Magic State Factory Catalog

[\![6644,\,6,\,2]\!]

One factory with n=6644 inputs, k=6 outputs and distance d=2.

Inequivalent gates at [[6644, 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—16d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![6643,\,6,\,2]\!] · [\![6468,\,6,\,2]\!] · [\![6970,\,6,\,2]\!] · [\![6178,\,6,\,2]\!] · [\![7161,\,6,\,2]\!] · [\![7162,\,6,\,2]\!] · [\![5882,\,6,\,2]\!] · [\![5626,\,6,\,2]\!] · [\![5610,\,6,\,2]\!] · [\![7986,\,6,\,2]\!] · [\![7994,\,6,\,2]\!] · [\![8116,\,6,\,2]\!]