Magic State Factory Catalog

[\![280,\,4,\,2]\!]

2 inequivalent factories with n=280 inputs, k=4 outputs and distance d=2.

Inequivalent gates at [[280, 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}—10d = 2Singh et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3} pure T6.12911d = 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: [\![279,\,4,\,2]\!] · [\![268,\,4,\,2]\!] · [\![248,\,4,\,2]\!] · [\![315,\,4,\,2]\!] · [\![316,\,4,\,2]\!] · [\![228,\,4,\,2]\!] · [\![348,\,4,\,2]\!] · [\![196,\,4,\,2]\!] · [\![188,\,4,\,2]\!] · [\![186,\,4,\,2]\!] · [\![378,\,4,\,2]\!] · [\![380,\,4,\,2]\!]