Exploiting the coherent medium approximation, I investigate a random walk on objects distributed randomly in continuous space when jump rate depends distance between two adjacent objects. In one dimension, it is shown that decays exponentially long limit, non-diffusive to diffusive transition occurs as density of sites increased. three dimensions, exists has super Gaussian decay.

Quantum walks are promising tools based on classical random walks, with plenty of applications such as many variants optimization. Here we introduce the semiclassical in discrete time, which algorithms that combines and quantum dynamics. Specifically, a walk can be understood where transition matrix encodes evolution. We have applied this algorithm to Szegedy’s walk, any arbitrary weighted grap...

The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one dimensional QRW. Then, the probability distributions on the positions induced by QRW in these algorithms are investigated, which also indicates the possibility of ob...

Jiangfeng Du,* Hui Li, Xiaodong Xu, Mingjun Shi, Jihui Wu, Xianyi Zhou, and Rongdian Han Structure Research Laboratory and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 2 Department of Physics, Faculty of Science, National University of Singapore, Lower Kent Ridge, Singapore 119260, Republic of Singapore Harrison M. Randall Laboratory of...