{"id":"14.2.2.a","row":5,"stored":{"file":"master_catalog.json","row":5,"construction":null,"columns_sha256":null},"parameters":{"n":14,"k":2,"d":2,"N":5,"r":3,"level":3},"gate":{"string":"0+1","human":"T0\u00b7T1","monomials":[[0],[1]],"sk_key":[[0],[1]],"sk_fingerprint":"68f83724f5668f5b","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[2],[3],[4],[2,3,4],[0,2,3],[0,2,4],[0,3,4],[1,2,3],[1,2,4],[1,3,4],[0,1,2],[0,1,3],[0,1,4],[0,1,2,3,4]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,10],"A_d":7,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1]],"CZ":[]},"rotation_powers":[[0,7],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[7,7],[8,7],[9,7],[10,7],[11,7],[12,7],[13,7]]},"metrics":{"gamma":2.807354922057604,"gamma_t":2.807354922057604,"gamma_rho":2.807354922057604,"gamma_claim":2.807354922057604,"gamma_t_claim":2.807354922057604,"gamma_rho_claim":2.807354922057604,"v_ex":2,"rate":0.14285714285714285,"t_count":2,"poly_degree":1,"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-row020-two-group","N":5,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at cae4982, outputs/factory_catalogue_l3.csv row 20","provenance":"two-group l=3 n=5 k=2 s_total=2 s_O=1 s_S=1","notes":"earlier publication: the k = 2 member of the Bravyi-Haah [[3k+8,k,2]] family (arXiv:2606.28518, App. F.3a)"}]},"references":[{"key":"bravyi2012magic","short":"Bravyi & Haah (2012)","full":"S. Bravyi and J. Haah, \"Magic-state distillation with low overhead,\" Phys. Rev. A 86, 052329 (2012).","url":"https://doi.org/10.1103/PhysRevA.86.052329","date":"2012-11-27"}]}