Magic State Factory Catalog

[\![56,\,8,\,3]\!]

One factory with n=56 inputs, k=8 outputs and distance d=3.

Inequivalent gates at [[56, 8, 3]]. 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 T1.77115d = 3Jain et al. (2026)

Same n and k at other distances: [\![56,\,8,\,2]\!]
Nearest lengths with the same k and d: [\![60,\,8,\,3]\!] · [\![62,\,8,\,3]\!] · [\![63,\,8,\,3]\!] · [\![64,\,8,\,3]\!] · [\![66,\,8,\,3]\!] · [\![68,\,8,\,3]\!] · [\![70,\,8,\,3]\!] · [\![74,\,8,\,3]\!] · [\![80,\,8,\,3]\!] · [\![82,\,8,\,3]\!] · [\![86,\,8,\,3]\!] · [\![90,\,8,\,3]\!]