Magic State Factory Catalog

[\![8778,\,5,\,2]\!]

One factory with n=8778 inputs, k=5 outputs and distance d=2.

Inequivalent gates at [[8778, 5, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{03}\cdot \mathrm{CS}_{04}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{13}\cdot \mathrm{CS}_{14}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{24}\cdot \mathrm{CS}_{34}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{014}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{024}\cdot \mathrm{CCZ}_{034}\cdot \mathrm{CCZ}_{123}\cdot \mathrm{CCZ}_{124}\cdot \mathrm{CCZ}_{134}\cdot \mathrm{CCZ}_{234}—16d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![8122,\,5,\,2]\!] · [\![7891,\,5,\,2]\!] · [\![7163,\,5,\,2]\!] · [\![7162,\,5,\,2]\!] · [\![7161,\,5,\,2]\!] · [\![6970,\,5,\,2]\!] · [\![6667,\,5,\,2]\!] · [\![11099,\,5,\,2]\!] · [\![11253,\,5,\,2]\!] · [\![11259,\,5,\,2]\!] · [\![6139,\,5,\,2]\!] · [\![6138,\,5,\,2]\!]