Home Parameters [\![511,\,15,\,5]\!] [\![511,\,15,\,5]\!] 2 inequivalent factories with n=511 inputs, k=15 outputs and distance d=5 .
Inequivalent gates at [[511, 15, 5]]. Click a column header to sort.
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{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{CS}_{0,1}\cdot \mathrm{CS}_{3,6}\cdot \mathrm{CS}_{4,12}\cdot \mathrm{CS}_{5,13}\cdot \mathrm{CS}_{9,14}\cdot \mathrm{CCZ}_{0,1,2}\cdot \mathrm{CCZ}_{0,1,3}\cdot \mathrm{CCZ}_{0,1,4}\cdot \mathrm{CCZ}_{0,1,}\cdots 68 terms — 33 d = 5 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} pure T 2.192 33 d = 5 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 : [\![1023,\,15,\,5]\!]