{"id":"189.1.7.a","row":822,"stored":{"file":"master_catalog.json","row":822,"construction":null,"columns_sha256":null},"parameters":{"n":189,"k":1,"d":7,"N":50,"r":49,"level":3},"gate":{"string":"0","human":"T0","monomials":[[0]],"sk_key":[[0]],"sk_fingerprint":"bc179efd84e614ba","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,2,3,4,6,7,8,10,11,13,14,15,19,20],[0,2,3,4,5,7,8,9,11,12,14,15,16,20,21],[0,3,4,5,6,8,9,10,12,13,15,16,17,21,22],[0,4,5,6,7,9,10,11,13,14,16,17,18,22,23],[0,1,2,3,4,5,12,13,17,18,20,23],[0,1,5,7,8,10,11,15,18,20,21],[0,2,6,8,9,11,12,16,19,21,22],[0,3,7,9,10,12,13,17,20,22,23],[0,1,2,3,6,7,15,18,19,20,21,23],[0,1,6,10,11,13,14,15,16,21,22],[0,2,7,11,12,14,15,16,17,22,23],[0,1,2,4,6,7,10,11,12,14,16,17,18,19,20,23],[0,1,4,5,6,10,12,14,17,18,21],[0,2,5,6,7,11,13,15,18,19,22],[0,3,6,7,8,12,14,16,19,20,23],[0,1,2,3,6,9,10,11,14,17,19,21],[0,2,3,4,7,10,11,12,15,18,20,22],[0,3,4,5,8,11,12,13,16,19,21,23],[0,1,2,3,5,7,8,9,10,11,12,15,17,19,22],[0,2,3,4,6,8,9,10,11,12,13,16,18,20,23],[0,1,2,5,6,8,9,12,15,17,20,21],[0,2,3,6,7,9,10,13,16,18,21,22],[0,3,4,7,8,10,11,14,17,19,22,23],[0,1,2,3,5,6,7,9,10,12,13,14,18,19,23],[0,1],[0,2],[0,3],[0,4],[0,5],[0,6],[0,7],[0,8],[0,9],[0,10],[0,11],[0,12],[0,13],[0,14],[0,15],[0,16],[0,17],[0,18],[0,19],[0,20],[0,21],[0,22],[0,23],[0,1,2,3,4,6,7,8,10,11,13,14,15,19,20,49],[0,2,3,4,5,7,8,9,11,12,14,15,16,20,21,49],[0,3,4,5,6,8,9,10,12,13,15,16,17,21,22,49],[0,4,5,6,7,9,10,11,13,14,16,17,18,22,23,49],[0,1,2,3,4,5,12,13,17,18,20,23,49],[0,1,5,7,8,10,11,15,18,20,21,49],[0,2,6,8,9,11,12,16,19,21,22,49],[0,3,7,9,10,12,13,17,20,22,23,49],[0,1,2,3,6,7,15,18,19,20,21,23,49],[0,1,6,10,11,13,14,15,16,21,22,49],[0,2,7,11,12,14,15,16,17,22,23,49],[0,1,2,4,6,7,10,11,12,14,16,17,18,19,20,23,49],[0,1,4,5,6,10,12,14,17,18,21,49],[0,2,5,6,7,11,13,15,18,19,22,49],[0,3,6,7,8,12,14,16,19,20,23,49],[0,1,2,3,6,9,10,11,14,17,19,21,49],[0,2,3,4,7,10,11,12,15,18,20,22,49],[0,3,4,5,8,11,12,13,16,19,21,23,49],[0,1,2,3,5,7,8,9,10,11,12,15,17,19,22,49],[0,2,3,4,6,8,9,10,11,12,13,16,18,20,23,49],[0,1,2,5,6,8,9,12,15,17,20,21,49],[0,2,3,6,7,9,10,13,16,18,21,22,49],[0,3,4,7,8,10,11,14,17,19,22,23,49],[0,1,2,3,5,6,7,9,10,12,13,14,18,19,23,49],[0,1,49],[0,2,49],[0,3,49],[0,4,49],[0,5,49],[0,6,49],[0,7,49],[0,8,49],[0,9,49],[0,10,49],[0,11,49],[0,12,49],[0,13,49],[0,14,49],[0,15,49],[0,16,49],[0,17,49],[0,18,49],[0,19,49],[0,20,49],[0,21,49],[0,22,49],[0,23,49],[0,24,25,29,30,31,33,49],[0,25,26,30,31,32,34,49],[0,24,25,26,27,29,30,32,49],[0,25,26,27,28,30,31,33,49],[0,26,27,28,29,31,32,34,49],[0,24,25,27,28,31,32,49],[0,25,26,28,29,32,33,49],[0,26,27,29,30,33,34,49],[0,24,25,27,28,29,33,34,49],[0,24,26,28,31,33,34,49],[0,24,27,30,31,32,33,34,49],[0,24,28,29,30,32,34,49],[0,24,49],[0,25,49],[0,26,49],[0,27,49],[0,28,49],[0,29,49],[0,30,49],[0,31,49],[0,32,49],[0,33,49],[0,34,49],[0,24,25,29,30,31,33,48,49],[0,25,26,30,31,32,34,48,49],[0,24,25,26,27,29,30,32,48,49],[0,25,26,27,28,30,31,33,48,49],[0,26,27,28,29,31,32,34,48,49],[0,24,25,27,28,31,32,48,49],[0,25,26,28,29,32,33,48,49],[0,26,27,29,30,33,34,48,49],[0,24,25,27,28,29,33,34,48,49],[0,24,26,28,31,33,34,48,49],[0,24,27,30,31,32,33,34,48,49],[0,24,28,29,30,32,34,48,49],[0,24,48,49],[0,25,48,49],[0,26,48,49],[0,27,48,49],[0,28,48,49],[0,29,48,49],[0,30,48,49],[0,31,48,49],[0,32,48,49],[0,33,48,49],[0,34,48,49],[0,36,42,48,49],[0,35,41,42,48,49],[0,35