Magic State Factory Catalog

[\![14235,\,12,\,2]\!]

One factory with n=14235 inputs, k=12 outputs and distance d=2.

Inequivalent gates at [[14235, 12, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CCZ}_{0,1,2}\cdot \mathrm{CCZ}_{0,1,3}\cdot \mathrm{CCZ}_{0,1,4}\cdot \mathrm{CCZ}_{0,1,5}\cdot \mathrm{CCZ}_{0,1,6}\cdot \mathrm{CCZ}_{0,1,7}\cdot \mathrm{CCZ}_{0,1,8}\cdot \mathrm{CCZ}_{0,1,9}\cdot \mathrm{CCZ}_{0,1,10}\cdot \mathrm{CCZ}_{0,1,11}\cdot \mathrm{CCZ}_{0,2,3}\cdot \mathrm{CCZ}_{0,2,4}\cdot \mathrm{CCZ}_{0,2,}\cdots 220 terms—16d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![15160,\,12,\,2]\!] · [\![15748,\,12,\,2]\!] · [\![16244,\,12,\,2]\!] · [\![12076,\,12,\,2]\!] · [\![12075,\,12,\,2]\!] · [\![11445,\,12,\,2]\!] · [\![10124,\,12,\,2]\!] · [\![9562,\,12,\,2]\!] · [\![20124,\,12,\,2]\!] · [\![8116,\,12,\,2]\!] · [\![20490,\,12,\,2]\!] · [\![7620,\,12,\,2]\!]