In this article, we consider a spin-spin interaction network governed by $XX + YY$ Hamiltonian. The vertices and edges of the network represent the spin objects and their interactions, respectively. We take a privilege to switch on or off any interaction, that assists us to perform multiple perfect state transfers in a graph simultaneously. We also build up a salable network allowing quantum communication between two arbitrary vertices. Later we utilize the combinatorial characteristics of hypercube graphs to propose a static routing schema to communicate simultaneously between a set of senders and a set of receivers in a planar network. Our construction is new and significantly powerful. We elaborate multiple examples of planar graphs supporting quantum routing where classical routing is not possible.

翻译：本文研究由$XX + YY$哈密顿量调控的自旋-自旋相互作用网络。网络的顶点与边分别代表自旋对象及其相互作用。我们拥有选择开启或关闭任意相互作用的特权，这有助于在网络中同时实现多个完美态传递。我们还构建了一个可扩展的网络，允许任意两个顶点之间的量子通信。随后利用超立方体图的组合特性，提出了一种静态路由方案，用于在平面网络中同时实现发送方集合与接收方集合之间的通信。该构造方案具有创新性且功能强大。我们通过多个平面图实例详细阐述了量子路由的实现，这些实例在经典路由中无法实现。