| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{T}_{0}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{34}\cdot \mathrm{CCZ}_{567} | 2.754 | 15 | 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{CCZ}_{567} | 2.447 | 15 | 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: [\![104,\,8,\,3]\!] · [\![96,\,8,\,3]\!] · [\![111,\,8,\,3]\!] · [\![94,\,8,\,3]\!] · [\![90,\,8,\,3]\!] · [\![86,\,8,\,3]\!] · [\![82,\,8,\,3]\!] · [\![80,\,8,\,3]\!] · [\![74,\,8,\,3]\!] · [\![70,\,8,\,3]\!] · [\![68,\,8,\,3]\!] · [\![66,\,8,\,3]\!]