Magic State Factory Catalog

[\![34,\,8,\,2]\!]

3 inequivalent factories with n=34 inputs, k=8 outputs and distance d=2.

Inequivalent gates at [[34, 8, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{T}_{0}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{34}\cdot \mathrm{CCZ}_{567}2.76611d = 2Singh et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{CS}_{34}\cdot \mathrm{CCZ}_{567}2.50311d = 2Singh et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{CCZ}_{567}2.28011d = 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: [\![32,\,8,\,2]\!] · [\![36,\,8,\,2]\!] · [\![30,\,8,\,2]\!] · [\![38,\,8,\,2]\!] · [\![40,\,8,\,2]\!] · [\![26,\,8,\,2]\!] · [\![24,\,8,\,2]\!] · [\![52,\,8,\,2]\!] · [\![56,\,8,\,2]\!] · [\![58,\,8,\,2]\!] · [\![70,\,8,\,2]\!] · [\![72,\,8,\,2]\!]