{"id":"20.3.2.c","row":18,"stored":{"file":"master_catalog.json","row":18,"construction":null,"columns_sha256":null},"parameters":{"n":20,"k":3,"d":2,"N":6,"r":3,"level":3},"gate":{"string":"0+1+2","human":"T0\u00b7T1\u00b7T2","monomials":[[0],[1],[2]],"sk_key":[[0],[1],[2]],"sk_fingerprint":"b0744d1878b2f54b","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,3,4],[0,1,3,5],[0,1,4],[0,1,5],[0,3],[0,3,4,5],[0,4,5],[1,3],[1,3,4,5],[1,4,5],[2,3],[2,3,4],[2,3,4,5],[2,3,5],[2,4],[2,4,5],[2,5],[3],[3,4,5],[4,5]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,11],"A_d":22,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,1],[3,2],[4,2],[5,2]],"CZ":[[3,4],[3,5]]},"rotation_powers":[[0,7],[2,7],[4,7],[7,7],[10,7],[13,3],[16,3],[17,3]]},"metrics":{"gamma":2.736965594166206,"gamma_t":2.736965594166206,"gamma_rho":2.736965594166206,"gamma_claim":2.736965594166206,"gamma_t_claim":2.736965594166206,"gamma_rho_claim":2.736965594166206,"v_ex":3,"rate":0.15,"t_count":3,"poly_degree":1,"effective_width":3},"provenance":{"regimes":["borrowed-identity search: symmetry-free"],"discovery":"pre-existing","strongest_claim":"found by the symmetry-free, targeted-output borrowed-identity search of Singh, Gidney and Jones (arXiv:2606.28518; borrowed_identities/), which solves for the check couplings of a chosen output; a verified witness, not a maximum","sources":[{"regime":"borrowed-identity search: symmetry-free","file":"borrowed_identities/circuits/unified_l3.json","label":"af-0779","N":6,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at 4627014, outputs/all_factories.csv line 779","provenance":"unified search l=3, gluing blocks=1+1+1"}]},"references":[{"key":"nezami2022classification","short":"Nezami & Haah (2022)","full":"S. Nezami and J. Haah, \"Classification of small triorthogonal codes,\" Phys. Rev. A 106, 012437 (2022).","url":"https://doi.org/10.1103/PhysRevA.106.012437","date":"2022-07-28"}]}