Magic State Factory Catalog

[\![38,\,7,\,2]\!]

2 inequivalent factories with n=38 inputs, k=7 outputs and distance d=2.

Inequivalent gates at [[38, 7, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{T}_{0}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{34}\cdot \mathrm{CS}_{56}3.24810d = 2Singh et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{T}_{6} pure T2.44110d = 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: [\![36,\,7,\,2]\!] · [\![34,\,7,\,2]\!] · [\![30,\,7,\,2]\!] · [\![28,\,7,\,2]\!] · [\![26,\,7,\,2]\!] · [\![24,\,7,\,2]\!] · [\![56,\,7,\,2]\!] · [\![57,\,7,\,2]\!] · [\![59,\,7,\,2]\!] · [\![113,\,7,\,2]\!] · [\![117,\,7,\,2]\!] · [\![120,\,7,\,2]\!]