{"id":"https://openalex.org/W7220389448","doi":"https://doi.org/10.48550/arxiv.2610.03705","title":"Unitary complexity in polynomial space","display_name":"Unitary complexity in polynomial space","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220389448","doi":"https://doi.org/10.48550/arxiv.2610.03705"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03705","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03705","pdf_url":"https://arxiv.org/pdf/2610.03705","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.03705","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036924443","display_name":"William Kretschmer","orcid":"https://orcid.org/0000-0002-7784-9817","observed_orcids":["https://orcid.org/0000-0002-7784-9817"]},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kretschmer, William","raw_affiliation_strings":["University of Texas at Austin "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas at Austin ","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020583189","display_name":"Ewin Tang","orcid":"https://orcid.org/0000-0002-7451-9687","observed_orcids":["https://orcid.org/0000-0002-7451-9687"]},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tang, Ewin","raw_affiliation_strings":["Princeton University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"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":0.9384999871253967,"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":0.9384999871253967,"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":0.0203000009059906,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.01889999955892563,"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/oracle-separation","display_name":"oracle separation","score":0.8259999752044678},{"id":"https://openalex.org/keywords/quantum-circuit-synthesis","display_name":"quantum circuit synthesis","score":0.35600000619888306}],"concepts":[{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.8366000056266785},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5702999830245972},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5602999925613403},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47119998931884766},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44940000772476196},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.44449999928474426},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42640000581741333},{"id":"https://openalex.org/C92043244","wikidata":"https://www.wikidata.org/wiki/Q7269023","display_name":"Quantum complexity theory","level":4,"score":0.41830000281333923},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.3894999921321869},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.38909998536109924},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.37929999828338623},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36399999260902405},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.36250001192092896},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.31630000472068787},{"id":"https://openalex.org/C188313703","wikidata":"https://www.wikidata.org/wiki/Q1972470","display_name":"Unitary operator","level":3,"score":0.3084000051021576},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C2776013622","wikidata":"https://www.wikidata.org/wiki/Q2103021","display_name":"Polynomial hierarchy","level":3,"score":0.28519999980926514},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2815000116825104},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.26080000400543213},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.257999986410141}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03705","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03705","pdf_url":"https://arxiv.org/pdf/2610.03705","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.2610.03705","doi":"https://doi.org/10.48550/arxiv.2610.03705","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03705","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":"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.03705","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03705","pdf_url":"https://arxiv.org/pdf/2610.03705","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":[{"id":"https://openalex.org/F4320309634","display_name":"Adolph C. and Mary Sprague Miller Institute for Basic Research in Science, University of California Berkeley","ror":null},{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220389448.pdf","grobid_xml":"https://content.openalex.org/works/W7220389448.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7220684430","https://openalex.org/W7171786125","https://openalex.org/W3195430465","https://openalex.org/W4306177282","https://openalex.org/W2342682362","https://openalex.org/W1988900139","https://openalex.org/W4399512732","https://openalex.org/W7133059614","https://openalex.org/W1539401159","https://openalex.org/W7160933269"],"abstract_inverted_index":{"We":[0,44,143,182],"show":[1,169,197],"that":[2,26,59,93,147,152,162,170,198,224,232],"if":[3],"quantum":[4,27],"commitments":[5,28],"exist,":[6],"then":[7],"either":[8,64],"there":[9],"is":[10],"no":[11],"polynomial-time":[12],"solution":[13],"to":[14,70,140,215,236],"the":[15,111,118,128,160,163,205],"unitary":[16,61,119,208,237],"synthesis":[17],"problem,":[18],"or":[19,74],"$\\mathsf{BPP}":[20],"\\neq":[21,108],"\\mathsf{NEXP}$.":[22],"Thus,":[23],"showing":[24],"unconditionally":[25],"exist":[29],"would":[30,99],"require":[31],"answering":[32],"at":[33],"least":[34],"one":[35],"of":[36,52,179,207],"two":[37,164],"longstanding":[38],"open":[39],"questions":[40],"in":[41,62,135,188,218],"complexity":[42,120],"theory.":[43],"prove":[45],"our":[46,190],"main":[47],"result":[48,231],"as":[49,106,176,204],"a":[50,53,230],"consequence":[51],"more":[54],"general":[55],"lemma,":[56],"which":[57,189],"shows":[58],"every":[60],"$\\mathsf{unitaryPSPACE}$":[63,98,199,225],"cannot":[65,157],"be":[66,76,174,213],"synthesized":[67,77],"efficiently":[68,78],"relative":[69,235],"any":[71],"classical":[72,102],"oracle,":[73],"can":[75,173,212,226],"with":[79,132],"an":[80,201],"oracle":[81,95],"for":[82,117],"$\\mathsf{NEXP}$":[83],"search":[84],"problems.":[85],"Our":[86,125],"lemma":[87],"has":[88,200],"other":[89,186],"noteworthy":[90],"consequences,":[91],"including":[92],"certain":[94],"separations":[96],"involving":[97],"imply":[100],"breakthrough":[101],"lower":[103],"bounds":[104],"such":[105],"$\\mathsf{NC}":[107],"\\mathsf{NP}$.":[109],"Along":[110],"way,":[112],"we":[113,156,168,196,222],"propose":[114],"new":[115],"definitions":[116,133,165,172,191],"classes":[121],"$\\mathsf{unitaryP}$":[122],"and":[123,138,150],"$\\mathsf{unitaryPSPACE}$.":[124],"changes":[126],"address":[127],"biggest":[129],"conceptual":[130],"issues":[131],"suggested":[134],"prior":[136],"work,":[137],"lead":[139],"elegant":[141],"proofs.":[142],"study":[144],"both":[145,171],"implementations":[146,151],"erase":[148,228],"garbage":[149],"allow":[153],"it,":[154],"because":[155],"rule":[158],"out":[159],"possibility":[161],"differ.":[166],"Nevertheless,":[167],"viewed":[175],"special":[177],"cases":[178],"each":[180],"other.":[181],"also":[183],"showcase":[184],"many":[185],"ways":[187],"are":[192],"robust.":[193],"For":[194],"example,":[195],"equivalent":[202],"characterization":[203],"set":[206],"transformations":[209],"whose":[210],"entries":[211],"computed":[214],"arbitrary":[216],"precision":[217],"polynomial":[219],"space.":[220],"Consequently,":[221],"deduce":[223],"generically":[227],"garbage,":[229],"provably":[233],"fails":[234],"oracles.":[238]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-06T00:00:00"}
