| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{T}_{0}\cdot \mathrm{CS}_{12}\cdot \mathrm{CCZ}_{123}\cdot \mathrm{CCZ}_{145}\cdot \mathrm{CCZ}_{146}\cdot \mathrm{CCZ}_{157}\cdot \mathrm{CCZ}_{245}\cdot \mathrm{CCZ}_{267} | — | 18 | d = 3 | Jain et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{46}\cdot \mathrm{CCZ}_{123}\cdot \mathrm{CCZ}_{145}\cdot \mathrm{CCZ}_{267}\cdot \mathrm{CCZ}_{346} | — | 18 | d = 3 | Jain et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{T}_{6}\cdot \mathrm{T}_{7} pure T | 1.878 | 14 | 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: [\![62,\,8,\,3]\!] · [\![64,\,8,\,3]\!] · [\![60,\,8,\,3]\!] · [\![66,\,8,\,3]\!] · [\![68,\,8,\,3]\!] · [\![56,\,8,\,3]\!] · [\![70,\,8,\,3]\!] · [\![74,\,8,\,3]\!] · [\![80,\,8,\,3]\!] · [\![82,\,8,\,3]\!] · [\![86,\,8,\,3]\!] · [\![90,\,8,\,3]\!]