| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2} pure T | 7.404 | 10 | d = 2 | Singh et al. (2026) |
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{12}\cdot \mathrm{CCZ}_{012} | — | 10 | 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: [\![509,\,3,\,2]\!] · [\![504,\,3,\,2]\!] · [\![525,\,3,\,2]\!] · [\![541,\,3,\,2]\!] · [\![561,\,3,\,2]\!] · [\![573,\,3,\,2]\!] · [\![635,\,3,\,2]\!] · [\![636,\,3,\,2]\!] · [\![661,\,3,\,2]\!] · [\![333,\,3,\,2]\!] · [\![316,\,3,\,2]\!] · [\![315,\,3,\,2]\!]