| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{T}_{0}\cdot \mathrm{CS}_{12}\cdot \mathrm{CCZ}_{345} | 2.618 | 13 | d = 3 | Jain et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{CCZ}_{345} | 2.415 | 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: [\![70,\,6,\,3]\!] · [\![68,\,6,\,3]\!] · [\![74,\,6,\,3]\!] · [\![67,\,6,\,3]\!] · [\![75,\,6,\,3]\!] · [\![66,\,6,\,3]\!] · [\![63,\,6,\,3]\!] · [\![79,\,6,\,3]\!] · [\![62,\,6,\,3]\!] · [\![80,\,6,\,3]\!] · [\![60,\,6,\,3]\!] · [\![59,\,6,\,3]\!]