Magic State Factory Catalog

[\![16,\,5,\,2]\!]

2 inequivalent factories with n=16 inputs, k=5 outputs and distance d=2.

Inequivalent gates at [[16, 5, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{014}—6d = 2Jain et al. (2026)
\mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{03}\cdot \mathrm{CS}_{04}—7d = 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: [\![18,\,5,\,2]\!] · [\![12,\,5,\,2]\!] · [\![20,\,5,\,2]\!] · [\![22,\,5,\,2]\!] · [\![26,\,5,\,2]\!] · [\![30,\,5,\,2]\!] · [\![42,\,5,\,2]\!] · [\![43,\,5,\,2]\!] · [\![58,\,5,\,2]\!] · [\![61,\,5,\,2]\!] · [\![87,\,5,\,2]\!] · [\![90,\,5,\,2]\!]