Magic State Factory Catalog

[\![34,\,9,\,2]\!]

3 inequivalent factories with n=34 inputs, k=9 outputs and distance d=2.

Inequivalent gates at [[34, 9, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{CCZ}_{345}\cdot \mathrm{CCZ}_{678}2.28012d = 2Singh et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{45}\cdot \mathrm{CCZ}_{678}2.50312d = 2Singh et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{CS}_{45}\cdot \mathrm{CCZ}_{678}2.28012d = 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,\,9,\,2]\!] · [\![30,\,9,\,2]\!] · [\![38,\,9,\,2]\!] · [\![40,\,9,\,2]\!] · [\![42,\,9,\,2]\!] · [\![44,\,9,\,2]\!] · [\![46,\,9,\,2]\!] · [\![20,\,9,\,2]\!] · [\![56,\,9,\,2]\!] · [\![70,\,9,\,2]\!] · [\![71,\,9,\,2]\!] · [\![111,\,9,\,2]\!]