Magic State Factory Catalog

[\![42,\,12,\,2]\!]

One factory with n=42 inputs, k=12 outputs and distance d=2.

Inequivalent gates at [[42, 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 286 terms—14d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![44,\,12,\,2]\!] · [\![72,\,12,\,2]\!] · [\![98,\,12,\,2]\!] · [\![100,\,12,\,2]\!] · [\![108,\,12,\,2]\!] · [\![195,\,12,\,2]\!] · [\![196,\,12,\,2]\!] · [\![204,\,12,\,2]\!] · [\![210,\,12,\,2]\!] · [\![212,\,12,\,2]\!] · [\![375,\,12,\,2]\!] · [\![376,\,12,\,2]\!]