| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{CS}_{01}\cdot \mathrm{CCZ}_{234} | 2.827 | 12 | d = 3 | Jain et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{34} | 2.827 | 12 | 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: [\![68,\,5,\,3]\!] · [\![65,\,5,\,3]\!] · [\![63,\,5,\,3]\!] · [\![71,\,5,\,3]\!] · [\![72,\,5,\,3]\!] · [\![60,\,5,\,3]\!] · [\![59,\,5,\,3]\!] · [\![75,\,5,\,3]\!] · [\![76,\,5,\,3]\!] · [\![57,\,5,\,3]\!] · [\![55,\,5,\,3]\!] · [\![79,\,5,\,3]\!]