{"id":"12.2.2.a","row":1,"stored":{"file":"master_catalog.json","row":1,"construction":null,"columns_sha256":null},"parameters":{"n":12,"k":2,"d":2,"N":4,"r":2,"level":3},"gate":{"string":"01","human":"CS01","monomials":[[0,1]],"sk_key":[[0,1]],"sk_fingerprint":"f076b3dc759b1665","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[2],[3],[2,3],[0,2],[0,3],[1,2],[1,3],[0,2,3],[1,2,3],[0,1,2],[0,1,3],[0,1,2,3]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,3],"A_d":18,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1]],"CZ":[]},"rotation_powers":[[0,3],[1,3],[3,5],[5,5],[7,3],[8,3],[9,3],[10,3]]},"metrics":{"gamma":2.584962500721156,"gamma_t":2.0,"gamma_rho":3.5849625007211565,"gamma_claim":2.584962500721156,"gamma_t_claim":2.0,"gamma_rho_claim":3.5849625007211565,"v_ex":1,"rate":0.16666666666666666,"t_count":3,"poly_degree":2,"effective_width":2},"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-row019-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 19","provenance":"two-group l=3 n=4 k=2 s_total=1 s_O=1 s_S=1","notes":"earlier publication: the T-to-CS factory [[12,2,2]] of Webster, Quintavalle and Bartlett (arXiv:2606.28518, introduction, ref. [33])"}]},"references":[{"key":"webster2023transversal","short":"Webster et al. (2023)","full":"M. A. Webster, A. O. Quintavalle, and S. D. Bartlett, \"Transversal diagonal logical operators for stabiliser codes,\" New J. Phys. 25, 103018 (2023).","url":"https://doi.org/10.1088/1367-2630/acfc5f","date":"2023-10-01"}]}