Magic State Factory Catalog

[\![26,\,5,\,2]\!]

2 inequivalent factories with n=26 inputs, k=5 outputs and distance d=2.

Inequivalent gates at [[26, 5, 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}3.1158d = 2Singh et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4} pure T2.3798d = 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: [\![22,\,5,\,2]\!] · [\![30,\,5,\,2]\!] · [\![20,\,5,\,2]\!] · [\![18,\,5,\,2]\!] · [\![16,\,5,\,2]\!] · [\![12,\,5,\,2]\!] · [\![42,\,5,\,2]\!] · [\![43,\,5,\,2]\!] · [\![58,\,5,\,2]\!] · [\![61,\,5,\,2]\!] · [\![87,\,5,\,2]\!] · [\![90,\,5,\,2]\!]