| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{T}_{0}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{34}\cdot \mathrm{CS}_{56} | 2.844 | 14 | d = 3 | Jain et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{CCZ}_{123}\cdot \mathrm{CCZ}_{456} | 2.641 | 14 | 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: [\![92,\,7,\,3]\!] · [\![95,\,7,\,3]\!] · [\![84,\,7,\,3]\!] · [\![79,\,7,\,3]\!] · [\![103,\,7,\,3]\!] · [\![104,\,7,\,3]\!] · [\![65,\,7,\,3]\!] · [\![63,\,7,\,3]\!] · [\![62,\,7,\,3]\!] · [\![61,\,7,\,3]\!] · [\![60,\,7,\,3]\!] · [\![59,\,7,\,3]\!]