Charge-Informed Quantum Error Correction

Fuente: arXiv
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Main Authors: Temkin, Vlad, Weinstein, Zack, Fan, Ruihua, Podolsky, Daniel, Altman, Ehud
Format: Preprint
Published: 2025
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author Temkin, Vlad
Weinstein, Zack
Fan, Ruihua
Podolsky, Daniel
Altman, Ehud
author_facet Temkin, Vlad
Weinstein, Zack
Fan, Ruihua
Podolsky, Daniel
Altman, Ehud
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_22119
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Charge-Informed Quantum Error Correction
Temkin, Vlad
Weinstein, Zack
Fan, Ruihua
Podolsky, Daniel
Altman, Ehud
Quantum Physics
Statistical Mechanics
Strongly Correlated Electrons
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.
title Charge-Informed Quantum Error Correction
topic Quantum Physics
Statistical Mechanics
Strongly Correlated Electrons
url https://arxiv.org/abs/2512.22119