Magic State Factory Catalog

[\![40,\,2,\,3]\!]

3 inequivalent factories with n=40 inputs, k=2 outputs and distance d=3.

Inequivalent gates at [[40, 2, 3]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CS}_{01}3.3588d = 3Wills et al. (2026); Jain et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{CS}_{01}—9d = 3Wills et al. (2026); Jain et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1} pure T2.7279d = 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.

Nearest lengths with the same k and d: [\![39,\,2,\,3]\!] · [\![38,\,2,\,3]\!] · [\![42,\,2,\,3]\!] · [\![37,\,2,\,3]\!] · [\![43,\,2,\,3]\!] · [\![36,\,2,\,3]\!] · [\![44,\,2,\,3]\!] · [\![35,\,2,\,3]\!] · [\![45,\,2,\,3]\!] · [\![34,\,2,\,3]\!] · [\![46,\,2,\,3]\!] · [\![47,\,2,\,3]\!]