Magic State Factory Catalog

[\![18,\,4,\,2]\!]

2 inequivalent factories with n=18 inputs, k=4 outputs and distance d=2.

Inequivalent gates at [[18, 4, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{03}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{13}\cdot \mathrm{CS}_{23}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{123}—6d = 2Campbell & Howard (2017)
\mathrm{CS}_{01}\cdot \mathrm{CS}_{23}3.1706d = 2Campbell & Howard (2017)

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: [\![16,\,4,\,2]\!] · [\![20,\,4,\,2]\!] · [\![22,\,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]\!]