Magic State Factory Catalog

[\![3332,\,6,\,2]\!]

One factory with n=3332 inputs, k=6 outputs and distance d=2.

Inequivalent gates at [[3332, 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: [\![3316,\,6,\,2]\!] · [\![3315,\,6,\,2]\!] · [\![3434,\,6,\,2]\!] · [\![3202,\,6,\,2]\!] · [\![3498,\,6,\,2]\!] · [\![3577,\,6,\,2]\!] · [\![3578,\,6,\,2]\!] · [\![3036,\,6,\,2]\!] · [\![2986,\,6,\,2]\!] · [\![2810,\,6,\,2]\!] · [\![2794,\,6,\,2]\!] · [\![3994,\,6,\,2]\!]