{"id":"61.3.3.a","row":423,"stored":{"file":"master_catalog.json","row":423,"construction":null,"columns_sha256":null},"parameters":{"n":61,"k":3,"d":3,"N":16,"r":13,"level":3},"gate":{"string":"0+1+2","human":"T0\u00b7T1\u00b7T2","monomials":[[0],[1],[2]],"sk_key":[[0],[1],[2]],"sk_fingerprint":"b0744d1878b2f54b","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,3],[0,3,4],[0,3,4,5],[0,3,5],[0,4],[0,4,5],[0,5],[1,7],[1,7,8],[1,7,8,9],[1,7,9],[1,8],[1,8,9],[1,9],[2,11],[2,11,12,13,14],[2,11,12,15],[2,11,13,15],[2,11,14,15],[2,11,15],[2,12,13,14],[2,12,15],[2,13,15],[2,14,15],[2,15],[3,4,5,6],[3,4,6],[3,5,6],[3,6],[4,5,6],[4,6],[5,6],[6],[7,8,9,10],[7,8,10],[7,9,10],[7,10],[8,9,10],[8,10],[9,10],[10],[11,12],[11,12,13],[11,12,13,14,15],[11,12,13,15],[11,12,14],[11,12,14,15],[11,13],[11,13,14],[11,13,14,15],[11,14],[12],[12,13],[12,13,14,15],[12,13,15],[12,14],[12,14,15],[13],[13,14],[13,14,15],[14]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,4],"A_d":145,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,3]],"CZ":[[2,11]]},"rotation_powers":[[0,7],[1,7],[4,7],[7,7],[8,7],[11,7],[14,7],[15,5],[20,5],[25,3],[27,3],[29,3],[31,3],[33,3],[35,3],[37,3],[39,3],[47,3],[48,3],[50,3],[57,3],[58,3],[60,3]]},"metrics":{"gamma":2.741878646885593,"gamma_t":2.741878646885593,"gamma_rho":2.741878646885593,"gamma_claim":2.741878646885593,"gamma_t_claim":2.741878646885593,"gamma_rho_claim":2.741878646885593,"v_ex":3,"rate":0.04918032786885246,"t_count":3,"poly_degree":1,"effective_width":3},"provenance":{"regimes":["AI search"],"discovery":"AI search","strongest_claim":"found by an AI search campaign; a verified witness, not a maximum","sources":[{"regime":"AI search","file":"/private/tmp/claude-501/-Users-shubhamjain-Documents-Claude-remote-magic-states-AI/25937cc1-0367-40c1-acc9-031067b831d4/scratchpad/msai_for_merge.jsonl","label":"msAI:8cc2da86ecbbf537","N":16,"d":3,"d_is_exact":true,"origin":"magic-states-AI/master_catalogue/master_catalogue.jsonl","provenance":"magic-states-AI/master_catalogue/master_catalogue.jsonl","notes":"gamma_campaign"}]},"references":[{"key":"shi2024triorthogonal","short":"Shi et al. (2024)","full":"M. Shi, H. Lu, J.-L. Kim, and P. Sol\u00e9, \"Triorthogonal codes and self-dual codes,\" Quantum Inf. Process. 23, 280 (2024).","url":"https://doi.org/10.1007/s11128-024-04485-9","date":"2024-07-20"}]}