| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{03}\cdot \mathrm{CS}_{04}\cdot \mathrm{CS}_{05}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{13}\cdot \mathrm{CS}_{14}\cdot \mathrm{CS}_{15}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{24}\cdot \mathrm{CS}_{25}\cdot \mathrm{CS}_{34}\cdot \mathrm{CS}_{35}\cdot \mathrm{CS}_{45}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{014}\cdot \mathrm{CCZ}_{023}\cdots 26 terms | — | 16 | 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} pure T | 2.126 | 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: [\![63,\,6,\,3]\!] · [\![60,\,6,\,3]\!] · [\![59,\,6,\,3]\!] · [\![58,\,6,\,3]\!] · [\![66,\,6,\,3]\!] · [\![67,\,6,\,3]\!] · [\![56,\,6,\,3]\!] · [\![68,\,6,\,3]\!] · [\![55,\,6,\,3]\!] · [\![70,\,6,\,3]\!] · [\![71,\,6,\,3]\!] · [\![52,\,6,\,3]\!]