Magic State Factory Catalog

[\![20,\,5,\,2]\!]

2 inequivalent factories with n=20 inputs, k=5 outputs and distance d=2.

Inequivalent gates at [[20, 5, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{CCZ}_{234}2.3228d = 2Singh et al. (2026)
\mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{124}—6d = 2Jain 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: [\![18,\,5,\,2]\!] · [\![22,\,5,\,2]\!] · [\![16,\,5,\,2]\!] · [\![26,\,5,\,2]\!] · [\![12,\,5,\,2]\!] · [\![30,\,5,\,2]\!] · [\![42,\,5,\,2]\!] · [\![43,\,5,\,2]\!] · [\![58,\,5,\,2]\!] · [\![61,\,5,\,2]\!] · [\![87,\,5,\,2]\!] · [\![90,\,5,\,2]\!]