控制根积中的量子态转移
Controlling quantum state transfer in rooted products
- Brigham Young University – Idaho（杨百翰大学爱达荷分校）
- Clarkson University（克拉克森大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明根积图可传递量子态转移性质，并利用强同谱顶点对和条件数控制，在稀疏图上构造高效高保真度态转移，即使原图无此性质。
AI中文摘要：
Godsil和McKay（1978）表明，根积是构造非同构但同谱的图对的有力工具。尽管缺乏便捷的张量积结构，我们证明根积对于构造具有良好量子态转移性质的图是有用的。特别地，我们证明了一个简单的传递原理：如果图$X$具有量子态转移，且$Y$是可控图，则它们的根积$X^Y$具有量子态转移（继承自$X$）。这补充了笛卡尔积保持完美态转移的一个众所周知的性质。然而，根积是显著更稀疏的图，更重要的是，即使$X$没有量子态转移，它也可以轻松地用于构造高效的高保真度态转移。我们的证明利用了根积产生大量强同谱顶点对的事实，并且其条件数可以由其悬挂子图控制。
英文摘要：
Godsil and McKay (1978) showed that the rooted product is a powerful tool for constructing non-isomorphic cospectral pairs of graphs. Despite lacking a convenient tensor product structure, we show that the rooted product is useful for constructing graphs with good quantum state transfer properties. In particular, we prove a simple transference principle: if a graph $X$ has quantum state transfer and $Y$ is a controllable graph, their rooted product $X^Y$ has quantum state transfer (inherited from $X$). This complements a folklore property of Cartesian product which preserves perfect state transfer. However, the rooted product is a significantly sparser graph and, more importantly, can be easily used to construct efficient high-fidelity state transfer even if $X$ has no quantum state transfer. Our proof exploits the fact that a rooted product creates a large number of strongly cospectral pairs of vertices and that its condition number can be controlled by its pendant subgraph.
