Magic State Factory Catalog

[\![20,\,3,\,2]\!]

3 inequivalent factories with n=20 inputs, k=3 outputs and distance d=2.

Inequivalent gates at [[20, 3, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{T}_{0}\cdot \mathrm{CS}_{12}3.3226d = 2Nezami & Haah (2022)
\mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CCZ}_{012}—6d = 2Jain et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2} pure T2.7376d = 2Nezami & Haah (2022)

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: [\![18,\,3,\,2]\!] · [\![24,\,3,\,2]\!] · [\![25,\,3,\,2]\!] · [\![12,\,3,\,2]\!] · [\![28,\,3,\,2]\!] · [\![29,\,3,\,2]\!] · [\![8,\,3,\,2]\!] · [\![56,\,3,\,2]\!] · [\![57,\,3,\,2]\!] · [\![60,\,3,\,2]\!] · [\![61,\,3,\,2]\!] · [\![63,\,3,\,2]\!]