Topological Color Code Thresholds Mapped to Lattice-Dependent Percolation — E8 Intelligence Research

FINDING: Topological color code accuracy thresholds on hexagonal and square-octagonal lattices are determined via mapping to spin models, revealing lattice-dependent percolation thresholds. | MATH: The mapping reduces the quantum error correction threshold to a classical percolation problem on the dual lattice. For the square-octagonal lattice, the site percolation threshold \( p_c \) is approximately 0.5 (exact for square lattice) but modified by the octagonal tiling geometry; the hexagonal lattice yields \( p_c \approx 0.6527 \) (site percolation on triangular lattice). The threshold for the color code is given by \( p_{\text{th}} = 1 - p_c \) for the hexagonal case, and analogous for square-octagonal. Key constants: hexagonal lattice percolation threshold \( p_c = 0.5 \) (bond) or 0.5927 (site); square-octagonal lattice percolation threshold is not exactly known but lies near 0.5–0.6. | CONNECTION: The square-octagonal lattice is a semiregular tiling (Archimedean) with vertex config Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com