| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2} pure T | 8.409 | 11 | d = 2 | Singh et al. (2026) |
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{12}\cdot \mathrm{CCZ}_{012} | — | 11 | d = 2 | Singh et al. (2026) |
These factories share n, k and d but prepare different magic states. No CNOT circuit with S, Z and CZ corrections turns one of these gates into another.
Nearest lengths with the same k and d: [\![1021,\,3,\,2]\!] · [\![1023,\,3,\,2]\!] · [\![1016,\,3,\,2]\!] · [\![1037,\,3,\,2]\!] · [\![1275,\,3,\,2]\!] · [\![1276,\,3,\,2]\!] · [\![1293,\,3,\,2]\!] · [\![725,\,3,\,2]\!] · [\![661,\,3,\,2]\!] · [\![636,\,3,\,2]\!] · [\![635,\,3,\,2]\!] · [\![573,\,3,\,2]\!]