{"id":"120.3.4.a","row":715,"stored":{"file":"master_catalog.json","row":715,"construction":null,"columns_sha256":null},"parameters":{"n":120,"k":3,"d":4,"N":13,"r":10,"level":3},"gate":{"string":"01+02","human":"CS01\u00b7CS02","monomials":[[0,1],[0,2]],"sk_key":[[0,1],[0,2]],"sk_fingerprint":"0166aa5e251ed314","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[0,1,3],[0,1,4],[0,1,5],[0,1,6],[0,1,7],[0,1,8],[0,1,9],[0,1,3,10],[0,1,3,11],[0,1,3,12],[0,1,4,10],[0,1,4,11],[0,1,4,12],[0,1,5,10],[0,1,5,11],[0,1,5,12],[0,1,6,10],[0,1,6,11],[0,1,6,12],[0,1,7,10],[0,1,7,11],[0,1,7,12],[0,1,8,10],[0,1,8,11],[0,1,8,12],[0,1,9,10],[0,1,9,11],[0,1,9,12],[0,2,3,10,11],[0,2,3,10,12],[0,2,3,11,12],[0,2,4,10,11],[0,2,4,10,12],[0,2,4,11,12],[0,2,5,10,11],[0,2,5,10,12],[0,2,5,11,12],[0,2,6,10,11],[0,2,6,10,12],[0,2,6,11,12],[0,2,7,10,11],[0,2,7,10,12],[0,2,7,11,12],[0,2,8,10,11],[0,2,8,10,12],[0,2,8,11,12],[0,2,9,10,11],[0,2,9,10,12],[0,2,9,11,12],[0,2,3,10,11,12],[0,2,4,10,11,12],[0,2,5,10,11,12],[0,2,6,10,11,12],[0,2,7,10,11,12],[0,2,8,10,11,12],[0,2,9,10,11,12],[0,1,3,4,5,7,10],[0,1,3,4,5,7,11],[0,1,3,4,5,7,12],[0,1,4,5,6,8,10],[0,1,4,5,6,8,11],[0,1,4,5,6,8,12],[0,1,3,6,7,8,10],[0,1,3,6,7,8,11],[0,1,3,6,7,8,12],[0,1,3,4,6,9,10],[0,1,3,4,6,9,11],[0,1,3,4,6,9,12],[0,1,5,6,7,9,10],[0,1,5,6,7,9,11],[0,1,5,6,7,9,12],[0,1,3,5,8,9,10],[0,1,3,5,8,9,11],[0,1,3,5,8,9,12],[0,1,4,7,8,9,10],[0,1,4,7,8,9,11],[0,1,4,7,8,9,12],[2,3,4,5,7,10,11,12],[2,4,5,6,8,10,11,12],[2,3,6,7,8,10,11,12],[2,3,4,6,9,10,11,12],[2,5,6,7,9,10,11,12],[2,3,5,8,9,10,11,12],[2,4,7,8,9,10,11,12],[0,2,3,5,6,7,10],[0,2,3,5,6,7,11],[0,2,3,5,6,7,12],[0,2,3,4,5,8,10],[0,2,3,4,5,8,11],[0,2,3,4,5,8,12],[0,2,4,6,7,8,10],[0,2,4,6,7,8,11],[0,2,4,6,7,8,12],[0,2,4,5,6,9,10],[0,2,4,5,6,9,11],[0,2,4,5,6,9,12],[0,2,3,4,7,9,10],[0,2,3,4,7,9,11],[0,2,3,4,7,9,12],[0,2,3,6,8,9,10],[0,2,3,6,8,9,11],[0,2,3,6,8,9,12],[0,2,5,7,8,9,10],[0,2,5,7,8,9,11],[0,2,5,7,8,9,12],[1,3,5,6,7,10,11,12],[1,3,4,5,8,10,11,12],[1,4,6,7,8,10,11,12],[1,4,5,6,9,10,11,12],[1,3,4,7,9,10,11,12],[1,3,6,8,9,10,11,12],[1,5,7,8,9,10,11,12],[2,3,4,5,6,7,8,9],[1,3,4,5,6,7,8,9,10],[1,3,4,5,6,7,8,9,11],[1,3,4,5,6,7,8,9,12],[1,3,4,5,6,7,8,9,10,11],[1,3,4,5,6,7,8,9,10,12],[1,3,4,5,6,7,8,9,11,12],[2,3,4,5,6,7,8,9,10,11,12]]},"distance":{"d":4,"is_exact":true,"upper":4,"witness":[0,1,62,90],"A_d":7344,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,3],[1,1],[2,3],[10,2],[11,2],[12,2]],"CZ":[[0,1],[0,2],[0,10],[0,11],[0,12],[1,3],[1,4],[1,5],[1,6],[1,7],[1,8],[1,9],[2,3],[2,4],[2,5],[2,6],[2,7],[2,8],[2,9],[10,11],[10,12],[11,12]]},"rotation_powers":null},"metrics":{"gamma":2.6609640474436813,"gamma_t":2.4534452978042594,"gamma_rho":null,"gamma_claim":2.6609640474436813,"gamma_t_claim":2.4534452978042594,"gamma_rho_claim":null,"v_ex":null,"rate":0.025,"t_count":4,"poly_degree":2,"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":"master_catalog/AI results","label":"CS01.CS12","N":13,"d":4,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits/n120_k3_d4_tau4_C7_S3_it08.json"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CS01.CS12","N":13,"d":4,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits \u00b7 catalogue.jsonl:329"}]},"references":[{"key":"jain2026symmetry","short":"Jain et al. (2026)","full":"S. P. Jain, A. Wills, and S. Singh, \"Symmetry and AI-assisted discovery of magic-state factories,\" arXiv:2610.06535 (2026).","url":"https://arxiv.org/abs/2610.06535","date":"2026-10-05"}]}