{"id":"https://openalex.org/W7143522772","doi":"https://doi.org/10.48550/arxiv.2603.25831","title":"Theory of (Co)homological Invariants on Quantum LDPC Codes","display_name":"Theory of (Co)homological Invariants on Quantum LDPC Codes","publication_year":2026,"publication_date":"2026-03-26","ids":{"openalex":"https://openalex.org/W7143522772","doi":"https://doi.org/10.48550/arxiv.2603.25831"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.25831","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.25831","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":null,"license_id":null,"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.2603.25831","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130964946","display_name":"Zimu Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Zimu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102219775","display_name":"Yuguo Shao","orcid":"https://orcid.org/0009-0000-6832-7702"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shao, Yuguo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130980858","display_name":"Fuchuan Wei","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wei, Fuchuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022847585","display_name":"Dafa Li","orcid":"https://orcid.org/0000-0003-4405-7095"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Yiming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5130969166","display_name":"Zi-Wen Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Zi-Wen","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":0.7591000199317932,"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":0.7591000199317932,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.0575999990105629,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.018300000578165054,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sheaf","display_name":"Sheaf","score":0.7340999841690063},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4115000069141388},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4106000065803528},{"id":"https://openalex.org/keywords/coherent-sheaf","display_name":"Coherent sheaf","score":0.33219999074935913},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.33009999990463257},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.31450000405311584}],"concepts":[{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.7340999841690063},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6843000054359436},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.439300000667572},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4115000069141388},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4106000065803528},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.352400004863739},{"id":"https://openalex.org/C143161588","wikidata":"https://www.wikidata.org/wiki/Q906907","display_name":"Coherent sheaf","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.33009999990463257},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.30399999022483826},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.302700012922287},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2854999899864197},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2750000059604645},{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.25831","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.25831","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.25831","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.25831","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"With":[0],"recent":[1],"breakthroughs":[2],"in":[3,83,180,239,269],"the":[4,14,65,75,94,102,116,141,190,197,264],"construction":[5],"of":[6,16,19,50,67,98,105,137,143,160,174,196,222],"good":[7,12,132],"qLDPC":[8,133,258],"codes":[9,54,73,134,156,162,179,213,241,259],"and":[10,135,177,218,242,254,260,274],"nearly":[11],"qLTCs,":[13],"study":[15],"(co)homological":[17,194],"invariants":[18,45,195,207,238],"quantum":[20,270],"code":[21,77,216],"complexes,":[22],"which":[23,113],"fundamentally":[24],"underlie":[25],"their":[26],"logical":[27,69,209],"operations,":[28],"has":[29],"become":[30],"evidently":[31],"important.":[32],"In":[33,248],"this":[34,90],"work,":[35],"we":[36,92,120,166,251],"establish":[37],"a":[38,47,80,168,185,202,233],"systematic":[39],"framework":[40,104,204],"for":[41,205,236,266],"mathematically":[42],"analyzing":[43],"these":[44],"across":[46],"broad":[48],"spectrum":[49],"constructions,":[51],"from":[52,71,184,211],"HGP":[53,72,161,176,187,240],"to":[55,74,214,245],"sheaf":[56,76,86,106,155,178,246],"codes,":[57],"by":[58,153,225],"synthesizing":[59],"advanced":[60],"math":[61],"tools.":[62],"We":[63],"generalize":[64],"notion":[66],"canonical":[68],"representatives":[70],"setting,":[78],"resolving":[79],"long-standing":[81],"challenge":[82],"explicitly":[84],"characterizing":[85],"codewords.":[87],"Building":[88],"on":[89,130,227],"foundation,":[91],"present":[93],"first":[95],"comprehensive":[96],"computation":[97],"cup":[99,125],"products":[100,126],"within":[101],"intricate":[103],"codes.":[107,247],"Given":[108],"Artin's":[109],"primitive":[110],"root":[111],"conjecture":[112],"holds":[114],"under":[115],"generalized":[117],"Riemann":[118],"hypothesis,":[119],"prove":[121],"that":[122,170],"$\\tilde\u0398(N)$":[123],"independent":[124],"can":[127],"be":[128],"supported":[129],"almost":[131],"qLTCs":[136],"length":[138],"N,":[139],"opening":[140],"possibility":[142],"achieving":[144],"linearly":[145],"many":[146],"parallel,":[147],"nontrivial,":[148],"constant-depth":[149],"multi-controlled-Z":[150],"gates.":[151],"Moreover,":[152],"interpreting":[154],"as":[157],"covering":[158],"spaces":[159],"via":[163],"graph":[164],"lifts,":[165],"propose":[167],"scheme":[169],"inductively":[171],"generates":[172],"families":[173],"both":[175],"an":[181],"interlaced":[182],"fashion":[183],"constant-size":[186],"code.":[188,199],"Notably,":[189],"induction":[191],"preserves":[192],"all":[193],"initial":[198],"This":[200],"provides":[201,232],"general":[203],"lifting":[206],"or":[208],"gates":[210],"small":[212,228],"infinite":[215],"families,":[217],"enables":[219],"efficient":[220],"verification":[221],"such":[223],"features":[224],"checking":[226],"instances.":[229],"Our":[230],"theory":[231],"substantive":[234],"methodology":[235],"studying":[237],"extends":[243],"it":[244],"doing":[249],"so,":[250],"reveal":[252],"deep":[253],"unexpected":[255],"connections":[256],"between":[257],"math,":[261],"thereby":[262],"laying":[263],"groundwork":[265],"future":[267],"advances":[268],"coding,":[271],"fault":[272],"tolerance,":[273],"physics.":[275]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-31T00:00:00"}
