| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2} pure T | 10.414 | 13 | d = 2 | Singh et al. (2026) |
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{12}\cdot \mathrm{CCZ}_{012} | — | 13 | 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: [\![4093,\,3,\,2]\!] · [\![4088,\,3,\,2]\!] · [\![4029,\,3,\,2]\!] · [\![3997,\,3,\,2]\!] · [\![4589,\,3,\,2]\!] · [\![5017,\,3,\,2]\!] · [\![5053,\,3,\,2]\!] · [\![5115,\,3,\,2]\!] · [\![5116,\,3,\,2]\!] · [\![2641,\,3,\,2]\!] · [\![2556,\,3,\,2]\!] · [\![2555,\,3,\,2]\!]