Magic State Factory Catalog

[\![48,\,7,\,3]\!]

2 inequivalent factories with n=48 inputs, k=7 outputs and distance d=3.

Inequivalent gates at [[48, 7, 3]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CS}_{01}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{034}\cdot \mathrm{CCZ}_{035}\cdot \mathrm{CCZ}_{046}\cdot \mathrm{CCZ}_{134}\cdot \mathrm{CCZ}_{156}—13d = 3Wills et al. (2026)
\mathrm{CS}_{01}\cdot \mathrm{CS}_{35}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{034}\cdot \mathrm{CCZ}_{156}\cdot \mathrm{CCZ}_{235}—13d = 3Wills 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: [\![44,\,7,\,3]\!] · [\![43,\,7,\,3]\!] · [\![55,\,7,\,3]\!] · [\![59,\,7,\,3]\!] · [\![60,\,7,\,3]\!] · [\![61,\,7,\,3]\!] · [\![62,\,7,\,3]\!] · [\![63,\,7,\,3]\!] · [\![65,\,7,\,3]\!] · [\![79,\,7,\,3]\!] · [\![84,\,7,\,3]\!] · [\![91,\,7,\,3]\!]