Magic State Factory Catalog

[\![13300,\,6,\,2]\!]

One factory with n=13300 inputs, k=6 outputs and distance d=2.

Inequivalent gates at [[13300, 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—17d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![13299,\,6,\,2]\!] · [\![12916,\,6,\,2]\!] · [\![12386,\,6,\,2]\!] · [\![12276,\,6,\,2]\!] · [\![14329,\,6,\,2]\!] · [\![14330,\,6,\,2]\!] · [\![15082,\,6,\,2]\!] · [\![11450,\,6,\,2]\!] · [\![11418,\,6,\,2]\!] · [\![11258,\,6,\,2]\!] · [\![11242,\,6,\,2]\!] · [\![16372,\,6,\,2]\!]