【作者】 张欣；

【导师】 薛鹏； 汪军；

【作者基本信息】 东南大学 ， 物理学， 2017， 硕士

【摘要】 经典的随机行走已经被广泛用于很多领域。经典行走在量子世界的对应-量子行走,与经典行走相比具有许多不同的性质。量子行走自1993年被提出后,就成为越来越多科研工作者探讨的热门话题。量子行走的速度要比经典行走快二次方倍,所以量子行走在发展算法方面具有更高的效率,并且是已被证明的能够用来构建通用的量子计算模型的简便方法。目前,量子行走在研究量子计算领域非常可靠,可以用来尝试解决很多物理,计算机科学,以及工程学等开放性的难题,前景令人非常的兴奋和激动。为了更好的发挥量子行走的作用,本文对量子行走做了更深入的探讨。主要的工作分为以下两个方面:第一,首先分析讨论了加依赖于位置的二次方的位相缺陷的一维量子行走的特征。在一些限定的条件下,行走者能够在固定的步数内回到初始位置,也即这种存在位相缺陷的量子行走具有准周期性。并且随着行走步数的增加回到初始位置的几率不断衰减。另外衰减的程度是与位相调制参数2π(p/q)相关,随着位相调制参数的增加,行走者回到初始位置的几率衰减程度增加。行走者回到初始位置的几率分布出现周期性的现象,并且周期的数值随位相调制参数的改变而改变。当行走的步数比较大时,行走者位置的几率分布呈现震荡衰减现象。第二,提出了二维量子行走的物理实现方案。一维量子行走已在很多体系中实现了,目前仅有寥寥可数的方案能够实现二维行走。但是大量的量子过程必须要在二维或更高维的量子行走中才能够实现。本篇文章利用线性光学元件,设计了合理有效的方案实现普适的二维量子行走。并且介绍了一种通过将光子的空间模式增加进来,扩大硬币的希尔伯特空间的维度的来实现多维量子行走的方法。随着行走步数的增加,方案中用到的实验元件呈线性增加,所以本篇文章提出的量子行走方案更易于实验实现。更多还原

【Abstract】 Classical random walk has been widely used in many fields.Quantum random walk-a quantum counterpart of classical walk,has different features with classical walk.Since it was put forward in 1993,it has become a hot topic for more and more researchers.Quantum walk spread quadratically faster than classical walk.Thus quantum walk would be more efficient in the development of the algorithm,and can be used to build a general quantum computing model.Nowadays,quantum walk is a trustable way to the research of quantum computation and is full of exciting open problems for physicists,computer scientists and engineers.In order to play the role of quantum walk better,we made a more indepth study of the quantum walk.In this paper,we first discussed the characteristics of one dimensional quantum walk with quadratic position-dependent phase disorder.Under certain conditions,the walker will return to the initial position within a fixed number of steps.In addition,the degree of attenuation is related to the phase modulation parameters.With the increase of the phase modulation parameters,the probability of walker returning back to the initial position is increased.The probability distribution is periodic,and the period varies with the changing of phase modulation parameters.When the number of steps is large enough,the probability distribution shows the trend of oscillatory attenuation.Secondly,we propose a scheme to realize two dimensional quantum walk.One dimensional quantum walk has been realized in many systems.There are only very few schemes to achieve two dimensional quantum walk.However,a large number of quantum processes must be realized in two-dimensional or higher dimensional quantum walk.In this paper,we use linear optical elements to design a reasonable and effective scheme to realize the universal two-dimensional quantum walk.And a method of expanding the dimension of the Hilbert space of coins is introduced.By increasing the spatial modes of photons,the purpose of expanding the Hilbert space of coins is achieved.And the number of experimental elements required in our scheme increase linearly with the growth of steps.Thus our scheme can be used to implement a large number of steps of multi-dimensional quantum walk feasibility and stability.更多还原