{"id":"95.1.7.a","row":634,"stored":{"file":"master_catalog.json","row":634,"construction":null,"columns_sha256":null},"parameters":{"n":95,"k":1,"d":7,"N":26,"r":25,"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":[[0,1,2,6,7,8,10],[0,2,3,7,8,9,11],[0,1,2,3,4,6,7,9],[0,2,3,4,5,7,8,10],[0,3,4,5,6,8,9,11],[0,1,2,4,5,8,9],[0,2,3,5,6,9,10],[0,3,4,6,7,10,11],[0,1,2,4,5,6,10,11],[0,1,3,5,8,10,11],[0,1,4,7,8,9,10,11],[0,1,5,6,7,9,11],[0,1],[0,2],[0,3],[0,4],[0,5],[0,6],[0,7],[0,8],[0,9],[0,10],[0,11],[0,1,2,6,7,8,10,25],[0,2,3,7,8,9,11,25],[0,1,2,3,4,6,7,9,25],[0,2,3,4,5,7,8,10,25],[0,3,4,5,6,8,9,11,25],[0,1,2,4,5,8,9,25],[0,2,3,5,6,9,10,25],[0,3,4,6,7,10,11,25],[0,1,2,4,5,6,10,11,25],[0,1,3,5,8,10,11,25],[0,1,4,7,8,9,10,11,25],[0,1,5,6,7,9,11,25],[0,1,25],[0,2,25],[0,3,25],[0,4,25],[0,5,25],[0,6,25],[0,7,25],[0,8,25],[0,9,25],[0,10,25],[0,11,25],[0,13,19,25],[0,12,18,19,25],[0,12,18,25],[0,17,19,25],[0,13,14,16,25],[0,17,18,25],[0,15,19,25],[0,12,15,19,25],[0,12,15,25],[0,14,16,25],[0,14,25],[0,17,25],[0,17,18,19,25],[0,13,14,25],[0,15,25],[0,16,19,25],[0,13,16,19,25],[0,13,19,24,25],[0,12,18,19,24,25],[0,12,18,24,25],[0,17,19,24,25],[0,13,14,16,24,25],[0,17,18,24,25],[0,15,19,24,25],[0,12,15,19,24,25],[0,12,15,24,25],[0,14,16,24,25],[0,14,24,25],[0,17,24,25],[0,17,18,19,24,25],[0,13,14,24,25],[0,15,24,25],[0,16,19,24,25],[0,13,16,19,24,25],[0,20,21,24,25],[0,21,22,24,25],[0,20,21,22,24,25],[0,20,22,24,25],[0,20,24,25],[0,21,24,25],[0,22,24,25],[0,20,21,23,24,25],[0,21,22,23,24,25],[0,20,21,22,23,24,25],[0,20,22,23,24,25],[0,20,23,24,25],[0,21,23,24,25],[0,22,23,24,25],[0,23,24,25]]},"distance":{"d":7,"is_exact":true,"upper":7,"witness":[15,38,51,63,75,78,79],"A_d":48645,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1]],"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],[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],[94,7]]},"metrics":{"gamma":2.3402297859494308,"gamma_t":2.3402297859494308,"gamma_rho":2.3402297859494308,"gamma_claim":2.3402297859494308,"gamma_t_claim":2.3402297859494308,"gamma_rho_claim":2.3402297859494308,"v_ex":1,"rate":0.010526315789473684,"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-95","N":26,"d":7,"d_is_exact":true,"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":"[[23,1,7]] Golay code (QR 23) doubled onto [[49,1,5]] (Table I and Table II)","notes":"earlier publication: the [[95,1,7]] code of Sullivan (2024), the Golay code doubled onto [[49,1,5]]"}]},"references":[{"key":"sullivan2024code","short":"Sullivan (2024)","full":"M. Sullivan, \"Code conversion with the quantum Golay code for a universal transversal gate set,\" Phys. Rev. A 109, 042416 (2024).","url":"https://doi.org/10.1103/PhysRevA.109.042416","date":"2024-04-18"}]}