Magic State Factory Catalog

[\![52,\,6,\,2]\!]

One factory with n=52 inputs, k=6 outputs and distance d=2.

Inequivalent gates at [[52, 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—8d = 2Singh et al. (2026)

Same n and k at other distances: [\![52,\,6,\,3]\!]
Nearest lengths with the same k and d: [\![56,\,6,\,2]\!] · [\![46,\,6,\,2]\!] · [\![58,\,6,\,2]\!] · [\![60,\,6,\,2]\!] · [\![42,\,6,\,2]\!] · [\![28,\,6,\,2]\!] · [\![26,\,6,\,2]\!] · [\![24,\,6,\,2]\!] · [\![14,\,6,\,2]\!] · [\![105,\,6,\,2]\!] · [\![106,\,6,\,2]\!] · [\![114,\,6,\,2]\!]