Magic State Factory Catalog

[\![26,\,6,\,2]\!]

3 inequivalent factories with n=26 inputs, k=6 outputs and distance d=2.

Inequivalent gates at [[26, 6, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5} pure T2.1159d = 2Bravyi & Haah (2012)
\mathrm{T}_{0}\cdot \mathrm{CS}_{12}\cdot \mathrm{CCZ}_{345}2.7009d = 2Singh et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{CCZ}_{345}2.3799d = 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: [\![24,\,6,\,2]\!] · [\![28,\,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]\!]