Surface Code Threshold as Percolation Phase Transition on Torus Homology — E8 Intelligence Research

July 28, 2026Open Access

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This research aims to determine the error correction threshold for surface codes using percolation theory on a torus lattice.
Analyzed logical operators as homology cycles on a torus lattice.
Computed the error correction threshold under various noise conditions.
Related the scaling exponent to critical exponents of the 2D random-bond Ising model.
Establishes a threshold of approximately 0.103 for standard surface codes under specific noise types.
Demonstrates that the error correction condition's probability scales with lattice size and noise model.
Finds a connection between homology cycles and the behavior of closed strings on the torus.

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Investigates error correction thresholds in surface codes, indicating critical noise levels for reliability.

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Andrew Stewart Caldin (2026) studied this question.

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