| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{T}_{0}\cdot \mathrm{CCZ}_{1,2,3}\cdot \mathrm{CCZ}_{4,5,6}\cdot \mathrm{CCZ}_{7,8,9}\cdot \mathrm{CCZ}_{10,11,12} | 2.183 | 20 | 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}\cdot \mathrm{T}_{8}\cdot \mathrm{T}_{9}\cdot \mathrm{T}_{10}\cdot \mathrm{T}_{11}\cdot \mathrm{T}_{12} pure T | 1.848 | 20 | 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: [\![100,\,13,\,3]\!] · [\![96,\,13,\,3]\!] · [\![95,\,13,\,3]\!] · [\![91,\,13,\,3]\!] · [\![88,\,13,\,3]\!] · [\![87,\,13,\,3]\!] · [\![79,\,13,\,3]\!]