Magic State Factory Catalog

[\![68,\,5,\,3]\!]

2 inequivalent factories with n=68 inputs, k=5 outputs and distance d=3.

Inequivalent gates at [[68, 5, 3]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CS}_{01}\cdot \mathrm{CCZ}_{234}2.84112d = 3Jain et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{34}2.84112d = 3Jain 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: [\![67,\,5,\,3]\!] · [\![65,\,5,\,3]\!] · [\![71,\,5,\,3]\!] · [\![72,\,5,\,3]\!] · [\![63,\,5,\,3]\!] · [\![75,\,5,\,3]\!] · [\![60,\,5,\,3]\!] · [\![76,\,5,\,3]\!] · [\![59,\,5,\,3]\!] · [\![57,\,5,\,3]\!] · [\![79,\,5,\,3]\!] · [\![55,\,5,\,3]\!]