发表机构
Dept. of Physics MIT WPU Pune, India（印度浦那 MIT WPU 物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文比较XZZX码与旋转表面码在时空关联噪声下的阈值，发现采用超图感知的MWPF解码器至关重要，且XZZX码在中等偏置下存在阈值最小值。
AI 中文摘要
虽然量子计算研究通常假设噪声是独立同分布的，但诸如关联噪声和时空误差等复杂错误模型仍未得到充分探索。本文在复杂噪声模型下评估了XZZX码和旋转表面码的性能。标准基于图的解码器难以处理偏置定制码上由关联错误产生的超边。为解决这一问题，我们采用了最小权重奇偶因子（MWPF）解码器，该解码器无需人工边分解即可原生处理综合征超图。我们的模拟表明，在强Z偏置电路级关联噪声（η=100）下，旋转码的阈值降至约0.36%，而XZZX码的阈值降至约0.70%。此外，在不同偏置比率下，XZZX码表现出明显的非单调阈值依赖性。虽然XZZX码在极端偏置下能有效吸收高密度Z型超边，但在中等偏置（η≈10）时出现阈值最小值，因为横向X和Y错误会主动桥接对角字符串，破坏该码的一维解耦对称性。这些发现表明，采用超图感知解码器至关重要，因为偏置定制码的性能对时空关联噪声的几何结构高度敏感。
英文摘要
While independent and identically distributed noise is typically assumed in quantum computing research, complex error models such as correlated and spatio-temporal errors remain underexplored. In this paper, the performance of $\mathrm{XZZX}$ and rotated surface codes is evaluated under these complex noise models. Standard graph-based decoders struggle with the hyperedges generated by correlated errors on bias-tailored codes. To address this, we employ the Minimum Weight Parity Factor (MWPF) decoder, which natively processes syndrome hypergraphs without artificial edge decomposition. Our simulations show that under strong Z-biased circuit-level correlated noise ($η=100$), the threshold of the rotated code degrades to $\approx 0.36\%$, while the $\mathrm{XZZX}$ code drops to $\approx 0.70\%$. Furthermore, a distinct non-monotonic threshold dependence is observed for the $\mathrm{XZZX}$ code across different bias ratios. While the $\mathrm{XZZX}$ code effectively absorbs high-density Z-type hyperedges at extreme biases, it exhibits a threshold minimum at moderate biases ($η\approx 10$) because transverse X and Y errors actively bridge the diagonal strings, breaking the code's one-dimensional decoupling symmetry. These findings demonstrate that utilizing hypergraph-aware decoders is critical, as the performance of bias-tailored codes is highly sensitive to the geometric structure of spatio-temporal correlated noise.
Comments11 pages, 8 plots, simulation codes available on GitHub
