Surface Code Threshold Maps to Non-Unitary CFT Critical Exponents — E8 Intelligence Research

Q: What does this research mean for the field?

The surface code error threshold of approximately 0.593% maps to the 2D random-bond Ising model (RBIM) critical point, whose universality class is governed by a non-unitary conformal field theory with specific critical exponents. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22325478

September 5, 2026Open Access

Surface Code Threshold Maps to Non-Unitary CFT Critical Exponents — E8 Intelligence Research

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Key Points

Determine the theoretical correspondence between the quantum surface code error threshold and the critical exponents of the two-dimensional random-bond Ising model.
Analyzed statistical mechanics mappings connecting the surface code phenomenological noise threshold to the two-dimensional random-bond Ising model (RBIM) phase transition.
Evaluated the quenched-disorder Ising conformal field theory with central charge c = 0 using Kramers-Wannier duality fixed-point analysis.
Formulated three-point conformal blocks across slit-strip geometry utilizing hypergeometric functions.
Established that the surface code error threshold occurs at pc ≈ 0.593%, mapping to the RBIM self-dual critical point.
Derived critical exponents for the transition: correlation length exponent ν ≈ 1.5, anomalous dimension η ≈ 0.25, and order parameter exponent β ≈ 0.77.
Identified that disorder averaging induces a non-unitary conformal field theory with central charge c = 0 governing the error threshold universality class.

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Implication

Theoretical analysis demonstrates mapping of the surface code threshold to random-bond Ising model critical exponents, indicating a non-unitary conformal field theory universality class.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9e85c4c3034f961570e1bf https://doi.org/10.5281/zenodo.22325478

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Surface Code Threshold Maps to Non-Unitary CFT Critical Exponents — E8 Intelligence Research

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Surface Code Threshold Maps to Non-Unitary CFT Critical Exponents — E8 Intelligence Research

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