标题： 持续量子记忆在迭代提升中 显示英文标题

标题： Persistent Quantum Memory in Iterated Lifts

摘要： 我们研究在由对称提升生成的完美图上的连续时间量子行走中的量子相干性，${\mathrm{HL}}'_2(G)$是一种规范的、无权的、无向的构造，定义为$G$的二分双覆盖的线图。 这种提升既是一种保持相干性的变换，也是一种产生相干性的变换：它在高度对称的基图中保持并放大结构化的量子干涉，并在随机或弱结构化的图中产生持续的相干性。 在如$K_4$、$K_5$和彼得森图这样的小图中，量子行走表现出明显的复兴和高返回概率，重复的$\mathrm{HL}'_2$提升会产生具有数千到数万个顶点的完美图塔，这些图保留周期性或准周期性相干性。 当应用于具有平坦或衰减返回行为的随机正则图或 Erdős--Rényi 图时，该提升引入了结构化的干涉，并显著放大了平均和峰值返回概率。 为了量化这些效果，我们评估了来自量子资源理论的标准相干度量，包括反参与比率（IPR）、纯度、相干性的相对熵以及对数相干数。 这些度量证实，$\mathrm{HL}'_2$提升使本征态去局域化，增加相干熵，并扩展量子态的基底支持。 这些结果表明，$\mathrm{HL}'_2$是一种可扩展且结构基础的组织量子干涉的机制，并引入了一种新的完美图族，这些图在无需谱调谐或工程权重的情况下支持长时间的量子相干性。 显示英文摘要

摘要： We study quantum coherence in continuous-time quantum walks on perfect graphs generated by the symmetric lift ${\mathrm{HL}}'_2(G)$, a canonical, unweighted, undirected construction defined as the line graph of a bipartite double cover of $G$. This lift acts as both a coherence-preserving and coherence-inducing transformation: it preserves and scales structured quantum interference in highly symmetric base graphs, and induces sustained coherence in random or weakly structured ones. In small graphs such as $K_4$, $K_5$, and the Petersen graph, where quantum walks exhibit sharp revivals and high return probability, repeated $\mathrm{HL}'_2$ lifting produces towers of perfect graphs with thousands to tens of thousands of vertices that retain periodic or quasi-periodic coherence. When applied to random regular or Erd\H{o}s--R\'enyi graphs with flat or decaying return behavior, the lift introduces structured interference and significant amplification of mean and peak return probabilities. To quantify these effects, we evaluate standard coherence metrics from quantum resource theory, including inverse participation ratio (IPR), purity, relative entropy of coherence, and the logarithmic coherence number. These measures confirm that $\mathrm{HL}'_2$ lifting delocalizes eigenstates, increases coherence entropy, and expands the basis support of quantum states. These results demonstrate that $\mathrm{HL}'_2$ is a scalable and structurally grounded mechanism for organizing quantum interference, and introduce a new family of perfect graphs that support long-time quantum coherence without spectral tuning or engineered weights.