Magic State Factory Catalog

[\![64,\,15,\,4]\!]

One factory with n=64 inputs, k=15 outputs and distance d=4.

Inequivalent gates at [[64, 15, 4]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CCZ}_{0,1,2}\cdot \mathrm{CCZ}_{0,3,4}\cdot \mathrm{CCZ}_{0,5,6}\cdot \mathrm{CCZ}_{1,7,8}\cdot \mathrm{CCZ}_{1,9,10}\cdot \mathrm{CCZ}_{2,11,12}\cdot \mathrm{CCZ}_{2,13,14}\cdot \mathrm{CCZ}_{3,7,11}\cdot \mathrm{CCZ}_{3,9,13}\cdot \mathrm{CCZ}_{4,8,12}\cdot \mathrm{CCZ}_{4,10,14}\cdot \mathrm{CCZ}_{5,7,1}\cdots 15 terms—22d = 4Rengaswamy et al. (2020); Vuillot & Breuckmann (2022); Gong et al. (2026)

Nearest lengths with the same k and d: [\![128,\,15,\,4]\!]