{"id":"26.6.2.a","row":44,"stored":{"file":"master_catalog.json","row":44,"construction":null,"columns_sha256":null},"parameters":{"n":26,"k":6,"d":2,"N":9,"r":3,"level":3},"gate":{"string":"0+1+2+3+4+5","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5","monomials":[[0],[1],[2],[3],[4],[5]],"sk_key":[[0],[1],[2],[3],[4],[5]],"sk_fingerprint":"4d2289762630b30d","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[6],[7],[8],[6,7,8],[0,6,7],[0,6,8],[0,7,8],[1,6,7],[1,6,8],[1,7,8],[2,6,7],[2,6,8],[2,7,8],[3,6,7],[3,6,8],[3,7,8],[4,6,7],[4,6,8],[4,7,8],[5,6,7],[5,6,8],[5,7,8],[0,1,2,3,4,5,6],[0,1,2,3,4,5,7],[0,1,2,3,4,5,8],[0,1,2,3,4,5,6,7,8]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,22],"A_d":49,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,1],[5,1]],"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],[14,7],[15,7],[16,7],[17,7],[18,7],[19,7],[20,7],[21,7],[22,7],[23,7],[24,7],[25,7]]},"metrics":{"gamma":2.115477217419936,"gamma_t":2.115477217419936,"gamma_rho":2.115477217419936,"gamma_claim":2.115477217419936,"gamma_t_claim":2.115477217419936,"gamma_rho_claim":2.115477217419936,"v_ex":6,"rate":0.23076923076923078,"t_count":6,"poly_degree":1,"effective_width":6},"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-row150-two-group","N":9,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at cae4982, outputs/factory_catalogue_l3.csv row 150","provenance":"two-group l=3 n=9 k=6 s_total=2 s_O=5 s_S=1","notes":"earlier publication: the k = 6 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"}]}