{"id":"https://openalex.org/W7221097666","doi":"https://doi.org/10.48550/arxiv.2610.12098","title":"Nearly Optimal T-Count for Symmetry-Based Quantum State Purification","display_name":"Nearly Optimal T-Count for Symmetry-Based Quantum State Purification","publication_year":2026,"publication_date":"2026-10-08","ids":{"openalex":"https://openalex.org/W7221097666","doi":"https://doi.org/10.48550/arxiv.2610.12098"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.12098","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12098","pdf_url":"https://arxiv.org/pdf/2610.12098","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/2610.12098","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158051999","display_name":"Jialiang Tang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tang, Jialiang","raw_affiliation_strings":["School of Computer Science and Technology , University of Chinese Academy of Sciences , Beijing 100049 , China","State Key Lab of Processors , Institute of Computing Technology , Chinese Academy of Sciences , Beijing 100190 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology , University of Chinese Academy of Sciences , Beijing 100049 , China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"State Key Lab of Processors , Institute of Computing Technology , Chinese Academy of Sciences , Beijing 100190 , China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153487756","display_name":"Junhong Nie","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Nie, Junhong","raw_affiliation_strings":["Shandong University , Jinan 250100 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shandong University , Jinan 250100 , China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101275673","display_name":"Keming He","orcid":"https://orcid.org/0009-0008-3745-1637","observed_orcids":["https://orcid.org/0009-0008-3745-1637"]},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I4405261251","display_name":"The Hong Kong University of Science and Technology (Guangzhou)","ror":"https://ror.org/050h0vm43","country_code":"CN","type":"education","lineage":["https://openalex.org/I4405261251"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"He, Keming","raw_affiliation_strings":["Thrust of Artificial Intelligence , Information Hub , The Hong Kong University of Science and Technology (Guangzhou) , Guangdong 511453 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Thrust of Artificial Intelligence , Information Hub , The Hong Kong University of Science and Technology (Guangzhou) , Guangdong 511453 , China","institution_ids":["https://openalex.org/I200769079","https://openalex.org/I4405261251"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100327887","display_name":"Xin Wang","orcid":"https://orcid.org/0000-0002-0641-3186","observed_orcids":["https://orcid.org/0000-0002-0641-3186"]},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I4405261251","display_name":"The Hong Kong University of Science and Technology (Guangzhou)","ror":"https://ror.org/050h0vm43","country_code":"CN","type":"education","lineage":["https://openalex.org/I4405261251"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"Wang, Xin","raw_affiliation_strings":["Thrust of Artificial Intelligence , Information Hub , The Hong Kong University of Science and Technology (Guangzhou) , Guangdong 511453 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Thrust of Artificial Intelligence , Information Hub , The Hong Kong University of Science and Technology (Guangzhou) , Guangdong 511453 , China","institution_ids":["https://openalex.org/I200769079","https://openalex.org/I4405261251"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5158134625","display_name":"Xiaoming Sun","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sun, Xiaoming","raw_affiliation_strings":["School of Computer Science and Technology , University of Chinese Academy of Sciences , Beijing 100049 , China","State Key Lab of Processors , Institute of Computing Technology , Chinese Academy of Sciences , Beijing 100190 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology , University of Chinese Academy of Sciences , Beijing 100049 , China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"State Key Lab of Processors , Institute of Computing Technology , Chinese Academy of Sciences , Beijing 100190 , China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"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":0.9984999895095825,"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":0.9984999895095825,"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":0.0012000000569969416,"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/T11804","display_name":"Quantum many-body systems","score":9.999999747378752e-05,"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-state-purification","display_name":"quantum state purification","score":0.9990000128746033},{"id":"https://openalex.org/keywords/t-count","display_name":"T-count","score":0.9049999713897705},{"id":"https://openalex.org/keywords/clifford-t-circuits","display_name":"Clifford+T circuits","score":0.8420000076293945},{"id":"https://openalex.org/keywords/block-encoding","display_name":"block encoding","score":0.6919999718666077},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.7239999771118164},{"id":"https://openalex.org/keywords/noisy-quantum-states","display_name":"noisy quantum states","score":0.49300000071525574},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"quantum error correction","score":0.5199999809265137}],"concepts":[{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5907999873161316},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.5565000176429749},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5260999798774719},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.5169000029563904},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49889999628067017},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.48179998993873596},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.4814999997615814},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.4507000148296356},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.444599986076355},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.42879998683929443},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.428600013256073},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.4230000078678131},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.3650999963283539},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3538999855518341},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35350000858306885},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.3508000075817108},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.34439998865127563},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3287000060081482},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.328000009059906},{"id":"https://openalex.org/C19271316","wikidata":"https://www.wikidata.org/wiki/Q7092353","display_name":"One-way