二维量子随机行走及其物理实现

Two-dimensional Quantum Random Walk and its Physical Realization

近年来量子随机行走相关课题因其非经典的特性,已经成为越来越多科研人员的研究热点。这篇文章中我们回顾了一维经典随机行走和一维量子随机行走模型,并且在分析两种二维经典随机行走模型的基础上,我们构建二维量子随机行走模型。通过对随机行走者的位置分布标准差的计算,我们可以证明基于这种二维量子随机行走模型的算法优于其他上述随机行走。除此之外,我们提出一个利用线性光学方法的实验方案,实现这种二维量子随机行走模型。

Quantum random walks have been much studied recently, largely due to their highly non-classical behaviors. In this paper, we review the classical and quantum random walks of one-dimensional, and analyze two classical two-dimensional models and compare them. Furthermore we propose a two-dimensional quantum random walk algorithm. We compute the standard deviation, thereby proving our two-dimensional algorithm is superior to that of one-dimension. We propose a scheme, which is based on single photon with pairs of qubits, to implement it.