Magic State Factory Catalog

[\![62,\,7,\,3]\!]

One factory with n=62 inputs, k=7 outputs and distance d=3.

Inequivalent gates at [[62, 7, 3]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{T}_{0}\cdot \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{03}\cdot \mathrm{CS}_{04}\cdot \mathrm{CS}_{05}\cdot \mathrm{CS}_{06}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{014}\cdot \mathrm{CCZ}_{015}\cdot \mathrm{CCZ}_{016}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{024}\cdot \mathrm{CCZ}_{035}\cdot \mathrm{CCZ}_{046}\cdot \mathrm{CCZ}_{056}\cdot \mathrm{CCZ}_{234}\cdot \mathrm{CCZ}_{236}\cdots 20 terms—17d = 3Jain et al. (2026)

Nearest lengths with the same k and d: [\![61,\,7,\,3]\!] · [\![63,\,7,\,3]\!] · [\![60,\,7,\,3]\!] · [\![59,\,7,\,3]\!] · [\![65,\,7,\,3]\!] · [\![55,\,7,\,3]\!] · [\![48,\,7,\,3]\!] · [\![79,\,7,\,3]\!] · [\![44,\,7,\,3]\!] · [\![43,\,7,\,3]\!] · [\![84,\,7,\,3]\!] · [\![91,\,7,\,3]\!]