| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2} pure T | 15.415 | 18 | d = 2 | Singh et al. (2026) |
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{12}\cdot \mathrm{CCZ}_{012} | — | 18 | 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: [\![131064,\,3,\,2]\!] · [\![163835,\,3,\,2]\!] · [\![81916,\,3,\,2]\!] · [\![81915,\,3,\,2]\!] · [\![65789,\,3,\,2]\!] · [\![65533,\,3,\,2]\!] · [\![65532,\,3,\,2]\!] · [\![65528,\,3,\,2]\!] · [\![48653,\,3,\,2]\!] · [\![41021,\,3,\,2]\!] · [\![40956,\,3,\,2]\!] · [\![40955,\,3,\,2]\!]