quantum computer","level":5,"score":0.3262999951839447},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.3249000012874603},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.30300000309944153},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.302700012922287},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.2937000095844269},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2906999886035919},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.2906000018119812},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.2768999934196472},{"id":"https://openalex.org/C5320026","wikidata":"https://www.wikidata.org/wiki/Q2122216","display_name":"Quantum information science","level":4,"score":0.2612000107765198},{"id":"https://openalex.org/C191608238","wikidata":"https://www.wikidata.org/wiki/Q5249552","display_name":"Decoherence-free subspaces","level":5,"score":0.257999986410141},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C69497775","wikidata":"https://www.wikidata.org/wiki/Q7269025","display_name":"Quantum convolutional code","level":5,"score":0.2547999918460846},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.25200000405311584},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.12098","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12098","pdf_url":"https://arxiv.org/pdf/2610.12098","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.2610.12098","doi":"https://doi.org/10.48550/arxiv.2610.12098","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.12098","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:2610.12098","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12098","pdf_url":"https://arxiv.org/pdf/2610.12098","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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221097666.pdf","grobid_xml":"https://content.openalex.org/works/W7221097666.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W132789698","https://openalex.org/W1800240078","https://openalex.org/W1839785972","https://openalex.org/W1866699241","https://openalex.org/W1979130667","https://openalex.org/W2006596905","https://openalex.org/W2028319489","https://openalex.org/W2030867075","https://openalex.org/W2058690713","https://openalex.org/W2058701696","https://openalex.org/W2079294297","https://openalex.org/W2114279687","https://openalex.org/W2535738892","https://openalex.org/W2770585428","https://openalex.org/W2781738013","https://openalex.org/W2795600567","https://openalex.org/W2805612073","https://openalex.org/W2806997737","https://openalex.org/W2934956484","https://openalex.org/W2937696121","https://openalex.org/W2985334210","https://openalex.org/W3138564161","https://openalex.org/W3207755657","https://openalex.org/W4286588240","https://openalex.org/W4330335310","https://openalex.org/W4392662757","https://openalex.org/W4396745888","https://openalex.org/W4403794933","https://openalex.org/W4405183524","https://openalex.org/W4406665043","https://openalex.org/W4409875055","https://openalex.org/W4414790518","https://openalex.org/W4415014697","https://openalex.org/W4416069235","https://openalex.org/W4416424508","https://openalex.org/W6891862721","https://openalex.org/W6910414955","https://openalex.org/W7083693219","https://openalex.org/W7126059187","https://openalex.org/W7127650660","https://openalex.org/W7154700099","https://openalex.org/W7162118427","https://openalex.org/W7162572422","https://openalex.org/W7167887606","https://openalex.org/W7215732663","https://openalex.org/W7220733266"],"related_works":["https://openalex.org/W4409875055","https://openalex.org/W4394868336","https://openalex.org/W2985334210","https://openalex.org/W4251678731","https://openalex.org/W7127650660","https://openalex.org/W6891862721","https://openalex.org/W4406665043","https://openalex.org/W2902431979","https://openalex.org/W7204236949","https://openalex.org/W2080803895"],"abstract_inverted_index":{"Protecting":[0],"quantum":[1,9,12,28,158],"information":[2],"from":[3],"noise":[4],"is":[5],"essential":[6],"for":[7,153],"reliable":[8],"computation":[10],"and":[11,44,95,126,147],"memories.":[13],"Quantum":[14],"state":[15,29,34,159],"purification":[16,56],"addresses":[17],"this":[18],"challenge":[19],"by":[20],"processing":[21],"multiple":[22],"noisy":[23],"copies":[24,60,146],"of":[25,35,61,107,139,145],"an":[26,32],"unknown":[27],"to":[30,52],"produce":[31],"output":[33],"higher":[36],"fidelity.":[37],"Here":[38],"we":[39,65,101],"establish":[40,134],"nearly":[41,136],"tight":[42],"upper":[43],"lower":[45],"bounds":[46],"on":[47],"the":[48,54,72,86,135,143,149],"non-Clifford":[49,140],"resources":[50],"required":[51],"implement":[53],"symmetric-projection":[55],"protocol.":[57],"For":[58],"$n$":[59],"a":[62,67,109],"$d$-dimensional":[63],"system,":[64],"construct":[66],"Clifford+T":[68,105],"circuit":[69],"that":[70,103],"block-encodes":[71],"symmetric":[73],"projector":[74],"with":[75,112,142],"operator-norm":[76],"error":[77,113],"at":[78,116],"most":[79],"$\u03b5$":[80],"using":[81,98],"$\\widetilde{O}(n)$":[82],"T":[83,119],"gates,":[84,120],"where":[85],"tilde-$O$":[87],"notation":[88],"suppresses":[89],"polylogarithmic":[90],"factors":[91],"in":[92,157],"$n$,":[93],"$d$,":[94],"$1/\u03b5$.":[96],"Conversely,":[97],"stabilizer":[99,128],"nullity,":[100],"prove":[102],"any":[104],"implementation":[106],"such":[108],"block":[110],"encoding":[111],"$\u03b5<\\frac{1}{2}\\sqrt{1-1/n}$":[114],"requires":[115],"least":[117],"$2n-2$":[118],"even":[121],"allowing":[122],"arbitrary":[123],"positive":[124],"normalization":[125],"clean":[127],"ancillas.":[129],"Taken":[130],"together,":[131],"these":[132],"results":[133],"optimal":[137],"scaling":[138],"cost":[141],"number":[144],"uncover":[148],"fundamental":[150],"resource":[151],"requirements":[152],"coherent":[154],"symmetry":[155],"projection":[156],"purification.":[160]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-10T00:00:00"}