| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{12}\cdot \mathrm{CCZ}_{012} | — | 8 | d = 2 | Singh et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2} pure T | 5.691 | 13 | 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: [\![156,\,3,\,2]\!] · [\![161,\,3,\,2]\!] · [\![133,\,3,\,2]\!] · [\![125,\,3,\,2]\!] · [\![124,\,3,\,2]\!] · [\![120,\,3,\,2]\!] · [\![117,\,3,\,2]\!] · [\![229,\,3,\,2]\!] · [\![76,\,3,\,2]\!] · [\![75,\,3,\,2]\!] · [\![63,\,3,\,2]\!] · [\![248,\,3,\,2]\!]