Magic State Factory Catalog

[\![404,\,6,\,2]\!]

One factory with n=404 inputs, k=6 outputs and distance d=2.

Inequivalent gates at [[404, 6, 2]]. 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}_{023}\cdot \mathrm{CCZ}_{024}\cdot \mathrm{CCZ}_{025}\cdot \mathrm{CCZ}_{034}\cdot \mathrm{CCZ}_{035}\cdot \mathrm{CCZ}_{045}\cdot \mathrm{CCZ}_{123}\cdot \mathrm{CCZ}_{124}\cdot \mathrm{CCZ}_{125}\cdot \mathrm{CCZ}_{134}\cdot \mathrm{CCZ}_{135}\cdot \mathrm{CCZ}_{145}\cdot \mathrm{CCZ}_{23}\cdots 20 terms—12d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![403,\,6,\,2]\!] · [\![410,\,6,\,2]\!] · [\![441,\,6,\,2]\!] · [\![442,\,6,\,2]\!] · [\![448,\,6,\,2]\!] · [\![346,\,6,\,2]\!] · [\![330,\,6,\,2]\!] · [\![490,\,6,\,2]\!] · [\![504,\,6,\,2]\!] · [\![506,\,6,\,2]\!] · [\![516,\,6,\,2]\!] · [\![282,\,6,\,2]\!]