Magic State Factory Catalog

[\![37,\,3,\,3]\!]

One factory with n=37 inputs, k=3 outputs and distance d=3.

Inequivalent gates at [[37, 3, 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{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{12}\cdot \mathrm{CCZ}_{012}—11d = 3Wills et al. (2026); Jain et al. (2026)

Nearest lengths with the same k and d: [\![36,\,3,\,3]\!] · [\![38,\,3,\,3]\!] · [\![35,\,3,\,3]\!] · [\![39,\,3,\,3]\!] · [\![40,\,3,\,3]\!] · [\![31,\,3,\,3]\!] · [\![43,\,3,\,3]\!] · [\![44,\,3,\,3]\!] · [\![45,\,3,\,3]\!] · [\![47,\,3,\,3]\!] · [\![48,\,3,\,3]\!] · [\![49,\,3,\,3]\!]