The surface code beyond Pauli channels: Logical noise coherence, information-theoretic measures, and errorfield-double phenomenology

• URL: http://arxiv.org/abs/2412.21055v2
• Date: Thu, 24 Apr 2025 16:45:42 GMT
• Title: The surface code beyond Pauli channels: Logical noise coherence, information-theoretic measures, and errorfield-double phenomenology
• Authors: Jan Behrends, Benjamin Béri,
• Abstract summary: We consider the surface code under errors featuring both coherent and incoherent components.<n>We show that for any nonzero incoherent noise component, the coherence of the logical noise is exponentially suppressed with the code distance.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the surface code under errors featuring both coherent and incoherent components and study the coherence of the corresponding logical noise channel and how this impacts information-theoretic measures of code performance, namely coherent information and quantum relative entropy. Using numerical simulations and a phenomenological field theory, focusing on the most general single-qubit X-error channel, we show that, for any nonzero incoherent noise component, the coherence of the logical noise is exponentially suppressed with the code distance. We also find that the information-theoretic measures require this suppression to detect optimal thresholds for Pauli recovery; they thus require increasingly large distances for increasing error coherence and ultimately break down for fully coherent errors. To obtain our results, we develop a statistical mechanics mapping and a corresponding matrix-product-state algorithm for approximate syndrome sampling. These methods enable the large-scale simulation of these non-Pauli errors, including their maximum-likelihood thresholds, away from the limits captured by previous approaches.

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