AI 中文总结
该研究关联量子纠错与格点杨-米尔斯理论，构建高阶形式码解码方法，定义中心片模型，推导相关判据与关联函数，区分全局通量抑制与局域谱信息。
AI 中文摘要
我们研究量子纠错、禁闭与格点杨-米尔斯理论之间的关系。首先，我们以高阶规范场的形式构建有限阿贝尔同调码的解码方法。对于正局域噪声，逻辑类是西村系综的拓扑 sector，最优解码误差由非平凡 sector 的相对权重决定。我们推导了逻辑概率、无序算符与信道环境信息之间的傅里叶关系，并给出了阈值的等高线与分数矩判据。随后，我们研究了一个四维$\boldsymbol{\text{Z}_N}$存储器及其与禁闭$\boldsymbol{\text{PSU}(N)}$真空的可能关联。最后，我们定义了一个耦合到威尔逊$\boldsymbol{\text{SU}(N)}$链变量的有限曲率中心片模型，在该模型中，条件逻辑概率是中心扭曲杨-米尔斯配分函数。强耦合展开给出了伴随校正子的主导有效相互作用，表明即使全局片 sector 混合，局域校正子关联仍可衰减。我们还证明，一对分离的校正子世界线的似然是中心单极子关联函数，其衰减决定了转移矩阵质量，这区分了全局通量 sector 的抑制与讨论质量间隙所需的局域谱信息。
英文摘要
We study the relationship between quantum error correction, confinement, and lattice Yang-Mills theory. We first formulate decoding for finite Abelian homological codes in terms of higher form gauge fields. For positive local noise, the logical classes are topological sectors of a Nishimori ensemble, and the optimal decoding error is determined by the relative weights of the nontrivial sectors. We derive Fourier relations between logical probabilities, disorder operators, and information in the channel environment, and we give contour and fractional moment criteria for a threshold. We then study a four dimensional $\Z_N$ memory and its possible relation to confining $\PSU(N)$ vacua. Finally, we define a finite curvature center sheet model coupled to Wilson $\SU(N)$ link variables. In this model the conditional logical probabilities are center twisted Yang-Mills partition functions. A strong coupling expansion gives the leading effective interaction for the syndrome and shows that local syndrome correlations can decay even when the global sheet sectors are mixed. We also show that the likelihood for a separated pair of syndrome worldlines is the center monopole correlator. Its decay determines a transfer matrix mass. This distinguishes the suppression of global flux sectors from the local spectral information needed to discuss a mass gap.
