| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{CCZ}_{012} | 3.017 | 10 | d = 3 | Jain et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2} pure T | 2.648 | 16 | d = 3 | Shi et al. (2024) |
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: [\![53,\,3,\,3]\!] · [\![57,\,3,\,3]\!] · [\![52,\,3,\,3]\!] · [\![51,\,3,\,3]\!] · [\![49,\,3,\,3]\!] · [\![61,\,3,\,3]\!] · [\![48,\,3,\,3]\!] · [\![47,\,3,\,3]\!] · [\![63,\,3,\,3]\!] · [\![45,\,3,\,3]\!] · [\![44,\,3,\,3]\!] · [\![43,\,3,\,3]\!]