{"id":"https://openalex.org/W7224787457","doi":"https://doi.org/10.48550/arxiv.2610.40235","title":"Three-dimensional QCA that are not stably circuits","display_name":"Three-dimensional QCA that are not stably circuits","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224787457","doi":"https://doi.org/10.48550/arxiv.2610.40235"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.40235","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.40235","pdf_url":"https://arxiv.org/pdf/2610.40235","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/2610.40235","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160238936","display_name":"Bowen Yang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yang, Bowen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5160238936"],"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/T11804","display_name":"Quantum many-body systems","score":0.33009999990463257,"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"}},"topics":[{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.33009999990463257,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.2442999929189682,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.10159999877214432,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-cellular-automata","display_name":"quantum cellular automata","score":0.9020000100135803},{"id":"https://openalex.org/keywords/stabilizer-circuits","display_name":"stabilizer circuits","score":0.609000027179718},{"id":"https://openalex.org/keywords/finitely-generated-groups","display_name":"finitely generated groups","score":0.6710000038146973},{"id":"https://openalex.org/keywords/quantum-dimension","display_name":"quantum dimension","score":0.6880000233650208},{"id":"https://openalex.org/keywords/topological-quantum-computation","display_name":"topological quantum computation","score":0.4480000138282776},{"id":"https://openalex.org/keywords/translation-invariance","display_name":"translation invariance","score":0.503000020980835}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6051999926567078},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.597000002861023},{"id":"https://openalex.org/C68576872","wikidata":"https://www.wikidata.org/wiki/Q4893239","display_name":"Quantum cellular automaton","level":3,"score":0.5602999925613403},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.5228000283241272},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5163000226020813},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.5015000104904175},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4997999966144562},{"id":"https://openalex.org/C2777446375","wikidata":"https://www.wikidata.org/wiki/Q5528","display_name":"Anyon","level":4,"score":0.4674000144004822},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4668000042438507},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4593000113964081},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.444599986076355},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3912999927997589},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3806999921798706},{"id":"https://openalex.org/C44201097","wikidata":"https://www.wikidata.org/wiki/Q192089","display_name":"Magic square","level":2,"score":0.3776000142097473},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.3483999967575073},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.3479999899864197},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.3361000120639801},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3352999985218048},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.3215000033378601},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.31520000100135803},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.30869999527931213},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.296099990606308},{"id":"https://openalex.org/C100856211","wikidata":"https://www.wikidata.org/wiki/Q674689","display_name":"Clifford algebra","level":3,"score":0.295199990272522},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.2897999882698059},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2849999964237213},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.2578999996185303},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25279998779296875}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.40235","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.40235","pdf_url":"https://arxiv.org/pdf/2610.40235","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.2610.40235","doi":"https://doi.org/10.48550/arxiv.2610.40235","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.40235","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:2610.40235","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.40235","pdf_url":"https://arxiv.org/pdf/2610.40235","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224787457.pdf","grobid_xml":"https://content.openalex.org/works/W7224787457.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2903211734","https://openalex.org/W2953464237","https://openalex.org/W4400611313","https://openalex.org/W4408217280","https://openalex.org/W4292749510","https://openalex.org/W7171473860","https://openalex.org/W4415057887","https://openalex.org/W2980759728","https://openalex.org/W2056460639","https://openalex.org/W4413306539"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2],"the":[3,46,52,81,84,89],"three-dimensional":[4,55],"chiral":[5],"$\\Z_p$":[6],"Clifford":[7,47],"quantum":[8,24,86],"cellular":[9],"automata":[10],"of":[11,14,33,54,73,83,88],"Haah":[12],"and":[13,35,60],"Sun--Yang--Wang--Tantivasadakarn--Chen":[15],"are,":[16],"for":[17],"every":[18],"odd":[19],"prime":[20],"$p$,":[21],"not":[22,63],"finite-depth":[23],"circuits,":[25],"even":[26],"after":[27],"tensoring":[28],"with":[29,37],"arbitrary":[30],"ancillary":[31],"degrees":[32],"freedom":[34],"composing":[36],"translations.":[38],"Previously":[39],"such":[40],"statements":[41],"were":[42],"known":[43],"only":[44],"inside":[45],"category.":[48],"As":[49],"a":[50,70],"consequence,":[51],"group":[53],"QCA":[56],"modulo":[57,93],"stabilized":[58],"circuits":[59],"translations":[61],"is":[62,69],"finitely":[64],"generated.":[65],"The":[66],"key":[67],"ingredient":[68],"new":[71],"invariant":[72],"invertible":[74],"subalgebras,":[75],"which":[76],"we":[77],"conjecture":[78],"to":[79],"be":[80],"square":[82],"total":[85],"dimension":[87],"hosted":[90],"anyon":[91],"theory,":[92],"rational":[94],"squares.":[95]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-10-31T00:00:00"}
