Magic State Factory Catalog

[\![20,\,4,\,2]\!]

3 inequivalent factories with n=20 inputs, k=4 outputs and distance d=2.

Inequivalent gates at [[20, 4, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3} pure T2.3227d = 2Bravyi & Haah (2012)
\mathrm{T}_{0}\cdot \mathrm{CCZ}_{123}2.7377d = 2Bravyi & Haah (2012)
\mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{03}\cdot \mathrm{CCZ}_{012}—6d = 2Jain 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: [\![18,\,4,\,2]\!] · [\![22,\,4,\,2]\!] · [\![16,\,4,\,2]\!] · [\![24,\,4,\,2]\!] · [\![28,\,4,\,2]\!] · [\![32,\,4,\,2]\!] · [\![42,\,4,\,2]\!] · [\![44,\,4,\,2]\!] · [\![56,\,4,\,2]\!] · [\![60,\,4,\,2]\!] · [\![62,\,4,\,2]\!] · [\![75,\,4,\,2]\!]