A Minimal Duality Estimate for the Surface-Code Threshold under Nearest-Neighbor Correlated Errors
Abstract
We apply the single-equation duality criterion to the square-octagonal random-bond Ising model recently obtained from an exact error-edge map for a surface code with nearest-neighbor correlated errors. The calculation is performed for the minimal cell after the error-edge reduction. For the symmetric case \(p1=p2=p3=p\), this gives \(pc=0.0288427147\), in close agreement with the reported numerical threshold of about \(3\%\).
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