Magic State Factory Catalog

[\![56,\,4,\,2]\!]

One factory with n=56 inputs, k=4 outputs and distance d=2.

Inequivalent gates at [[56, 4, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{123}—7d = 2Singh et al. (2026)

Same n and k at other distances: [\![56,\,4,\,3]\!]
Nearest lengths with the same k and d: [\![60,\,4,\,2]\!] · [\![62,\,4,\,2]\!] · [\![44,\,4,\,2]\!] · [\![42,\,4,\,2]\!] · [\![75,\,4,\,2]\!] · [\![76,\,4,\,2]\!] · [\![32,\,4,\,2]\!] · [\![28,\,4,\,2]\!] · [\![84,\,4,\,2]\!] · [\![24,\,4,\,2]\!] · [\![22,\,4,\,2]\!] · [\![90,\,4,\,2]\!]