论文标题
非理性的量子步行
Irrational quantum walks
论文作者
论文摘要
图G的邻接矩阵是在G的顶点进行连续时间量子步行的哈密顿量。尽管邻接矩阵的条目是整数，但其特征值通常是不合理的，因此，步行的行为通常不是周期性的。因此，我们通常只能计算到步行参数的数值近似值。在本文中，我们开发了理论，以精确研究综合哈密顿量产生的任何量子步行。结果，我们提供了精确的方法来计算混合矩阵的平均值，并确定在给定的图中是否出现相当好（或几乎）完美的状态传输。我们还使用我们的方法研究量子步行矩阵条目引起的美丽曲线的几何特性，并讨论这些结果的可能应用。
The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenvalues are generally irrational and, because of this, the behaviour of the walk is typically not periodic. In consequence we can usually only compute numerical approximations to parameters of the walk. In this paper, we develop theory to exactly study any quantum walk generated by an integral Hamiltonian. As a result, we provide exact methods to compute the average of the mixing matrices, and to decide whether pretty good (or almost) perfect state transfer occurs in a given graph. We also use our methods to study geometric properties of beautiful curves arising from entries of the quantum walk matrix, and discuss possible applications of these results.
