Magic State Factory Catalog

[\![52,\,2,\,3]\!]

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

Inequivalent gates at [[52, 2, 3]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CS}_{01}3.5979d = 3Wills et al. (2026); Jain et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1} pure T2.9669d = 3Wills et al. (2026); Jain 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,\,2,\,4]\!]
Nearest lengths with the same k and d: [\![51,\,2,\,3]\!] · [\![54,\,2,\,3]\!] · [\![48,\,2,\,3]\!] · [\![56,\,2,\,3]\!] · [\![47,\,2,\,3]\!] · [\![46,\,2,\,3]\!] · [\![45,\,2,\,3]\!] · [\![44,\,2,\,3]\!] · [\![43,\,2,\,3]\!] · [\![42,\,2,\,3]\!] · [\![63,\,2,\,3]\!] · [\![40,\,2,\,3]\!]