| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{CCZ}_{4,5,6}\cdot \mathrm{CCZ}_{7,8,9}\cdot \mathrm{CCZ}_{10,11,12}\cdot \mathrm{CCZ}_{13,14,15} | 2.033 | 23 | 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}\cdot \mathrm{T}_{13}\cdot \mathrm{T}_{14}\cdot \mathrm{T}_{15} pure T | 1.771 | 29 | d = 3 | Haah & Hastings (2018) |
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,\,16,\,3]\!] · [\![99,\,16,\,3]\!] · [\![127,\,16,\,3]\!] · [\![155,\,16,\,3]\!] · [\![63,\,16,\,3]\!]