论文标题
优化在一维晶格中多粒量子行走的传播
Optimization for the propagation of a multiparticle quantum walk in a one-dimensional lattice
论文作者
论文摘要
量子步行是经典随机步行的量子，表现出非古典行为，并在各个方面都优于经典随机行走。众所周知，单个粒子可以通过离散时间量子步行传播，其二次时间缩放位置分布的差异，在经典的随机步行中击败线性时间缩放。在本文中，我们考虑了一维晶格中多个颗粒的离散时间量子步行，并研究了关节硬币态的优化以增强晶格中颗粒的空间传播。我们研究了长期极限以多个颗粒的位置分布的渐近演化，并通过分析优化关节硬币状态，以得出量子行走演化后粒子之间位置分布的最大方差。一个有趣的结果是，优化的硬币状态始终具有特定的交换对称性，可以以两个断开连接的完整子图组成的图来表征，而交换对称性可以显着影响粒子之间的位置相关性，显示了硬币对称性在多个粒子传播中的关键作用。我们进一步研究了优化的硬币状态的纠缠，以显示硬币相关性与颗粒位置分布的关系。
The quantum walk is a quantum counterpart of the classical random walk that exhibits nonclassical behaviors and outperforms the classical random walk in various aspects. It has been known that a single particle can be propagated by a discrete-time quantum walk with a quadratic time scaling in the variance of position distribution, beating the linear time scaling in a classical random walk. In this paper, we consider the discrete-time quantum walk for multiple particles in a one-dimensional lattice, and investigate the optimization of the joint coin state to enhance the spatial propagation of the particles in the lattice. We study the asymptotic evolution of position distribution for multiple particles in the long-time limit, and analytically optimize the joint coin state to derive the maximum variance of the position distribution between the particles after the evolution of the quantum walk. An interesting result is that an optimized coin state always possesses specific exchange symmetry which can be characterized by a graph consisting of two disconnected complete subgraphs and the exchange symmetry can significantly influence the position correlations between the particles, showing the critical role of coin symmetry in the propagation of multiple particles by the quantum walk. We further study the entanglement of the optimized coin states to show the relation of the coin correlations to the particle position distribution.
