| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CCZ}_{012} | — | 11 | d = 4 | Wills et al. (2026); Jain et al. (2026) |
| \mathrm{CCZ}_{012} | 2.292 | 10 | d = 4 | Jacinto 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.
Same n and k at other distances: [\![48,\,3,\,3]\!]
Nearest lengths with the same k and d: [\![64,\,3,\,4]\!] · [\![66,\,3,\,4]\!] · [\![72,\,3,\,4]\!] · [\![77,\,3,\,4]\!] · [\![80,\,3,\,4]\!] · [\![84,\,3,\,4]\!] · [\![116,\,3,\,4]\!] · [\![120,\,3,\,4]\!] · [\![172,\,3,\,4]\!] · [\![188,\,3,\,4]\!]