Magic State Factory Catalog

[\![56,\,9,\,2]\!]

One factory with n=56 inputs, k=9 outputs and distance d=2.

Inequivalent gates at [[56, 9, 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}_{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}\cdot \mathrm{CS}_{26}\cdot \mathrm{CS}_{27}\cdot \mathrm{CS}_{28}\cdot \mathrm{CS}_{34}\cdot \mathrm{CS}_{35}\cdot \mathrm{CS}_{}\cdots 120 terms—11d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![46,\,9,\,2]\!] · [\![44,\,9,\,2]\!] · [\![42,\,9,\,2]\!] · [\![70,\,9,\,2]\!] · [\![71,\,9,\,2]\!] · [\![40,\,9,\,2]\!] · [\![38,\,9,\,2]\!] · [\![34,\,9,\,2]\!] · [\![32,\,9,\,2]\!] · [\![30,\,9,\,2]\!] · [\![20,\,9,\,2]\!] · [\![111,\,9,\,2]\!]