Magic State Factory Catalog

[\![60,\,4,\,3]\!]

2 inequivalent factories with n=60 inputs, k=4 outputs and distance d=3.

Inequivalent gates at [[60, 4, 3]]. Click a column header to sort.
output gate \gamma_\rho N distance cited
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{CS}_{23}2.72711d = 3Jain et al. (2026)
\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3} pure T2.46511d = 3Shi et al. (2024)

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.

Same n and k at other distances: [\![60,\,4,\,2]\!]
Nearest lengths with the same k and d: [\![59,\,4,\,3]\!] · [\![58,\,4,\,3]\!] · [\![62,\,4,\,3]\!] · [\![63,\,4,\,3]\!] · [\![56,\,4,\,3]\!] · [\![64,\,4,\,3]\!] · [\![55,\,4,\,3]\!] · [\![54,\,4,\,3]\!] · [\![66,\,4,\,3]\!] · [\![67,\,4,\,3]\!] · [\![52,\,4,\,3]\!] · [\![68,\,4,\,3]\!]