{"id":"https://openalex.org/W7148332094","doi":"https://doi.org/10.48550/arxiv.2604.01197","title":"Learning and Generating Mixed States Prepared by Shallow Channel Circuits","display_name":"Learning and Generating Mixed States Prepared by Shallow Channel Circuits","publication_year":2026,"publication_date":"2026-04-01","ids":{"openalex":"https://openalex.org/W7148332094","doi":"https://doi.org/10.48550/arxiv.2604.01197"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.01197","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01197","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.01197","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132790905","display_name":"Fangjun Hu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hu, Fangjun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054278545","display_name":"Christian Kokail","orcid":"https://orcid.org/0000-0001-8024-4272"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kokail, Christian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086599456","display_name":"Milan Kornja\u010da","orcid":"https://orcid.org/0000-0003-3828-6377"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kornja\u010da, Milan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041307969","display_name":"Pedro L. S. Lopes","orcid":"https://orcid.org/0000-0003-3181-8369"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lopes, Pedro L. S.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013338763","display_name":"Weiyuan Gong","orcid":"https://orcid.org/0000-0002-6599-8110"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gong, Weiyuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057117506","display_name":"Sheng-Tao Wang","orcid":"https://orcid.org/0000-0003-1403-5901"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Sheng-Tao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132788942","display_name":"Xun Gao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gao, Xun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5080149221","display_name":"Stefan Ostermann","orcid":"https://orcid.org/0000-0002-9762-9010"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ostermann, Stefan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.8102999925613403,"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":0.8102999925613403,"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":0.1500999927520752,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.009499999694526196,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/overhead","display_name":"Overhead (engineering)","score":0.6011999845504761},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5533999800682068},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.5126000046730042},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.4828000068664551},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4657000005245209},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.4546999931335449},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.44760000705718994},{"id":"https://openalex.org/keywords/quantum-circuit","display_name":"Quantum circuit","score":0.4456999897956848},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4390000104904175}],"concepts":[{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.6011999845504761},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5533999800682068},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.5126000046730042},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.487199991941452},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.4828000068664551},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4657000005245209},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.4546999931335449},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.44760000705718994},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.4456999897956848},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4390000104904175},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43540000915527344},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4113999903202057},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35600000619888306},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.33340001106262207},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.328000009059906},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3271999955177307},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.31349998712539673},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.31349998712539673},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.31310001015663147},{"id":"https://openalex.org/C90702460","wikidata":"https://www.wikidata.org/wiki/Q1055112","display_name":"Circuit complexity","level":3,"score":0.30309998989105225},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C131017901","wikidata":"https://www.wikidata.org/wiki/Q170451","display_name":"Logic gate","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.26589998602867126},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.2619999945163727},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.25679999589920044}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.01197","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01197","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,"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":"doi:10.48550/arxiv.2604.01197","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01197","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Learning":[0],"quantum":[1,11,165],"states":[2,28,47],"from":[3,89],"measurement":[4,90],"data":[5],"is":[6,71,145],"a":[7,30,62,106,161,190],"central":[8],"problem":[9,22],"in":[10,37,48,82,116,128],"information":[12],"and":[13,122,139,152,195],"computational":[14],"complexity.":[15],"In":[16,173],"this":[17,83,114],"work,":[18],"we":[19,43],"study":[20],"the":[21,49,56,74,129,143,148,174],"of":[23,41,96,131,193],"learning":[24],"to":[25,55],"generate":[26],"mixed":[27,38,80,101],"on":[29,45,155,169],"finite-dimensional":[31],"lattice.":[32],"Motivated":[33],"by":[34],"recent":[35],"developments":[36],"state":[39,53,81,115],"phases":[40],"matter,":[42],"focus":[44],"arbitrary":[46],"trivial":[50,57,99],"phase.":[51],"A":[52],"belongs":[54],"phase":[58,100],"if":[59],"there":[60],"exists":[61],"shallow":[63,107,170],"preparation":[64,150],"channel":[65,109,171],"circuit":[66,110,137,151],"under":[67],"which":[68],"local":[69,108],"reversibility":[70],"preserved":[72],"throughout":[73],"preparation.":[75],"We":[76],"prove":[77],"that":[78,111],"any":[79],"class":[84],"can":[85],"be":[86],"efficiently":[87],"learned":[88],"access":[91],"alone.":[92],"Specifically,":[93],"given":[94,147],"copies":[95],"an":[97,181],"unknown":[98],"state,":[102],"our":[103,177],"algorithm":[104,183],"outputs":[105],"approximately":[112],"generates":[113],"trace":[117],"distance.":[118],"The":[119],"sample":[120],"complexity":[121],"runtime":[123],"are":[124],"polynomial":[125,191],"(or":[126,135],"quasi-polynomial)":[127],"number":[130],"qubits,":[132],"assuming":[133],"constant":[134],"polylogarithmic)":[136],"depth":[138],"gate":[140],"locality.":[141],"Importantly,":[142],"learner":[144],"not":[146],"original":[149],"relies":[153],"only":[154,189],"its":[156],"existence.":[157],"Our":[158],"results":[159],"provide":[160],"structural":[162],"foundation":[163],"for":[164,184],"generative":[166],"models":[167,187],"based":[168],"circuits.":[172],"classical":[175,185],"limit,":[176],"framework":[178],"also":[179],"inspires":[180],"efficient":[182],"diffusion":[186],"using":[188],"overhead":[192],"training":[194],"generation.":[196]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-04-03T00:00:00"}