Magic State Factory Catalog

[\![56,\,6,\,2]\!]

One factory with n=56 inputs, k=6 outputs and distance d=2.

Inequivalent gates at [[56, 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—9d = 2Singh et al. (2026)

Same n and k at other distances: [\![56,\,6,\,3]\!]
Nearest lengths with the same k and d: [\![58,\,6,\,2]\!] · [\![52,\,6,\,2]\!] · [\![60,\,6,\,2]\!] · [\![46,\,6,\,2]\!] · [\![42,\,6,\,2]\!] · [\![28,\,6,\,2]\!] · [\![26,\,6,\,2]\!] · [\![24,\,6,\,2]\!] · [\![14,\,6,\,2]\!] · [\![105,\,6,\,2]\!] · [\![106,\,6,\,2]\!] · [\![114,\,6,\,2]\!]