Magic State Factory Catalog

[\![4977,\,12,\,2]\!]

One factory with n=4977 inputs, k=12 outputs and distance d=2.

Inequivalent gates at [[4977, 12, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{CS}_{0,1}\cdot \mathrm{CS}_{0,2}\cdot \mathrm{CS}_{0,3}\cdot \mathrm{CS}_{0,4}\cdot \mathrm{CS}_{0,5}\cdot \mathrm{CS}_{0,6}\cdot \mathrm{CS}_{0,7}\cdot \mathrm{CS}_{0,8}\cdot \mathrm{CS}_{0,9}\cdot \mathrm{CS}_{0,10}\cdot \mathrm{CS}_{0,11}\cdot \mathrm{CS}_{1,2}\cdot \mathrm{CS}_{1,3}\cdot \mathrm{CS}_{1,4}\cdot \mathrm{CS}_{1,5}\cdot \mathrm{CS}_{1,6}\cdot \mathrm{CS}_{1,7}\cdot \mathrm{CS}_{1,8}\cdot \mathrm{CS}_{1,9}\cdot \mathrm{C}\cdots 66 terms—18d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![4052,\,12,\,2]\!] · [\![6132,\,12,\,2]\!] · [\![3556,\,12,\,2]\!] · [\![2516,\,12,\,2]\!] · [\![2449,\,12,\,2]\!] · [\![7620,\,12,\,2]\!] · [\![8116,\,12,\,2]\!] · [\![1575,\,12,\,2]\!] · [\![1252,\,12,\,2]\!] · [\![1185,\,12,\,2]\!] · [\![882,\,12,\,2]\!] · [\![819,\,12,\,2]\!]