Magic State Factory Catalog

[\![4088,\,6,\,2]\!]

One factory with n=4088 inputs, k=6 outputs and distance d=2.

Inequivalent gates at [[4088, 6, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{03}\cdot \mathrm{CS}_{04}\cdot \mathrm{CS}_{05}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{13}\cdot \mathrm{CS}_{14}\cdot \mathrm{CS}_{15}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{24}\cdot \mathrm{CS}_{25}\cdot \mathrm{CS}_{34}\cdot \mathrm{CS}_{35}\cdot \mathrm{CS}_{45}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{014}\cdot \mathrm{CCZ}_{015}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{024}\cdots 35 terms—15d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![4090,\,6,\,2]\!] · [\![4070,\,6,\,2]\!] · [\![4020,\,6,\,2]\!] · [\![4156,\,6,\,2]\!] · [\![3994,\,6,\,2]\!] · [\![3578,\,6,\,2]\!] · [\![3577,\,6,\,2]\!] · [\![3498,\,6,\,2]\!] · [\![3434,\,6,\,2]\!] · [\![3332,\,6,\,2]\!] · [\![3316,\,6,\,2]\!] · [\![3315,\,6,\,2]\!]