Averaging in SU(2) open quantum random walk

We study the average position and the symmetry of the distribution in the SU（2） open quantum random walk （OQRW）. We show that the average position in the central limit theorem （CLT） is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT.

Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

In this paper we define direct product of graphs and give a recipe for obtaining probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph is obtained by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determining probability of walk on compficated graphs. Using this method, we calculate the probability of Continuous-time classical and quantum random walks on many of finite direct product Cayley graphs （complete cycle, complete Kn, charter and n-cube）. Also, we inquire that the classical state the stationary uniform distribution is reached as t→∞ but for quantum state is not always satisfied.

Alternative Coins for Quantum Random Walk Search Optimized for a Hypercube

The present paper is focused on non-uniform quantum coins for the quantum random walk search algorithm. This is an alternative to the modification of the shift operator, which divides the search space into two parts. This method changes the quantum coins, while the shift operator remains unchanged and sustains the hypercube topology. The results discussed in this paper are obtained by both theoretical calculations and numerical simulations.

The effect of phase fluctuation and beam splitter fluctuation on two-photon quantum random walk

In the optical quantum random walk system,phase nuctuation and Deam splitter uuctuation are two unavoldable decoherence factors.These two factors degrade the performance of quantum random walk by destroying coherence,and even degrade it into a classical one.We propose a scheme for the simulation of quantum random walk using phase shifters,tunable beam splitters,and photodetectors.This proposed scheme enables us to analyze the effect of phase fluctuation and beam splitter fluctuation on two-photon quantum random walk.Furthermore,it is helpful to guide the control of phase fluctuation and beam snlitter fluctuation in the exneriment.

Optimized quantum random-walk search algorithm for multi-solution search

This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.

Decoherence in optimized quantum random-walk search algorithm

This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative.

Effects of systematic phase errors on optimized quantum random-walk search algorithm

This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover＇s algorithm.

Return Probability of the Open Quantum Random Walk with Time-Dependence

We study the open quantum random walk (OQRW) with time-dependence on the one-dimensional lattice space and obtain the associated limit distribution. As an application we study the return probability of the OQRW. We also ask, "What is the average time for the return probability of the OQRW?"

Optical implementation of quantum random walks using weak cross-Kerr media

Weak cross-Kerr media provides additional degrees of freedom of qubits in quantum information processing.In this paper,by exploiting weak cross-Kerr nonlinearity,we propose an optical implementation scheme of one-dimensional quantum random walks. The random walks are described by the interaction of single photons with cross-Kerr media.The proposed scheme can also be used to implement one-dimensional quantum random walks on an infinite line.

Average position in quantum walks with a U(2) coin

We investigated discrete-time quantum walks with an arbitary unitary coin.Here we discover that the average position x=max（x） sin（α＋γ）,while the initial state is 1/2～（1/2）（｜0L＋i｜0R）.We verify the result,and obtain some symmetry properties of quantum walks with a U（2） coin with ｜0L and ｜0R as the initial state.

Brun-Type Formalism for Decoherence in Two-Dimensional Quantum Walks

We study decoherence in the quantum walk on the xy-plane. We generalize the method of decoherent coin quantum walk, introduced by [T.A. Brun, et al., Phys. Rev. A 67 （2003） 032304], which could be applicable to all sorts of decoherence in two-dimensional quantum walks, irrespective of the unitary transformation governing the walk. As an application we study decoherence in the presence of broken line noise in which the quantum walk is governed by the two-dimensional ttadamard operator.

Ito’s Formula for the Discrete-Time Quantum Walk in Two Dimensions

Following Konno [1], it is natural to ask: What is the Ito’s formula for the discrete time quantum walk on a graph different than Z, the set of integers? In this paper we answer the question for the discrete time quantum walk on Z2, the square lattice.

基于交替量子随机行走的改进AES和离散余弦变换的图像加密算法

随着科学技术手段飞速发展,图像加密算法被破解的风险也逐渐增加.AES(advanced encryption standard)算法虽然性能优越,但也存在着密钥固定等问题,未来量子计算机的问世将会对此造成重大威胁.首先,该文采用离散余弦变换(discrete cosine transform,DCT)对明文图像进行DCT域的变换;其次,利用交替量子随机行走构造概率分布矩阵,对概率分布矩阵进行预处理,与DCT后的明文进行逐位异或的操作;最后,计算概率分布矩阵的奇异值,并给出对应的十六进制表达式作为AES的密钥,随机提取概率分布矩阵的一个元素,按照AES算法的编码规则构建轮常量Rcon,进而改进AES算法的加密迭代函数.测试结果表明,该算法具有很好的加密效果和较高的鲁棒性,密文图像相邻像素在3个方向上的相关系数可以达到0.0015的显著效果.

