Magic State Factory Catalog

[\![47,\,6,\,3]\!]

One factory with n=47 inputs, k=6 outputs and distance d=3.

Inequivalent gates at [[47, 6, 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{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{03}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{13}\cdot \mathrm{CS}_{23}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{014}\cdot \mathrm{CCZ}_{015}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{024}\cdot \mathrm{CCZ}_{025}\cdot \mathrm{CCZ}_{034}\cdot \mathrm{CCZ}_{035}\cdot \mathrm{CCZ}_{045}\cdot \mathrm{CCZ}_{12}\cdots 24 terms—12d = 3Wills et al. (2026); Jain et al. (2026)

Nearest lengths with the same k and d: [\![48,\,6,\,3]\!] · [\![44,\,6,\,3]\!] · [\![43,\,6,\,3]\!] · [\![51,\,6,\,3]\!] · [\![52,\,6,\,3]\!] · [\![39,\,6,\,3]\!] · [\![55,\,6,\,3]\!] · [\![56,\,6,\,3]\!] · [\![58,\,6,\,3]\!] · [\![59,\,6,\,3]\!] · [\![60,\,6,\,3]\!] · [\![62,\,6,\,3]\!]