Magic State Factory Catalog

[\![56,\,8,\,2]\!]

One factory with n=56 inputs, k=8 outputs and distance d=2.

Inequivalent gates at [[56, 8, 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} pure T2.80711d = 2Singh et al. (2026)

Same n and k at other distances: [\![56,\,8,\,3]\!]
Nearest lengths with the same k and d: [\![58,\,8,\,2]\!] · [\![52,\,8,\,2]\!] · [\![70,\,8,\,2]\!] · [\![40,\,8,\,2]\!] · [\![72,\,8,\,2]\!] · [\![38,\,8,\,2]\!] · [\![36,\,8,\,2]\!] · [\![34,\,8,\,2]\!] · [\![32,\,8,\,2]\!] · [\![30,\,8,\,2]\!] · [\![26,\,8,\,2]\!] · [\![24,\,8,\,2]\!]