Magic State Factory Catalog

[\![44,\,7,\,3]\!]

One factory with n=44 inputs, k=7 outputs and distance d=3.

Inequivalent gates at [[44, 7, 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{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{03}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{13}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{45}\cdot \mathrm{CS}_{46}\cdot \mathrm{CS}_{56}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{123}\cdot \mathrm{CCZ}_{456}—14d = 3Wills et al. (2026); Jain et al. (2026)

Nearest lengths with the same k and d: [\![43,\,7,\,3]\!] · [\![48,\,7,\,3]\!] · [\![55,\,7,\,3]\!] · [\![59,\,7,\,3]\!] · [\![60,\,7,\,3]\!] · [\![61,\,7,\,3]\!] · [\![62,\,7,\,3]\!] · [\![63,\,7,\,3]\!] · [\![65,\,7,\,3]\!] · [\![79,\,7,\,3]\!] · [\![84,\,7,\,3]\!] · [\![91,\,7,\,3]\!]