| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{345} | 2.803 | 13 | d = 3 | Jain et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{CS}_{12}\cdot \mathrm{CCZ}_{345} | 2.803 | 13 | d = 3 | Jain et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{45} | 2.803 | 13 | d = 3 | Jain et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{CCZ}_{345} | 2.600 | 13 | 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: [\![88,\,6,\,3]\!] · [\![84,\,6,\,3]\!] · [\![83,\,6,\,3]\!] · [\![91,\,6,\,3]\!] · [\![92,\,6,\,3]\!] · [\![80,\,6,\,3]\!] · [\![79,\,6,\,3]\!] · [\![96,\,6,\,3]\!] · [\![75,\,6,\,3]\!] · [\![74,\,6,\,3]\!] · [\![71,\,6,\,3]\!] · [\![70,\,6,\,3]\!]