非理性量子漫步

IF 1.6 2区 数学 Q2 MATHEMATICS, APPLIED
G. Coutinho, P. Baptista, C. Godsil, Thomás Jung Spier, R. Werner
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引用次数: 1

摘要

图G的邻接矩阵是G顶点上连续时间量子行走的哈密顿量。虽然邻接矩阵的条目是整数,但它的特征值通常是无理性的,因此,行走的行为通常不是周期性的。因此,我们通常只能计算步行参数的数值近似值。在本文中,我们发展了一个理论来精确地研究由积分哈密顿量产生的任何量子行走。因此,我们提供了精确的方法来计算混合矩阵的平均值,并决定在给定的图中是否发生相当好的(或几乎)完美的状态转移。我们还用我们的方法研究了由量子行走矩阵的入口产生的美丽曲线的几何性质,并讨论了这些结果的可能应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Irrational Quantum Walks
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.
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
19
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