| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{014}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{024}\cdot \mathrm{CCZ}_{035}\cdot \mathrm{CCZ}_{123}\cdot \mathrm{CCZ}_{125}\cdot \mathrm{CCZ}_{135}\cdot \mathrm{CCZ}_{345} | — | 13 | d = 4 | Jain et al. (2026) |
| \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{345} | 2.000 | 13 | d = 4 | Haah & Hastings (2018); Gong et al. (2026); Jacinto 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: [\![77,\,6,\,4]\!] · [\![92,\,6,\,4]\!] · [\![100,\,6,\,4]\!]