Two-dimensional Quantum Walk Models

Dan Li, Michael Mc Gettrick, Weiwei Zhang +1 more

Dan Li, Michael Mc Gettrick, Weiwei Zhang +1 more

友之 星谷

Peng Xue

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.

Jozef Košík

Abstract We present an overview of two models of quantum random walk. In the first model, the discrete quantum random walk, we present the explicit solution for the recurring amplitude of the quantum random walk on a one-dimensional lattice. We also introduce a new method of solving the problem of random walk in the most general case and use it to derive the hitting amplitude for quantum random walk on the hypercube. The second is a special model based on a local interaction between neighboring spin-1/2 particles on a one-dimensional lattice. We present explicit results for the relevant quantities and obtain an upper bound on the speed of convergence to limiting probability distribution.

João Fernando Doriguello Diniz