Magic State Factory Catalog

[\![60,\,7,\,3]\!]

2 inequivalent factories with n=60 inputs, k=7 outputs and distance d=3.

Inequivalent gates at [[60, 7, 3]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{T}_{0}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{4}\cdot \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{03}\cdot \mathrm{CS}_{04}\cdot \mathrm{CS}_{05}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{14}\cdot \mathrm{CS}_{16}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{25}\cdot \mathrm{CS}_{26}\cdot \mathrm{CS}_{36}\cdot \mathrm{CS}_{45}\cdot \mathrm{CS}_{46}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{014}\cdot \mathrm{CCZ}_{015}\cdot \mathrm{CCZ}_{016}\cdot \mathrm{CCZ}_{}\cdots 37 terms—14d = 3Jain et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{03}\cdot \mathrm{CS}_{04}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{13}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{45}\cdot \mathrm{CS}_{56}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{014}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{024}\cdot \mathrm{CCZ}_{034}\cdot \mathrm{CCZ}_{123}\cdot \mathrm{CCZ}_{145}\cdot \mathrm{CCZ}_{156}\cdot \mathrm{CCZ}_{245}\cdots 23 terms—14d = 3Jain et al. (2026)

These factories share n, k and d but prepare different magic states. No CNOT circuit with S, Z and CZ corrections turns one of these gates into another.

Nearest lengths with the same k and d: [\![59,\,7,\,3]\!] · [\![61,\,7,\,3]\!] · [\![62,\,7,\,3]\!] · [\![63,\,7,\,3]\!] · [\![55,\,7,\,3]\!] · [\![65,\,7,\,3]\!] · [\![48,\,7,\,3]\!] · [\![44,\,7,\,3]\!] · [\![43,\,7,\,3]\!] · [\![79,\,7,\,3]\!] · [\![84,\,7,\,3]\!] · [\![91,\,7,\,3]\!]