非阿贝尔码中的混合态拓扑序与纠错阈值：严格结果
Mixed-state topological order and error-correction thresholds in non-Abelian codes: rigorous results
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中文总结 AI 辅助
研究非阿贝尔码受噪声影响时的恢复阈值，提出通用严格技术，可捕捉二维码受任意局部噪声影响，证明一定噪声强度下逻辑信息可高精度恢复，噪声破坏态有混合态拓扑序特征，还介绍了方法在高维及相关噪声模型的应用。
中文摘要 AI 辅助
我们提出了一种通用且数学严格的技术来界定受噪声影响的拓扑码的恢复阈值。该方法能捕捉对包括表面码、非阿贝尔量子双重码和弦网码等二维码的码态施加任意（可能非泡利）局部噪声信道的影响。在每种情况下，我们证明对于噪声强度直至某个明确常数，任何初始编码的逻辑信息都能高精度恢复，且噪声破坏态呈现混合态拓扑序的关键特征：长程纠缠和涌现的高阶对称性。我们还描述了如何将这些方法应用于更高维度和相关噪声模型。
英文摘要
We present a versatile and mathematically rigorous technique for bounding recovery thresholds in topological codes subject to noise. Our method captures the effect of applying an arbitrary (possibly non-Pauli) local noise channel to the code state of a broad class of two-dimensional codes, including surface codes, non-Abelian quantum doubles, and string-net codes. In each case, we prove that for noise strengths up to some explicit constant value, any initially encoded logical information can be recovered to high precision, and that the noise-corrupted state exhibits key hallmarks of mixed-state topological order: long-range entanglement and emergent higher-form symmetries. We also describe how these methods can be adapted to higher dimensions and correlated noise models.
