{"id":"https://openalex.org/W7220964343","doi":"https://doi.org/10.48550/arxiv.2610.08714","title":"Quantum Algorithms for Multivariable Polynomial Transformations: From Efficient Synthesis to Quantum Channel Transformations","display_name":"Quantum Algorithms for Multivariable Polynomial Transformations: From Efficient Synthesis to Quantum Channel Transformations","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220964343","doi":"https://doi.org/10.48550/arxiv.2610.08714"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.08714","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08714","pdf_url":"https://arxiv.org/pdf/2610.08714","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/2610.08714","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157683318","display_name":"Zheyu Shen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shen, Zheyu","raw_affiliation_strings":["Center on Frontiers of Computing Studies , School of Computer Science , Peking University , Beijing 100871 , China","School of Physics , Peking University , Beijing 100871 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center on Frontiers of Computing Studies , School of Computer Science , Peking University , Beijing 100871 , China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"School of Physics , Peking University , Beijing 100871 , China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157900067","display_name":"Yusen Wu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wu, Yusen","raw_affiliation_strings":["School of Artificial Intelligence , Beijing Normal University , Beijing 100875 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence , Beijing Normal University , Beijing 100875 , China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090412627","display_name":"Xiao Yuan","orcid":"https://orcid.org/0000-0003-0205-6545","observed_orcids":["https://orcid.org/0000-0003-0205-6545"]},"institutions":[{"id":"https://openalex.org/I187400657","display_name":"South China Normal University","ror":"https://ror.org/01kq0pv72","country_code":"CN","type":"education","lineage":["https://openalex.org/I187400657"]},{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan, Xiao","raw_affiliation_strings":["Center on Frontiers of Computing Studies , School of Computer Science , Peking University , Beijing 100871 , China","Kong Joint Laboratory of Quantum Matter , South China Normal University , Guangzhou 510006 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center on Frontiers of Computing Studies , School of Computer Science , Peking University , Beijing 100871 , China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"Kong Joint Laboratory of Quantum Matter , South China Normal University , Guangzhou 510006 , China","institution_ids":["https://openalex.org/I187400657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157979394","display_name":"Xiao-Ming Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Xiao-Ming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5157908211","display_name":"Yukun Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Zhang, Yukun","raw_affiliation_strings":["Center on Frontiers of Computing Studies , School of Computer Science , Peking University , Beijing 100871 , China","Mathematical Institute , University of Oxford , Woodstock Road , Oxford OX2 6GG , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center on Frontiers of Computing Studies , School of Computer Science , Peking University , Beijing 100871 , China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"Mathematical Institute , University of Oxford , Woodstock Road , Oxford OX2 6GG , United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"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":0.9990000128746033,"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":0.9990000128746033,"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":0.0006000000284984708,"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":0.0,"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/quantum-signal-processing","display_name":"quantum signal processing","score":0.6470000147819519},{"id":"https://openalex.org/keywords/noncommutative-polynomials","display_name":"noncommutative polynomials","score":0.7559999823570251},{"id":"https://openalex.org/keywords/kraus-operators","display_name":"Kraus operators","score":0.7250000238418579},{"id":"https://openalex.org/keywords/completely-positive-maps","display_name":"completely positive maps","score":0.859000027179718},{"id":"https://openalex.org/keywords/choi-matrix","display_name":"Choi matrix","score":0.640999972820282},{"id":"https://openalex.org/keywords/query-complexity","display_name":"query complexity","score":0.5260000228881836},{"id":"https://openalex.org/keywords/network-synthesis","display_name":"network synthesis","score":0.492000013589859}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6456000208854675},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.579800009727478},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.550599992275238},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5200999975204468},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4740999937057495},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.4675999879837036},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41920000314712524},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.4146000146865845},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.39969998598098755},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3741999864578247},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.3709999918937683},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.3474999964237213},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