{"id":"72.3.6.a","row":513,"stored":{"file":"master_catalog.json","row":513,"construction":null,"columns_sha256":null},"parameters":{"n":72,"k":3,"d":6,"N":18,"r":15,"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":[[9],[5,9],[4,9],[4,5,9],[3,9],[3,5,9],[3,4,9],[3,4,5,9],[10],[8,10],[7,10],[7,8,10],[6,10],[6,8,10],[6,7,10],[6,7,8,10],[11],[0,2,3,4,5,8,11],[0,4,5,7,11],[2,3,7,8,11],[0,1,2,5,6,11],[1,3,4,6,8,11],[1,2,4,6,7,11],[0,1,3,5,6,7,8,11],[12],[1,3,5,8,12],[0,1,2,3,7,12],[0,2,5,7,8,12],[0,1,3,4,5,6,12],[0,4,6,8,12],[2,4,5,6,7,12],[1,2,3,4,6,7,8,12],[13],[0,3,4,8,13],[0,1,5,7,13],[1,3,4,5,7,8,13],[1,2,3,5,6,13],[0,1,2,4,5,6,8,13],[0,2,3,6,7,13],[2,4,6,7,8,13],[14],[0,1,2,4,8,14],[1,2,3,4,5,7,14],[0,3,5,7,8,14],[2,3,4,6,14],[0,1,3,6,8,14],[1,5,6,7,14],[0,2,4,5,6,7,8,14],[15],[0,1,4,5,8,15],[2,3,5,7,15],[0,1,2,3,4,7,8,15],[0,2,4,6,15],[1,2,5,6,8,15],[0,3,4,5,6,7,15],[1,3,6,7,8,15],[16],[1,2,3,8,16],[0,2,3,4,7,16],[0,1,4,7,8,16],[1,4,5,6,16],[2,3,4,5,6,8,16],[0,1,2,3,5,6,7,16],[0,5,6,7,8,16],[17],[2,5,8,17],[1,4,7,17],[1,2,4,5,7,8,17],[0,3,6,17],[0,2,3,5,6,8,17],[0,1,3,4,6,7,17],[0,1,2,3,4,5,6,7,8,17]]},"distance":{"d":6,"is_exact":true,"upper":6,"witness":[3,6,8,11,40,43],"A_d":37632,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,2],[1,2],[2,2]],"CZ":[[0,1],[0,2],[1,2]]},"rotation_powers":[[16,3],[17,3],[22,3],[23,3],[24,3],[27,3],[28,3],[31,3],[32,3],[34,3],[36,3],[38,3],[40,3],[42,3],[45,3],[47,3],[50,3],[51,3],[54,3],[55,3],[60,3],[61,3],[62,3],[63,3],[64,3],[67,3],[69,3],[70,3]]},"metrics":{"gamma":1.7737056144690833,"gamma_t":1.3008196747328498,"gamma_rho":2.0,"gamma_claim":1.7737056144690833,"gamma_t_claim":1.3008196747328498,"gamma_rho_claim":2.0,"v_ex":2,"rate":0.041666666666666664,"t_count":7,"poly_degree":3,"effective_width":3},"provenance":{"regimes":["Gong et al.: F8 codes concatenated with 8T->CCZ"],"discovery":"pre-existing","strongest_claim":"a concatenated protocol of Gong, Pattison, Rall and Wills (arXiv:2608.09727): an F8 code fed by copies of the 8T->CCZ protocol, rebuilt from the paper's construction and written as one circuit on 18 wires; a verified witness, not a maximum","sources":[{"regime":"Gong et al.: F8 codes concatenated with 8T->CCZ","file":"literature_imports/ccz72_d6/factories.json","label":"GPRW-72T-CCZ","N":18,"d":6,"d_is_exact":true,"origin":"A. Gong, C. A. Pattison, P. Rall, and A. Wills, \"Magic State Distillation via Codes over Binary Extension Fields,\" arXiv:2608.09727 (2026)","provenance":"(8T -> CCZ) * (9CCZ -> CCZ) of Table 7: the F8 code of Construction 4.5, Eq. (49), binarised in the self-dual normal basis of Eq. (46), each of its nine input CCZ states made by its own 8T -> CCZ, written as one circuit with the nine inner checks as wires 9..17","notes":"A_6 = 37632. The paper states 10^{4.58} p^6 (Table 7). Its Eq. (189) with its Table 5 and the 8T -> CCZ error weights (12, 12, 4) p^2 gives exactly 37632, which is 10^4.576. Clifford correction: Z on each output and CZ on each pair, since transversal U_7 over F_8 deposits (-1)^[u != 0] on the logical qudit u"}]},"references":[{"key":"gong2026magic","short":"Gong et al. (2026)","full":"A. Gong, C. A. Pattison, P. Rall, and A. Wills, \"Magic State Distillation via Codes over Binary Extension Fields,\" arXiv:2608.09727 (2026).","url":"https://arxiv.org/abs/2608.09727","date":"2026-08-10"}]}