| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{03}\cdot \mathrm{CS}_{04}\cdot \mathrm{CS}_{05}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{13}\cdot \mathrm{CS}_{14}\cdot \mathrm{CS}_{15}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{24}\cdot \mathrm{CS}_{25}\cdot \mathrm{CS}_{34}\cdot \mathrm{CS}_{35}\cdot \mathrm{CS}_{45}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{014}\cdot \mathrm{CCZ}_{015}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{024}\cdots 35 terms | — | 8 | d = 2 | Singh et al. (2026) |
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{45} | 3.000 | 8 | d = 2 | Singh 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: [\![26,\,6,\,2]\!] · [\![28,\,6,\,2]\!] · [\![14,\,6,\,2]\!] · [\![42,\,6,\,2]\!] · [\![46,\,6,\,2]\!] · [\![52,\,6,\,2]\!] · [\![56,\,6,\,2]\!] · [\![58,\,6,\,2]\!] · [\![60,\,6,\,2]\!] · [\![105,\,6,\,2]\!] · [\![106,\,6,\,2]\!] · [\![114,\,6,\,2]\!]