Magic State Factory Catalog

[\![820,\,6,\,2]\!]

One factory with n=820 inputs, k=6 outputs and distance d=2.

Inequivalent gates at [[820, 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—13d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![819,\,6,\,2]\!] · [\![889,\,6,\,2]\!] · [\![890,\,6,\,2]\!] · [\![916,\,6,\,2]\!] · [\![722,\,6,\,2]\!] · [\![698,\,6,\,2]\!] · [\![946,\,6,\,2]\!] · [\![682,\,6,\,2]\!] · [\![658,\,6,\,2]\!] · [\![1008,\,6,\,2]\!] · [\![1012,\,6,\,2]\!] · [\![1016,\,6,\,2]\!]