| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{45}\cdot \mathrm{CS}_{67} | 3.170 | 10 | d = 2 | Singh et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{45}\cdot \mathrm{CS}_{67} | 2.848 | 11 | 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: [\![34,\,8,\,2]\!] · [\![38,\,8,\,2]\!] · [\![32,\,8,\,2]\!] · [\![40,\,8,\,2]\!] · [\![30,\,8,\,2]\!] · [\![26,\,8,\,2]\!] · [\![24,\,8,\,2]\!] · [\![52,\,8,\,2]\!] · [\![56,\,8,\,2]\!] · [\![58,\,8,\,2]\!] · [\![70,\,8,\,2]\!] · [\![72,\,8,\,2]\!]