{"id":"https://openalex.org/W7203488511","doi":"https://doi.org/10.48550/arxiv.2608.13491","title":"Strong unitary designs in optimal depth and space","display_name":"Strong unitary designs in optimal depth and space","publication_year":2026,"publication_date":"2026-08-13","ids":{"openalex":"https://openalex.org/W7203488511","doi":"https://doi.org/10.48550/arxiv.2608.13491"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2608.13491","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13491","pdf_url":"https://arxiv.org/pdf/2608.13491","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":"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/2608.13491","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093264930","display_name":"Teodor Parella-Dilm\u00e9","orcid":"https://orcid.org/0009-0000-7593-2417","observed_orcids":["https://orcid.org/0009-0000-7593-2417"]},"institutions":[{"id":"https://openalex.org/I179630473","display_name":"Institute of Photonic Sciences","ror":"https://ror.org/03g5ew477","country_code":"ES","type":"facility","lineage":["https://openalex.org/I179630473","https://openalex.org/I4210132884","https://openalex.org/I4387153040","https://openalex.org/I9617848"]},{"id":"https://openalex.org/I4210132884","display_name":"Barcelona Institute of Science and Technology","ror":"https://ror.org/03kpps236","country_code":"ES","type":"education","lineage":["https://openalex.org/I4210132884"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Parella-Dilm\u00e9, Teodor","raw_affiliation_strings":["ICFO -Institut de Ci\u00e8ncies Fot\u00f2niques , The Barcelona Institute of Science and Technology , Avinguda Carl Friedrich Gauss 3 , 08860 Castelldefels (Barcelona) , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ICFO -Institut de Ci\u00e8ncies Fot\u00f2niques , The Barcelona Institute of Science and Technology , Avinguda Carl Friedrich Gauss 3 , 08860 Castelldefels (Barcelona) , Spain","institution_ids":["https://openalex.org/I179630473","https://openalex.org/I4210132884"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5115457702","display_name":"J\u00falia Barber\u00e0-Rodr\u00edguez","orcid":"https://orcid.org/0009-0004-8445-3345","observed_orcids":["https://orcid.org/0009-0004-8445-3345"]},"institutions":[{"id":"https://openalex.org/I179630473","display_name":"Institute of Photonic Sciences","ror":"https://ror.org/03g5ew477","country_code":"ES","type":"facility","lineage":["https://openalex.org/I179630473","https://openalex.org/I4210132884","https://openalex.org/I4387153040","https://openalex.org/I9617848"]},{"id":"https://openalex.org/I4210132884","display_name":"Barcelona Institute of Science and Technology","ror":"https://ror.org/03kpps236","country_code":"ES","type":"education","lineage":["https://openalex.org/I4210132884"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Barber\u00e0-Rodr\u00edguez, J\u00falia","raw_affiliation_strings":["ICFO -Institut de Ci\u00e8ncies Fot\u00f2niques , The Barcelona Institute of Science and Technology , Avinguda Carl Friedrich Gauss 3 , 08860 Castelldefels (Barcelona) , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ICFO -Institut de Ci\u00e8ncies Fot\u00f2niques , The Barcelona Institute of Science and Technology , Avinguda Carl Friedrich Gauss 3 , 08860 Castelldefels (Barcelona) , Spain","institution_ids":["https://openalex.org/I179630473","https://openalex.org/I4210132884"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034539197","display_name":"Salvatore F. E. Oliviero","orcid":"https://orcid.org/0000-0003-3569-085X","observed_orcids":["https://orcid.org/0000-0003-3569-085X"]},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Oliviero, Salvatore F. E.","raw_affiliation_strings":["Dahlem Center for Complex Quantum Systems , Department of Physics , Freie Universit\u00e4t Berlin , Arnimallee 14 , 14195 Berlin , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dahlem Center for Complex Quantum Systems , Department of Physics , Freie Universit\u00e4t Berlin , Arnimallee 14 , 14195 Berlin , Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069155094","display_name":"Antonio Anna Mele","orcid":"https://orcid.org/0000-0002-1009-7331","observed_orcids":["https://orcid.org/0000-0002-1009-7331"]},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mele, Antonio A.","raw_affiliation_strings":["Dahlem Center for Complex Quantum Systems , Department of Physics , Freie Universit\u00e4t Berlin , Arnimallee 14 , 14195 Berlin , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dahlem Center for Complex Quantum Systems , Department of Physics , Freie Universit\u00e4t Berlin , Arnimallee 14 , 14195 Berlin , Germany","institution_ids":["https://openalex.org/I75951250"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"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":0.9868000149726868,"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":0.9868000149726868,"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":0.007000000216066837,"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":0.003599999938160181,"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/haar-random-unitaries","display_name":"Haar random unitaries","score":0.824999988079071},{"id":"https://openalex.org/keywords/quantum-scrambling","display_name":"quantum scrambling","score":0.6349999904632568},{"id":"https://openalex.org/keywords/quantum-circuit-depth","display_name":"quantum circuit depth","score":0.3230000138282776}],"concepts":[{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.762499988079071},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6169999837875366},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.590399980545044},{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.5224000215530396},{"id":"https://openalex.org/C99072794","wikidata":"https://www.wikidata.org/wiki/Q1500617","display_name":"Unitary group","level":3,"score":0.5027999877929688},{"id":"https://openalex.org/C182548165","wikidata":"https://www.wikidata.org/wiki/Q2261483","display_name":"Scrambling","level":2,"score":0.47519999742507935},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.4602000117301941},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.453900009393692},{"id":"https://openalex.org/C11902944","wikidata":"https://www.wikidata.org/wiki/Q5121662","display_name":"Circular