一维格点上的离散时间量子行走
Discrete-time quantum walks on one-dimensional lattices
摘要：
本文研究了一维格点上的离散时间量子行走。我们发现，相干动力学依赖于初始状态和硬币参数。对于无限大的格点，我们导出了返回概率的显式表达式，该表达式具有标度行为$P(0,t)\sim t^{-1}$，并且不依赖于行走的初始状态。在长时间内，概率分布表现出不同的模式，这取决于初始状态，硬币参数和晶格尺寸。对于大的阈值$ε$，平均混合时间$M_ε$接近线性$N$（晶格的大小）中的极限概率。最后，我们在无限格点和偶数格点上引入了另一种量子行走，并证明了这种行走与具有对称初态和硬币参数的传统量子行走是等价的.
英文摘要：
In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the return probability, which shows scaling behavior $P(0,t)\sim t^{-1}$ and does not depends on the initial states of the walk. In the long-time limit, the probability distribution shows various patterns, depending on the initial states, coin parameters and the lattice size. The average mixing time $M_ε$ closes to the limiting probability in linear $N$ (size of the lattice) for large values of thresholds $ε$. Finally, we introduce another kind of quantum walk on infinite or even-numbered size of lattices, and show that the walk is equivalent to the traditional quantum walk with symmetrical initial state and coin parameter.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
