Charge-Informed Quantum Error Correction

• URL: http://arxiv.org/abs/2512.22119v1
• Date: Fri, 26 Dec 2025 18:59:21 GMT
• Title: Charge-Informed Quantum Error Correction
• Authors: Vlad Temkin, Zack Weinstein, Ruihua Fan, Daniel Podolsky, Ehud Altman,
• Abstract summary: We investigate the statistical physics of quantum error correction in $rm U(1)$-enriched topological quantum memories.<n>The error threshold of the optimal decoder corresponds to a continuous phase transition in a disordered two-dimensional integer loop model on the Nishimori line.<n>We show that the optimal decoding transition exhibits Berezinskii-Kosterlitz-Thouless with a modified universal jump in winding number variance.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the statistical physics of quantum error correction in ${\rm U}(1)$ symmetry-enriched topological quantum memories. Starting from a phenomenological error model of charge-conserving noise, we study the optimal decoder assuming the local charges of each anyon can be measured. The error threshold of the optimal decoder corresponds to a continuous phase transition in a disordered two-dimensional integer loop model on the Nishimori line. Using an effective replica field theory analysis and Monte Carlo numerics, we show that the optimal decoding transition exhibits Berezinskii-Kosterlitz-Thouless universality with a modified universal jump in winding number variance. We further generalize the model beyond the Nishimori line, which defines a large class of suboptimal decoders. At low nonzero temperatures and strong disorder, we find numerical evidence of a disorder-dominated loop-glass phase which corresponds to a "confidently incorrect" decoder. The zero-temperature limit defines the minimum-cost flow decoder, which serves as the ${\rm U}(1)$ analog of minimum-weight perfect matching in $\mathbb{Z}_2$ topological codes. Both the optimal and minimum-cost flow decoders are shown to dramatically outperform the charge-agnostic optimal decoder in symmetry-enriched topological codes.

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