,41,48,49],[0,40,42,48,49],[0,36,37,39,48,49],[0,40,41,48,49],[0,38,42,48,49],[0,35,38,42,48,49],[0,35,38,48,49],[0,37,39,48,49],[0,37,48,49],[0,40,48,49],[0,40,41,42,48,49],[0,36,37,48,49],[0,38,48,49],[0,39,42,48,49],[0,36,39,42,48,49],[0,36,42,47,48,49],[0,35,41,42,47,48,49],[0,35,41,47,48,49],[0,40,42,47,48,49],[0,36,37,39,47,48,49],[0,40,41,47,48,49],[0,38,42,47,48,49],[0,35,38,42,47,48,49],[0,35,38,47,48,49],[0,37,39,47,48,49],[0,37,47,48,49],[0,40,47,48,49],[0,40,41,42,47,48,49],[0,36,37,47,48,49],[0,38,47,48,49],[0,39,42,47,48,49],[0,36,39,42,47,48,49],[0,43,44,47,48,49],[0,44,45,47,48,49],[0,43,44,45,47,48,49],[0,43,45,47,48,49],[0,43,47,48,49],[0,44,47,48,49],[0,45,47,48,49],[0,43,44,46,47,48,49],[0,44,45,46,47,48,49],[0,43,44,45,46,47,48,49],[0,43,45,46,47,48,49],[0,43,46,47,48,49],[0,44,46,47,48,49],[0,45,46,47,48,49],[0,46,47,48,49]]},"distance":{"d":7,"is_exact":false,"upper":9,"witness":[41,88,94,95,105,107,109,120,136],"A_d":null,"certified":{"d":9,"is_exact":false,"met":true,"source":"Jain and Albert (arXiv:2408.12752), Table II: [[47,1,11]] quantum QR code (extended QR [48,24,12]) doubled onto [[95,1,7]]; the doubling theorem of their Sec. III gives d >= min(d_sd, d_tri + 2) = 9, with d_sd at least the classical distance less one (their Lemma 2.4)"}},"clifford":{"kind":"powers","correction":{"S":[[0,2],[49,1]],"CZ":[[0,49]]},"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],[26,7],[27,7],[28,7],[29,7],[30,7],[31,7],[32,7],[33,7],[34,7],[35,7],[36,7],[37,7],[38,7],[39,7],[40,7],[41,7],[42,7],[43,7],[44,7],[45,7],[46,7],[47,7],[48,7],[49,7],[50,7],[51,7],[52,7],[53,7],[54,7],[55,7],[56,7],[57,7],[58,7],[59,7],[60,7],[61,7],[62,7],[63,7],[64,7],[65,7],[66,7],[67,7],[68,7],[69,7],[70,7],[71,7],[72,7],[73,7],[74,7],[75,7],[76,7],[77,7],[78,7],[79,7],[80,7],[81,7],[82,7],[83,7],[84,7],[85,7],[86,7],[87,7],[88,7],[89,7],[90,7],[91,7],[92,7],[93,7]]},"metrics":{"gamma":2.693725102160739,"gamma_t":2.693725102160739,"gamma_rho":2.693725102160739,"gamma_claim":2.385621874580711,"gamma_t_claim":2.385621874580711,"gamma_rho_claim":2.385621874580711,"v_ex":1,"rate":0.005291005291005291,"t_count":1,"poly_degree":1,"effective_width":1},"provenance":{"regimes":["Jain-Albert doubling: weak triply even family"],"discovery":"pre-existing","strongest_claim":"a code of the weak triply even family of Jain and Albert (arXiv:2408.12752, Table II; transversal_t_codes/): quadratic-residue CSS codes doubled onto [[95,1,7]], rebuilt here from the paper's construction, where T on some qubits and T-dagger on the rest is a logical T; a verified witness, not a maximum","sources":[{"regime":"Jain-Albert doubling: weak triply even family","file":"transversal_t_codes/factories.json","label":"JA-189","N":50,"d":7,"d_is_exact":false,"origin":"S. P. Jain and V. V. Albert, \"Transversal Clifford and T-gate codes of short length and high distance\", IEEE J. Sel. Areas Inf. Theory 6, 127 (2025), arXiv:2408.12752","provenance":"[[47,1,11]] quantum QR code (extended QR [48,24,12]) doubled onto [[95,1,7]] (Table II)"}]},"references":[{"key":"jain2025transversal","short":"Jain & Albert (2025)","full":"S. P. Jain and V. V. Albert, \"Transversal Clifford and T-gate codes of short length and high distance,\" IEEE J. Sel. Areas Inf. Theory 6, 127-137 (2025); arXiv:2408.12752.","url":"https://doi.org/10.1109/JSAIT.2025.3570832","date":"2025-05-16"}]}