| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2} pure T | 12.415 | 15 | d = 2 | Singh et al. (2026) |
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{12}\cdot \mathrm{CCZ}_{012} | — | 15 | 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: [\![16381,\,3,\,2]\!] · [\![16376,\,3,\,2]\!] · [\![16317,\,3,\,2]\!] · [\![14029,\,3,\,2]\!] · [\![12390,\,3,\,2]\!] · [\![20413,\,3,\,2]\!] · [\![20475,\,3,\,2]\!] · [\![20476,\,3,\,2]\!] · [\![11453,\,3,\,2]\!] · [\![11025,\,3,\,2]\!] · [\![10236,\,3,\,2]\!] · [\![10235,\,3,\,2]\!]