.34279999136924744},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.34060001373291016},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.34060001373291016},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.32989999651908875},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.32199999690055847},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.31859999895095825},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.3050000071525574},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.2937999963760376},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2874000072479248},{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.2782000005245209}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.08714","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08714","pdf_url":"https://arxiv.org/pdf/2610.08714","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.2610.08714","doi":"https://doi.org/10.48550/arxiv.2610.08714","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.08714","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:2610.08714","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08714","pdf_url":"https://arxiv.org/pdf/2610.08714","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/G1861222841","display_name":null,"funder_award_id":"62501060","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3124986","display_name":null,"funder_award_id":"U2330201","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4429991381","display_name":null,"funder_award_id":"U2330201","funder_id":"https://openalex.org/F4320336475","funder_display_name":"National Safety Academic Fund"},{"id":"https://openalex.org/G5899096921","display_name":null,"funder_award_id":"Z25110100810000","funder_id":"https://openalex.org/F4320335843","funder_display_name":"Beijing Science and Technology Planning Project"},{"id":"https://openalex.org/G6398213329","display_name":null,"funder_award_id":"62371050","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6869791763","display_name":null,"funder_award_id":"2023ZD0300200","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335843","display_name":"Beijing Science and Technology Planning Project","ror":null},{"id":"https://openalex.org/F4320336475","display_name":"National Safety Academic Fund","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220964343.pdf","grobid_xml":"https://content.openalex.org/works/W7220964343.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7167686733","https://openalex.org/W7214717492","https://openalex.org/W7220392607","https://openalex.org/W4403882867","https://openalex.org/W7212157395","https://openalex.org/W2971753965","https://openalex.org/W2573911918","https://openalex.org/W4388514747","https://openalex.org/W2805612073","https://openalex.org/W4280585166"],"abstract_inverted_index":{"Polynomial":[0],"transformations":[1,28,187],"are":[2],"basic":[3],"primitives":[4],"in":[5,96],"quantum":[6,8,155,199,216,220],"algorithms:":[7],"signal":[9],"processing":[10],"and":[11,67,78,218],"singular":[12],"value":[13],"transformation":[14],"compile":[15],"univariate":[16],"polynomials":[17,50],"into":[18],"circuits":[19],"with":[20,72,99],"query":[21,143],"complexity":[22],"essentially":[23],"set":[24],"by":[25,189],"degree.":[26],"Multivariable":[27],"of":[29,62,170],"noncommuting":[30],"matrices,":[31],"however,":[32],"lack":[33],"a":[34,40,58,63,85,110,119,124,206,212],"comparable":[35],"synthesis":[36,153],"theory.":[37],"We":[38],"develop":[39],"complete":[41,90,125],"constructive":[42],"theory":[43],"under":[44,81],"joint":[45],"block":[46],"access":[47,161],"for":[48,128,214],"all":[49],"contractive":[51,139,168],"on":[52,102,130],"the":[53,115,131,138,142],"prescribed":[54,132],"matrix":[55,146],"domain.":[56,133],"Given":[57,158],"compact":[59],"finite-state":[60],"description":[61],"degree-$D$":[64],"polynomial":[65,97,152,172],"$P$":[66,71],"$0<\u03c4<1$,":[68],"we":[69,163],"synthesize":[70,164],"$(1+\u03c4)$-optimal":[73],"normalization":[74],"using":[75],"$O(D/\\sqrt\u03c4)$":[76],"queries,":[77],"exactly":[79],"$D$":[80],"row-block":[82],"access,":[83],"matching":[84],"degree":[86],"lower":[87],"bound.":[88],"The":[89,104],"circuit":[91],"realization":[92,140],"is":[93,109],"classically":[94],"computable":[95],"time":[98],"polylogarithmic":[100],"dependence":[101],"accuracy.":[103],"key":[105],"to":[106,154,205],"our":[107,148],"construction":[108],"finite":[111,166],"algorithmic":[112],"Schur--Agler":[113],"theorem:":[114],"coefficient":[116],"recurrence":[117],"defines":[118],"polynomial-dimensional":[120],"continuation":[121],"space":[122],"supporting":[123],"semidefinite":[126],"certificate":[127,136],"contractivity":[129],"Factoring":[134],"this":[135],"yields":[137],"underlying":[141],"algorithm.":[144],"Beyond":[145],"transformations,":[147],"framework":[149],"lifts":[150],"multivariable":[151,209],"channel":[156],"transformations.":[157],"coherent":[159,180],"Kraus":[160,183],"$K=\\{K_a\\}_a$,":[162],"any":[165],"jointly":[167],"family":[169],"noncommutative":[171],"maps":[173],"$K\\mapsto\\{F_b(K)\\}_b$":[174],"as":[175,197,211],"completely":[176],"positive":[177],"operations,":[178],"allowing":[179],"interference":[181],"among":[182],"histories.":[184],"Furthermore,":[185],"channel-level":[186],"specified":[188],"causal":[190],"Choi":[191],"data":[192],"can":[193],"be":[194],"synthesized":[195],"explicitly":[196],"fixed-order":[198],"combs.":[200],"Collectively,":[201],"these":[202],"results":[203],"point":[204],"broader":[207],"program:":[208],"approximation":[210],"language":[213],"multi-operator":[215],"algorithms":[217],"higher-order":[219],"information":[221],"processing.":[222]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-09T00:00:00"}