| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{CCZ}_{012} | 3.585 | 5 | d = 2 | Singh et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{CS}_{01}\cdot \mathrm{CS}_{02} | — | 6 | d = 2 | Jain 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: [\![25,\,3,\,2]\!] · [\![20,\,3,\,2]\!] · [\![28,\,3,\,2]\!] · [\![29,\,3,\,2]\!] · [\![18,\,3,\,2]\!] · [\![12,\,3,\,2]\!] · [\![8,\,3,\,2]\!] · [\![56,\,3,\,2]\!] · [\![57,\,3,\,2]\!] · [\![60,\,3,\,2]\!] · [\![61,\,3,\,2]\!] · [\![63,\,3,\,2]\!]