Magic State Factory Catalog

[\![76,\,4,\,4]\!]

2 inequivalent factories with n=76 inputs, k=4 outputs and distance d=4.

Inequivalent gates at [[76, 4, 4]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}—13d = 4Jain et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{CS}_{01}\cdot \mathrm{CS}_{23}—13d = 4Jain 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: [\![76,\,4,\,2]\!]
Nearest lengths with the same k and d: [\![77,\,4,\,4]\!] · [\![72,\,4,\,4]\!] · [\![80,\,4,\,4]\!] · [\![48,\,4,\,4]\!] · [\![120,\,4,\,4]\!] · [\![160,\,4,\,4]\!]