Magic State Factory Catalog

[\![28,\,6,\,2]\!]

2 inequivalent factories with n=28 inputs, k=6 outputs and distance d=2.

Inequivalent gates at [[28, 6, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{45}2.8079d = 2Singh et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{CS}_{45}2.4859d = 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: [\![26,\,6,\,2]\!] · [\![24,\,6,\,2]\!] · [\![14,\,6,\,2]\!] · [\![42,\,6,\,2]\!] · [\![46,\,6,\,2]\!] · [\![52,\,6,\,2]\!] · [\![56,\,6,\,2]\!] · [\![58,\,6,\,2]\!] · [\![60,\,6,\,2]\!] · [\![105,\,6,\,2]\!] · [\![106,\,6,\,2]\!] · [\![114,\,6,\,2]\!]