Magic State Factory Catalog

[\![12,\,3,\,2]\!]

One factory with n=12 inputs, k=3 outputs and distance d=2.

Inequivalent gates at [[12, 3, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{12}\cdot \mathrm{CCZ}_{012}—5d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![8,\,3,\,2]\!] · [\![18,\,3,\,2]\!] · [\![20,\,3,\,2]\!] · [\![24,\,3,\,2]\!] · [\![25,\,3,\,2]\!] · [\![28,\,3,\,2]\!] · [\![29,\,3,\,2]\!] · [\![56,\,3,\,2]\!] · [\![57,\,3,\,2]\!] · [\![60,\,3,\,2]\!] · [\![61,\,3,\,2]\!] · [\![63,\,3,\,2]\!]