Zeng Meng, Yong Ee Hou
Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore.
Sci Rep. 2017 Sep 20;7(1):12024. doi: 10.1038/s41598-017-12077-0.
Quantum Walk (QW) has very different transport properties to its classical counterpart due to interference effects. Here we study the discrete-time quantum walk (DTQW) with on-site static/dynamic phase disorder following either binary or uniform distribution in both one and two dimensions. For one dimension, we consider the Hadamard coin; for two dimensions, we consider either a 2-level Hadamard coin (Hadamard walk) or a 4-level Grover coin (Grover walk) for the rotation in coin-space. We study the transport properties e.g. inverse participation ratio (IPR) and the standard deviation of the density function (σ) as well as the coin-position entanglement entropy (EE), due to the two types of phase disorders and the two types of coins. Our numerical simulations show that the dimensionality, the type of coins, and whether the disorder is static or dynamic play a pivotal role and lead to interesting behaviors of the DTQW. The distribution of the phase disorder has very minor effects on the quantum walk.
由于干涉效应，量子行走（QW）与其经典对应物具有非常不同的输运特性。在这里，我们研究在一维和二维中遵循二元或均匀分布的具有在位静态/动态相位无序的离散时间量子行走（DTQW）。对于一维，我们考虑哈达玛硬币；对于二维，我们考虑用于硬币空间旋转的2能级哈达玛硬币（哈达玛行走）或4能级格罗弗硬币（格罗弗行走）。由于两种类型的相位无序和两种类型的硬币，我们研究了输运特性，例如逆参与率（IPR）、密度函数的标准差（σ）以及硬币-位置纠缠熵（EE）。我们的数值模拟表明，维度、硬币类型以及无序是静态还是动态起着关键作用，并导致DTQW出现有趣的行为。相位无序的分布对量子行走的影响非常小。
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