{"id":"14.6.2.a","row":6,"stored":{"file":"master_catalog.json","row":6,"construction":null,"columns_sha256":null},"parameters":{"n":14,"k":6,"d":2,"N":7,"r":1,"level":3},"gate":{"string":"012+345","human":"CCZ012\u00b7CCZ345","monomials":[[0,1,2],[3,4,5]],"sk_key":[[0,1,2],[3,4,5]],"sk_fingerprint":"7c05f5a651b43d16","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[6],[4,6],[5,6],[0,3,6],[1,3,6],[2,3,6],[3,4,6],[3,5,6],[4,5,6],[0,1,3,6],[0,2,3,6],[1,2,3,6],[3,4,5,6],[0,1,2,3,6]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,1],"A_d":91,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,2],[1,2],[2,2],[3,3],[4,2],[5,2],[6,1]],"CZ":[[0,1],[0,2],[1,2],[3,4],[3,5],[3,6],[4,5]]},"rotation_powers":[[0,5],[1,7],[2,3],[3,3],[4,3],[5,3],[6,5],[12,3],[13,3]]},"metrics":{"gamma":1.222392421336448,"gamma_t":0.1069152039165119,"gamma_rho":1.8073549220576042,"gamma_claim":1.222392421336448,"gamma_t_claim":0.1069152039165119,"gamma_rho_claim":1.8073549220576042,"v_ex":4,"rate":0.42857142857142855,"t_count":13,"poly_degree":3,"effective_width":6},"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/circuits_l3.json","label":"l3-row147-symmetry-free","N":7,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at cae4982, outputs/factory_catalogue_l3.csv row 147","provenance":"symmetry-free l=3 parts=3+3 checks=1","notes":"earlier publication: Campbell and Howard (2017), Example IV.2: 14 T states for two CCZ gates, the N = 2 member of their 6N + 2 family (arXiv:2606.28518, two-group circuits, ref. [24])"}]},"references":[{"key":"campbell2017unified","short":"Campbell & Howard (2017)","full":"E. T. Campbell and M. Howard, \"Unified framework for magic state distillation and multiqubit gate synthesis with reduced resource cost,\" Phys. Rev. A 95, 022316 (2017).","url":"https://doi.org/10.1103/PhysRevA.95.022316","date":"2017-02-09"}]}