Magic State Factory Catalog

[\![1331,\,9,\,2]\!]

One factory with n=1331 inputs, k=9 outputs and distance d=2.

Inequivalent gates at [[1331, 9, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{T}_{6}\cdot \mathrm{T}_{7}\cdot \mathrm{T}_{8}\cdot \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{03}\cdot \mathrm{CS}_{04}\cdot \mathrm{CS}_{05}\cdot \mathrm{CS}_{06}\cdot \mathrm{CS}_{07}\cdot \mathrm{CS}_{08}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{13}\cdot \mathrm{CS}_{14}\cdot \mathrm{CS}_{15}\cdot \mathrm{CS}_{16}\cdot \mathrm{CS}_{17}\cdot \mathrm{CS}_{18}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{24}\cdot \mathrm{CS}_{25}\cdots 129 terms—13d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![1351,\,9,\,2]\!] · [\![1279,\,9,\,2]\!] · [\![1271,\,9,\,2]\!] · [\![1270,\,9,\,2]\!] · [\![1397,\,9,\,2]\!] · [\![1398,\,9,\,2]\!] · [\![1410,\,9,\,2]\!] · [\![1426,\,9,\,2]\!] · [\![1427,\,9,\,2]\!] · [\![1207,\,9,\,2]\!] · [\![1204,\,9,\,2]\!] · [\![1197,\,9,\,2]\!]