalex.org/W4213068077","https://openalex.org/W4221161984","https://openalex.org/W4229706427","https://openalex.org/W4297793372","https://openalex.org/W4298425892","https://openalex.org/W4307479171","https://openalex.org/W4376639597","https://openalex.org/W4381797999","https://openalex.org/W4386875125","https://openalex.org/W4390097871","https://openalex.org/W4390098448","https://openalex.org/W4390575965","https://openalex.org/W4404364971","https://openalex.org/W4411319991","https://openalex.org/W4414922337","https://openalex.org/W4415257487","https://openalex.org/W4417071261","https://openalex.org/W6929703915","https://openalex.org/W6947820376","https://openalex.org/W7119219142","https://openalex.org/W7128611745","https://openalex.org/W7220389448","https://openalex.org/W7220964343"],"related_works":["https://openalex.org/W3195430465","https://openalex.org/W7220389448","https://openalex.org/W7171786125","https://openalex.org/W7220684430","https://openalex.org/W4390097871","https://openalex.org/W7133059614","https://openalex.org/W7202090422","https://openalex.org/W7211975734","https://openalex.org/W4399512732","https://openalex.org/W4416050137"],"abstract_inverted_index":{"Unitary":[0],"synthesis":[1,126,161],"complexity":[2,18,38],"studies":[3],"the":[4,47,64,110,116,133,145,148,159,187,195,206,222,229,240],"computational":[5],"cost":[6],"of":[7,73,144,228,242],"applying":[8],"a":[9,70,121,141,181,235],"target":[10,134],"unitary":[11,41,48,135,160],"to":[12,113,140,158,218,238],"an":[13,104],"unknown":[14],"quantum":[15],"state,":[16],"extending":[17],"theory":[19],"beyond":[20],"its":[21],"traditional":[22],"focus":[23],"on":[24,136,153],"problems":[25],"with":[26,180],"classical":[27],"inputs":[28],"and":[29,32,44,54,67,80,85,88,93,128,164,169,201,231],"outputs.":[30],"Rosenthal":[31],"Yuen":[33],"(ITCS":[34],"2022)":[35],"introduced":[36],"two":[37],"classes":[39],"for":[40,46,120,213],"synthesis:":[42],"$\\mathsf{unitaryQIP}$":[43],"$\\mathsf{unitaryPSPACE}$":[45,172,214],"families":[49,173],"implementable":[50],"via":[51,194],"interactive":[52],"proofs":[53],"in":[55,124,177],"polynomial":[56,178],"space,":[57],"respectively.":[58],"In":[59],"this":[60],"work,":[61],"we":[62,102,151,208,232],"prove":[63,98],"equality":[65],"$\\mathsf{unitaryQIP}=\\mathsf{unitaryPSPACE}$":[66],"thereby":[68],"establish":[69],"unitary-complexity":[71],"analogue":[72],"$\\mathsf{QIP}":[74],"=":[75],"\\mathsf{PSPACE}$":[76],"(Jain,":[77],"Ji,":[78],"Upadhyay,":[79],"Watrous,":[81],"J.":[82],"ACM":[83],"2011)":[84],"$\\mathsf{stateQIP}=\\mathsf{statePSPACE}$":[86],"(Rosenthal":[87,200],"Yuen,":[89,94,129,202],"ITCS":[90,203],"2022;":[91],"Metger":[92],"FOCS":[95,130],"2023).":[96],"To":[97],"$\\mathsf{unitaryQIP}":[99],"\\subseteq":[100,197],"\\mathsf{unitaryPSPACE}$,":[101],"use":[103],"acceptance":[105],"rigidity":[106],"lemma":[107],"derived":[108],"from":[109],"soundness":[111],"condition":[112],"show":[114,170,209],"that":[115,171,210],"polynomial-space":[117,142],"prover":[118],"constructed":[119],"fixed":[122],"input":[123],"state":[125],"(Metger":[127],"2023)":[131],"implements":[132],"every":[137],"input,":[138,230],"leading":[139],"simulation":[143],"protocol.":[146],"For":[147],"reverse":[149],"inclusion,":[150],"build":[152],"OpenAI's":[154],"recently":[155],"announced":[156],"solution":[157],"problem":[162],"(Aaronson":[163],"Kuperberg,":[165],"Theory":[166],"Comput.":[167],"2007),":[168],"can":[174,215],"be":[175,216],"synthesized":[176],"time":[179],"$\\mathsf{PSPACE}$":[182],"oracle.":[183],"We":[184],"then":[185],"implement":[186],"oracle":[188],"queries":[189],"using":[190],"auxiliary":[191],"states":[192],"prepared":[193],"$\\mathsf{statePSPACE}":[196],"\\mathsf{stateQIP}$":[198],"protocol":[199,212],"2022).":[204],"Beyond":[205],"equality,":[207],"our":[211],"parallelized":[217],"constant":[219],"rounds":[220],"when":[221],"verifier":[223],"receives":[224],"polynomially":[225],"many":[226],"copies":[227],"also":[233],"obtain":[234],"complexity-theoretic":[236],"barrier":[237],"proving":[239],"existence":[241],"$\\mathsf{EFI}$":[243],"pairs.":[244]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-11-04T00:00:00"}