基于Hopfield网络“伪吸引子”与交替量子随机行走的抗攻击彩色图像加密方案

近年来,图像信息的安全传输已成为互联网领域的重要研究课题.本文提出了一种将Hopfield网络伪吸引子特性与交替量子随机行走概率分布矩阵相结合的抗攻击彩色图像加密方案.研究发现,若控制Hopfield网络状态矩阵的精度参数,将交替量子随机行走产生的概率分布矩阵4分块中的1个子块M1作为伪随机数矩阵参与加密,Hopfield网络的训练矩阵与输入矩阵分别为矩阵M1的4分块中的2个对角子块之一时,能产生伪吸引子.该伪吸引子的矩阵形式通过张量运算、进制转换等处理后,能作为密钥矩阵对原始图像进行基于空间域上的像素值排序自适应置乱以及元素数值的混淆,生成加密图像.其中,密钥矩阵是图像加密中的关键部分,具备优异统计学属性的密钥矩阵能极大的提高图像加密的效果.本文所提加密方案在统计学特性测试中,实现了平均信息熵为7.999 4,像素数改变率的平均值为99.621 8%,统一平均变化强度的平均值为33.537 9%,平均相关性为0.003 9等.同时本文还对所提加密方案进行了各种噪声模拟测试以验证其实际应用中遇到常见噪声及攻击干扰情况下的鲁棒性.

量子计算机:量子算法与物理实现

量子算法与物理实现是量子计算机研究中的两个基本问题。本文首先总结了相关领域的主要进展,并讨论了有代表性的量子算法,特别介绍了用于求解线性方程组的量子算法,分析了影响新量子算法提出的因素。然后,探讨了物理实现的迪文森佐判据,并介绍了典型的实现方案及性能比较。同时,也关注了对量子计算机研究持有异议的观点。最后,对量子计算机的新研究方向作了探讨。

工作电流对二频机抖激光陀螺角随机游走影响的研究

理论上分析了二频机抖激光陀螺中由量子噪声和抖动噪声产生的角随机游走的影响因素;讨论了工作电流对量子噪声、比例因子的影响;根据陀螺参数定量的估计了抖动噪声产生的角随机游走的数量级。实验结果表明:电流在全测量范围内对陀螺比例因子的影响约为5ppm;对于本单位自行生产的二频机抖激光陀螺来说,由抖动噪声产生的角随机游走是总角随机游走的主要贡献者,比量子噪声产生的角随机游走大约高一个数量级。

有机半导体Terazulene单晶双极电荷传输性质的理论研究

利用密度泛函方法计算Terazulene单晶的重组能和分子间电子耦合,结合Marcus电荷转移速率理论以及随机行走技术模拟电荷迁移率,分别研究Terazulene单晶中电子与空穴的角分辨各向异性迁移率及平均迁移率.结果表明,Terazulene单晶具有均衡的电子与空穴传输性质,并分析了具体原因.由于p型有机半导体Naphthodithiophene(NDT)的分子共轭长度与Terazulene接近,通过比较Terazulene单晶和NDT单晶中电荷传输的差异,从理论上理解分子结构对有机半导体材料电荷传输性能的影响.

Return Probability of the Fibonacci Quantum Walk

In this paper the return probability of the one-dimensional discrete-time quantum walk is studied. We derive probabilistic formulas for the return probability related to the quantum walk governed by the Fibonacci coin.

基于DNA编码与交替量子随机行走的彩色图像加密算法

近年来,图像加密技术备受关注.随着人们对通信隐私及网络安全重视程度的提高,对信息加密技术的要求更加严格,图像作为信息的载体之一,因携带信息的有效性和生动性而受到重视.本文提出一种基于DNA编码与交替量子随机行走的彩色图像加密算法.量子随机行走作为出色的密码学工具参与算法流程中各个部分,DNA编码作为核心加密方式完成算法.本文详细描述加密、解密流程,并对所提出算法进行仿真实验验证与结果分析.仿真阶段设计模拟密钥参数,编码进行彩色图像加密、解密实验,并进行了相关分析.实验结果表明,本文提出的彩色图像加密算法能够进行安全有效的彩色图像加密,且相关分析表示其加密后图像直方图平稳、像素相关性系数趋近于0、密钥空间2^(128),三通道信息熵达到7.997以上,能够抵御统计攻击、穷举攻击等攻击手段.此外,DNA编码除新颖的编码及运算方式之外还有其独特的生物学特性,为密码学的研究提供了新的思路与方向.

基于IBM Q平台的量子算法研究

为探究多比特量子算法在量子芯片和模拟器中的实现现状,分别在IBM量子芯片和模拟器上运行Grover搜索算法、量子随机行走算法以及量子傅里叶变换算法。针对2 bit Grover搜索算法和2 bit量子随机行走算法,分析测量次数对运行结果的影响并选用最高可模拟次数对量子芯片和模拟器的运算结果进行比对。设计并运行5 bit量子傅里叶变换算法和3 bit Grover搜索算法,分别采用IBM Q模拟器进行最高次数的模拟。实验结果表明,量子芯片测试结果并没有随测量次数的增加而优化,模拟器计算结果的准确度明显优于量子芯片。