Magic State Factory Catalog

[\![136,\,7,\,4]\!]

2 inequivalent factories with n=136 inputs, k=7 outputs and distance d=4.

Inequivalent gates at [[136, 7, 4]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{014}\cdot \mathrm{CCZ}_{015}\cdot \mathrm{CCZ}_{016}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{024}\cdot \mathrm{CCZ}_{025}\cdot \mathrm{CCZ}_{034}\cdot \mathrm{CCZ}_{056}\cdot \mathrm{CCZ}_{126}\cdot \mathrm{CCZ}_{135}\cdot \mathrm{CCZ}_{136}\cdot \mathrm{CCZ}_{146}\cdot \mathrm{CCZ}_{235}\cdot \mathrm{CCZ}_{236}\cdot \mathrm{CCZ}_{24}\cdots 20 terms—16d = 4Jain et al. (2026)
\mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{014}\cdot \mathrm{CCZ}_{015}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{024}\cdot \mathrm{CCZ}_{034}\cdot \mathrm{CCZ}_{125}\cdot \mathrm{CCZ}_{236}\cdot \mathrm{CCZ}_{256}\cdot \mathrm{CCZ}_{345}\cdot \mathrm{CCZ}_{346}\cdot \mathrm{CCZ}_{356}\cdot \mathrm{CCZ}_{456}—17d = 4Jain 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.

Same n and k at other distances: [\![136,\,7,\,2]\!]
Nearest lengths with the same k and d: [\![77,\,7,\,4]\!]