| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{T}_{0}\cdot \mathrm{CCZ}_{123} | 2.648 | 11 | d = 3 | Jain et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{CS}_{23} | 2.648 | 11 | d = 3 | Jain 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: [\![54,\,4,\,3]\!] · [\![56,\,4,\,3]\!] · [\![52,\,4,\,3]\!] · [\![58,\,4,\,3]\!] · [\![51,\,4,\,3]\!] · [\![59,\,4,\,3]\!] · [\![50,\,4,\,3]\!] · [\![60,\,4,\,3]\!] · [\![48,\,4,\,3]\!] · [\![62,\,4,\,3]\!] · [\![47,\,4,\,3]\!] · [\![63,\,4,\,3]\!]