{"id":"8.3.2.a","row":0,"stored":{"file":"master_catalog.json","row":0,"construction":null,"columns_sha256":null},"parameters":{"n":8,"k":3,"d":2,"N":4,"r":1,"level":3},"gate":{"string":"012","human":"CCZ012","monomials":[[0,1,2]],"sk_key":[[0,1,2]],"sk_fingerprint":"d0c21becf7c06e56","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[3],[0,3],[1,3],[2,3],[0,1,3],[0,2,3],[1,2,3],[0,1,2,3]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,1],"A_d":28,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,2],[1,2],[2,2]],"CZ":[[0,1],[0,2],[1,2]]},"rotation_powers":[[1,3],[2,3],[3,3],[7,3]]},"metrics":{"gamma":1.4150374992788437,"gamma_t":0.19264507794239583,"gamma_rho":2.0,"gamma_claim":1.4150374992788437,"gamma_t_claim":0.19264507794239583,"gamma_rho_claim":2.0,"v_ex":2,"rate":0.375,"t_count":7,"poly_degree":3,"effective_width":3},"provenance":{"regimes":["borrowed-identity search: two-group"],"discovery":"pre-existing","strongest_claim":"found by the two-group borrowed-identity search of Singh, Gidney and Jones (arXiv:2606.28518; borrowed_identities/): an identity circuit symmetric within its output and check blocks, with its output-only gates removed; a verified witness, not a maximum","sources":[{"regime":"borrowed-identity search: two-group","file":"borrowed_identities/circuits/circuits_l3.json","label":"l3-row049-two-group","N":4,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at cae4982, outputs/factory_catalogue_l3.csv row 49","provenance":"two-group l=3 n=4 k=3 s_total=1 s_O=1 s_S=1","notes":"earlier publication: the 8 T -> CCZ factory of Eastin (2013) and Jones (2013) (arXiv:2606.28518, malleable circuits)"}]},"references":[{"key":"bombin2007exact","short":"Bomb\u00edn & Martin-Delgado (2007)","full":"H. Bomb\u00edn and M. A. Martin-Delgado, \"Exact topological quantum order in D=3 and beyond: Branyons and brane-net condensates,\" Phys. Rev. B 75, 075103 (2007).","url":"https://doi.org/10.1103/PhysRevB.75.075103","date":"2007-02"}]}