Magic State Factory Catalog

[\![682,\,6,\,2]\!]

One factory with n=682 inputs, k=6 outputs and distance d=2.

Inequivalent gates at [[682, 6, 2]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{014}\cdot \mathrm{CCZ}_{015}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{024}\cdot \mathrm{CCZ}_{025}\cdot \mathrm{CCZ}_{034}\cdot \mathrm{CCZ}_{035}\cdot \mathrm{CCZ}_{045}\cdot \mathrm{CCZ}_{123}\cdot \mathrm{CCZ}_{124}\cdot \mathrm{CCZ}_{125}\cdot \mathrm{CCZ}_{134}\cdot \mathrm{C}\cdots 26 terms—11d = 2Singh et al. (2026)

Nearest lengths with the same k and d: [\![698,\,6,\,2]\!] · [\![658,\,6,\,2]\!] · [\![722,\,6,\,2]\!] · [\![570,\,6,\,2]\!] · [\![554,\,6,\,2]\!] · [\![819,\,6,\,2]\!] · [\![820,\,6,\,2]\!] · [\![516,\,6,\,2]\!] · [\![506,\,6,\,2]\!] · [\![504,\,6,\,2]\!] · [\![490,\,6,\,2]\!] · [\![889,\,6,\,2]\!]