{"id":"18.4.2.b","row":13,"stored":{"file":"master_catalog.json","row":13,"construction":null,"columns_sha256":null},"parameters":{"n":18,"k":4,"d":2,"N":6,"r":2,"level":3},"gate":{"string":"01+23","human":"CS01\u00b7CS23","monomials":[[0,1],[2,3]],"sk_key":[[0,1],[2,3]],"sk_fingerprint":"4c6da188308a72a6","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[4],[5],[3,4],[3,5],[0,2,4],[0,2,5],[0,4,5],[1,2,4],[1,2,5],[1,4,5],[2,3,4],[2,3,5],[2,4,5],[3,4,5],[0,1,2,4],[0,1,2,5],[0,1,4,5],[2,3,4,5]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,2],"A_d":45,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,1],[2,3],[3,1],[4,2],[5,2]],"CZ":[[2,4],[2,5],[4,5]]},"rotation_powers":null},"metrics":{"gamma":2.1699250014423126,"gamma_t":1.5849625007211563,"gamma_rho":3.1699250014423126,"gamma_claim":2.1699250014423126,"gamma_t_claim":1.5849625007211563,"gamma_rho_claim":3.1699250014423126,"v_ex":2,"rate":0.2222222222222222,"t_count":6,"poly_degree":2,"effective_width":4},"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-row085-symmetry-free","N":6,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at cae4982, outputs/factory_catalogue_l3.csv row 85","provenance":"symmetry-free l=3 parts=2+2 checks=2","notes":"earlier publication: Campbell and Howard (2017), Example IV.3: 18 T states for two CS gates with output error 45 eps^2"}]},"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"}]}