多体随机行走在量子系统中的呈现

项目名称： 多体随机行走在量子系统中的呈现

项目编号： No.11274272

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 李有泉

作者单位： 浙江大学

项目金额： 78万元

中文摘要： 量子随机行走具有完全不同于经典随机行走的性质，近年来逐渐受到人们的关注。目前实验上已经在若干物理体系中实现了量子随机行走，这为人们利用量子随机行走模拟研究量子体系中的新奇物理现象提供了可能性。此外，随着近年来量子信息的发展，量子随机行走作为量子计算中有潜力的算法也被广泛研究。值得注意的是，与单体量子行走相比，多体量子行走能够呈现出更加丰富的现象。并且，目前实验上已经实现了两体量子随机行走，并且研究了其关联等性质。与实验相比，理论上关于多体量子随机行走的研究尚比较匮乏。在本项目中，我们将研究不同量子体系中多体量子随机行走的特性，揭示体系参数及初始状态对随机行走性质的影响，进一步预言一些新的量子现象。同时，我们将从理论上提出一些新的可以实现量子随机行走的体系，为实验提供理论参考。此外，我们将用该量子随机行走模拟研究量子信息中的算法、退相干等问题。

中文关键词： 量子随机行走；经典系统；量子系统；动力学性质；相干度

英文摘要： The properties of quntum random walk are different from those of classical random walk, which is attracting more and more attention recently. Now the quantum random walk has been realized in some physical systems. So it is possible for one to simulate and study some novel effects in quantum systems via the quantum random walk. Additionally, with the development of quantum information, the quantum random walk, as a potential algorithm, has been researched widely. Note that comparing to one-body quantum random walk, many-body quantum random walk can exhibit more fascinating phenomena.Since the two-body quantun random walk has been realized in experiment, and some corresponding properties have been studied, there are few theoretical works focused on many-body quantum random walk. In this project, we will study the properties of many-body quantum random walk in different quantum systems and show the effects of the parameters and the initial states of the system on the quantum random walk in order to predict some new quantum phenonena. We also will give some quantum system where the quantum random walk may be realized, which may be useful for the experiment. Additionally, we will use such a quantum random walk system to simulate some problems, like the algorithm and decoherent etc, in quantum information.

英文关键词： quantum walk；classical system；quantum system；dynamical property；degree of coherence