Magic State Factory Catalog

[\![26612,\,6,\,2]\!]

One factory with n=26612 inputs, k=6 outputs and distance d=2.

Inequivalent gates at [[26612, 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—18d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![26611,\,6,\,2]\!] · [\![24658,\,6,\,2]\!] · [\![28665,\,6,\,2]\!] · [\![24322,\,6,\,2]\!] · [\![22522,\,6,\,2]\!] · [\![22506,\,6,\,2]\!] · [\![22330,\,6,\,2]\!] · [\![32760,\,6,\,2]\!] · [\![32884,\,6,\,2]\!] · [\![34036,\,6,\,2]\!] · [\![17028,\,6,\,2]\!] · [\![16378,\,6,\,2]\!]