Magic State Factory Catalog

[\![52,\,6,\,3]\!]

2 inequivalent factories with n=52 inputs, k=6 outputs and distance d=3.

Inequivalent gates at [[52, 6, 3]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{T}_{0}\cdot \mathrm{CS}_{01}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{45}\cdot \mathrm{CCZ}_{123}\cdot \mathrm{CCZ}_{145}—13d = 3Wills 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} pure T1.96613d = 3Wills 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.

Same n and k at other distances: [\![52,\,6,\,2]\!]
Nearest lengths with the same k and d: [\![51,\,6,\,3]\!] · [\![55,\,6,\,3]\!] · [\![48,\,6,\,3]\!] · [\![56,\,6,\,3]\!] · [\![47,\,6,\,3]\!] · [\![58,\,6,\,3]\!] · [\![59,\,6,\,3]\!] · [\![44,\,6,\,3]\!] · [\![60,\,6,\,3]\!] · [\![43,\,6,\,3]\!] · [\![62,\,6,\,3]\!] · [\![63,\,6,\,3]\!]