Magic State Factory Catalog

[\![168,\,7,\,2]\!]

One factory with n=168 inputs, k=7 outputs and distance d=2.

Inequivalent gates at [[168, 7, 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}_{05}\cdot \mathrm{CS}_{06}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{13}\cdot \mathrm{CS}_{14}\cdot \mathrm{CS}_{15}\cdot \mathrm{CS}_{16}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{24}\cdot \mathrm{CS}_{25}\cdot \mathrm{CS}_{26}\cdot \mathrm{CS}_{34}\cdot \mathrm{CS}_{35}\cdot \mathrm{CS}_{36}\cdot \mathrm{CS}_{45}\cdot \mathrm{CS}_{46}\cdot \mathrm{CS}_{56}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{01}\cdots 56 terms—10d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![136,\,7,\,2]\!] · [\![135,\,7,\,2]\!] · [\![132,\,7,\,2]\!] · [\![121,\,7,\,2]\!] · [\![120,\,7,\,2]\!] · [\![117,\,7,\,2]\!] · [\![113,\,7,\,2]\!] · [\![225,\,7,\,2]\!] · [\![233,\,7,\,2]\!] · [\![248,\,7,\,2]\!] · [\![249,\,7,\,2]\!] · [\![261,\,7,\,2]\!]