Magic State Factory Catalog

[\![24,\,4,\,2]\!]

2 inequivalent factories with n=24 inputs, k=4 outputs and distance d=2.

Inequivalent gates at [[24, 4, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{123}—6d = 2Singh et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3} pure T2.5857d = 2Singh 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: [\![22,\,4,\,2]\!] · [\![20,\,4,\,2]\!] · [\![28,\,4,\,2]\!] · [\![18,\,4,\,2]\!] · [\![16,\,4,\,2]\!] · [\![32,\,4,\,2]\!] · [\![42,\,4,\,2]\!] · [\![44,\,4,\,2]\!] · [\![56,\,4,\,2]\!] · [\![60,\,4,\,2]\!] · [\![62,\,4,\,2]\!] · [\![75,\,4,\,2]\!]