| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{CS}_{01} | 3.236 | 8 | d = 3 | Nezami & Haah (2022) |
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{CS}_{01} | — | 8 | d = 3 | Wills et al. (2026); Jain et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{T}_{1} pure T | 2.605 | 8 | d = 3 | Nezami & Haah (2022) |
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: [\![34,\,2,\,3]\!] · [\![36,\,2,\,3]\!] · [\![37,\,2,\,3]\!] · [\![32,\,2,\,3]\!] · [\![38,\,2,\,3]\!] · [\![31,\,2,\,3]\!] · [\![39,\,2,\,3]\!] · [\![30,\,2,\,3]\!] · [\![40,\,2,\,3]\!] · [\![28,\,2,\,3]\!] · [\![42,\,2,\,3]\!] · [\![43,\,2,\,3]\!]