论文标题
二手步行的汉密尔顿人
Hamiltonians of Bipartite Walks
论文作者
论文摘要
在本文中，我们介绍了一个称为双方步行的离散量子步行模型。双方步道包括许多已知的离散量子步行型号，例如弧形散步，顶点脸步行。对于量子步行的过渡矩阵，有一个与之相关的哈密顿量。我们将研究双方步行的汉密尔顿人。令$ s $为偏斜的对称矩阵。我们主要对$ $的哈密顿人感兴趣。我们证明，当双方图的邻接矩阵可逆时，哈密顿量可以写成$是$ $。我们表明，弧形散步和顶点脚步是双方步行的特殊情况。通过汉密尔顿人，双方步行的现象导致了连续步行的现象。我们详细介绍了如何在路径上使用双方步行，以在连续步行中构建通用的完美状态转移。
In this paper, we introduce a discrete quantum walk model called bipartite walks. Bipartite walks include many known discrete quantum walk models, like arc-reversal walks, vertex-face walks. For the transition matrix of a quantum walk, there is a Hamiltonian associated with it. We will study the Hamiltonians of the bipartite walks. Let $S$ be a skew-symmetric matrix. We are mainly interested in the Hamiltonians of the form $iS$. We show that the Hamiltonian can be written as $iS$ if and only if the adjacency matrix of the bipartite graph is invertible. We show that arc-reversal walks and vertex-face walks are special cases of bipartite walks. Via the Hamiltonians, phenomena of bipartite walks lead to phenomena of continuous walks. We show in detail how we use bipartite walks on paths to construct universal perfect state transfer in continuous walks.
