| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2} pure T | 9.412 | 12 | d = 2 | Singh et al. (2026) |
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{12}\cdot \mathrm{CCZ}_{012} | — | 12 | 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: [\![2045,\,3,\,2]\!] · [\![2040,\,3,\,2]\!] · [\![2013,\,3,\,2]\!] · [\![1717,\,3,\,2]\!] · [\![2541,\,3,\,2]\!] · [\![2555,\,3,\,2]\!] · [\![2556,\,3,\,2]\!] · [\![1485,\,3,\,2]\!] · [\![2641,\,3,\,2]\!] · [\![1293,\,3,\,2]\!] · [\![1276,\,3,\,2]\!] · [\![1275,\,3,\,2]\!]