ensemble","level":4,"score":0.42890000343322754},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.414900004863739},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3930000066757202},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.3714999854564667},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.3562999963760376},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3538999855518341},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.33719998598098755},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3334999978542328},{"id":"https://openalex.org/C188313703","wikidata":"https://www.wikidata.org/wiki/Q1972470","display_name":"Unitary operator","level":3,"score":0.32179999351501465},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.313400000333786},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.310699999332428},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.3003999888896942},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C179371143","wikidata":"https://www.wikidata.org/wiki/Q2495534","display_name":"Unitary transformation","level":3,"score":0.2928999960422516},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29010000824928284},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28459998965263367},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.28279998898506165},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.2705000042915344},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.27000001072883606},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.266400009393692},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.2615000009536743}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.13491","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13491","pdf_url":"https://arxiv.org/pdf/2608.13491","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.13491","doi":"https://doi.org/10.48550/arxiv.2608.13491","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.13491","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.13491","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13491","pdf_url":"https://arxiv.org/pdf/2608.13491","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1587758330","display_name":null,"funder_award_id":"SPP 2514","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G1688234926","display_name":null,"funder_award_id":"CRC-183","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G1908469581","display_name":null,"funder_award_id":"CEX2019-000910-S","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G2763573136","display_name":null,"funder_award_id":"CEX2019-000910-S","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4526231891","display_name":null,"funder_award_id":"MCIN / AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5080475149","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6482940084","display_name":null,"funder_award_id":"CEX2019-000910-S","funder_id":"https://openalex.org/F4320315803","funder_display_name":"Centres de Recerca de Catalunya"},{"id":"https://openalex.org/G7084143925","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8180681537","display_name":null,"funder_award_id":"CEX2019-000910","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320315803","display_name":"Centres de Recerca de Catalunya","ror":"https://ror.org/01bkbaq61"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321505","display_name":"Generalitat de Catalunya","ror":"https://ror.org/01bg62x04"},{"id":"https://openalex.org/F4320330828","display_name":"QuantERA","ror":null},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":"https://ror.org/003x0zc53"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203488511.pdf","grobid_xml":"https://content.openalex.org/works/W7203488511.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Unitary":[0],"designs":[1,29,91,179],"provide":[2],"finite-moment":[3],"approximations":[4],"to":[5,21,175],"Haar-random":[6],"unitaries,":[7],"with":[8,169],"wide-ranging":[9],"applications":[10],"across":[11],"physics":[12],"and":[13,18,64,83,109,152,172],"quantum":[14,25,45],"information,":[15],"from":[16,40],"scrambling":[17,73],"black-hole":[19],"dynamics":[20],"foundational":[22],"primitives":[23],"in":[24,54,95,118],"algorithms.":[26],"Strong":[27],"unitary":[28,51,90,116,178],"capture":[30],"a":[31,50,136],"more":[32],"demanding":[33],"operational":[34],"notion":[35],"of":[36,180],"approximation,":[37],"requiring":[38],"indistinguishability":[39],"Haar":[41],"randomness":[42],"even":[43],"for":[44,140],"algorithms":[46],"that":[47,72],"may":[48],"access":[49],"not":[52],"only":[53,99,126],"the":[55,69,76,100,127,141,147,161],"forward":[56],"direction,":[57],"but":[58],"also":[59],"through":[60],"its":[61],"inverse,":[62],"transpose,":[63],"complex":[65],"conjugate.":[66],"Motivated":[67],"by":[68],"physical":[70],"requirement":[71],"arise":[74],"within":[75],"system":[77,101,130],"itself,":[78],"Schuster,":[79],"Ma,":[80],"Lombardi,":[81],"Brand\u00e3o,":[82],"Huang":[84],"(arXiv:2509.26310)":[85],"left":[86],"open":[87],"whether":[88],"strong":[89,114,177],"can":[92],"be":[93],"generated":[94],"logarithmic":[96],"depth":[97,124],"using":[98,125],"qubits.":[102,131],"For":[103],"every":[104],"fixed":[105,182],"design":[106,171],"order":[107],"$k$":[108],"measurable-error":[110],"tolerance,":[111],"we":[112,167],"construct":[113],"approximate":[115],"$k$-designs":[117],"optimal":[119],"$\u0398(\\log":[120],"n)$":[121],"all-to-all":[122],"circuit":[123],"$n$":[128],"original":[129],"Our":[132],"new":[133],"ingredient":[134],"is":[135],"logarithmic-depth":[137],"Pauli-mixing":[138],"bound":[139,159],"perfect-matching":[142],"ensemble,":[143],"whose":[144],"layers":[145],"pair":[146],"qubits":[148],"uniformly":[149],"at":[150],"random":[151,155],"apply":[153],"independent":[154],"two-qubit":[156],"gates.":[157],"This":[158],"controls":[160],"mixed":[162],"forward-reverse":[163],"two-query":[164],"case,":[165],"which":[166],"combine":[168],"existing":[170],"gluing":[173],"results":[174],"obtain":[176],"arbitrary":[181],"order.":[183]},"counts_by_year":[],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2026-08-15T00:00:00"}