量子Harr小波变换及其逻辑实现

由于量子计算相比于经典计算的突出优越性,量子小波变换的实现对于小波变换的理论完善和实际应用具有重要的意义.在给出了正移置换矩阵的量子逻辑线路后,运用矩阵扩展Kronecker积,基于W-H变换和正移置换矩阵对Harr小波矩阵进行了分解,给出了相应的数学表达式和量子逻辑线路.并对其实现复杂度和物理实现可能性进行了分析.     

量子Haar小波变换算法设计及应用

设计了基于通用量子语言Q_language的量子Haar小波变换算法,该算法对于小波变换的应用和量子算法的完善具有重要的意义.分析了3个量子位Haar小波变换过程,给出了量子Haar小波变换算法的Q_language语言描述,并分析得出其时间和空间复杂度,然后给出了实现量子Haar小渡变换应用方法.     

量子Daubechies-D（4）小波变换算法及应用研究

由于量子计算相比经典计算具有突出的优越性,设计基于通用量子语言Q_language的量子Daubechies-D（4）小波变换算法对于小波变换的应用和量子算法的完善具有重要的意义。文章分析了Daubechies-D（4）小波变换过程,给出了量子Daubechies-D（4）小波变换算法的Q_language语言描述,并分析得出其时间和空间复杂度,给出了实现量子Daubechies-D（4）小波变换应用方法。     

多量子位量子小波变换逻辑线路及仿真实现

由于量子计算相比于经典计算的突出优越性,量子小波变换的实现对于小波变换的理论完善和实际应用具有重要的意义,而逻辑线路是该变换实现的基础。应用多量子算符代数理论设计了3量子位Haar和D^（4）小波变换的逻辑线路,进而将逻辑线路转化成核磁共振系统可以实现的脉冲序列,并在量子计算仿真器（QCE）上进行了模拟实现,验证了逻辑线路的合理性。     

量子图像水印技术在电力大数据中的应用

为保证电力大数据的安全和处理效果,本文提出一种基于量子图像水印技术的嵌入及提取方法。该方法首先将原载体灰色图像用量子表示,并利用量子小波变换四次分解原载体图像得到子图,再通过量子离散余弦变换对子图进行系数转换。通过对系数矩阵进行奇异值分解得到对角矩阵,再利用量子广义Arnold变换和Logistic映射对水印进行置乱,并进行奇异值分解,从而实现量子水印的嵌入。嵌入的水印图像被分解后,每个像素的灰度信息为一个均衡的量子叠加态,测量后整幅图像为一个均匀的白噪声。水印图像的提取过程为嵌入的逆过程。仿真结果表明,相对经典图像水印,量子图像水印技术计算复杂度更低,计算速度更快,嵌入的水印图像具有很好的安全性,并且不影响载体图像的视觉效果。     

基于矩阵方法的量子纠错码构造

根据由简单无向图构造的量子纠错码与量子稳定子码的关系,利用与图对应的对称矩阵直接给出量子稳定子码的稳定子,由此提出一种基于矩阵方法的量子纠错码构造方法,通过将子矩阵变换为循环矩阵,找到满足特殊性质的矩阵,并证明对任意素数p>3,量子MDS码［［9,5,3］］p和［［8,4,3］］p存在,对任意素数p>7,量子MDS码［［9,3,4］］p存在。     

基于矩阵初等变换的量子可逆逻辑电路双向综合算法

基于矩阵初等变换,提出了量子可逆逻辑电路双向综合算法。该算法依据两数字间的汉明距离,通过交换矩阵行号或矩阵元素对量子可逆逻辑电路的矩阵进行初等行变换。在变换的过程中,利用邻接矩阵的电路转化规则,生成任意给定置换的量子可逆逻辑电路。与其它同类算法相比,由于不需要穷尽搜索,该算法的时空复杂度有大幅降低;又由于采用任意n量子扩展通用Toffoli门,该算法可综合任一置换(奇或偶置换)的量子可逆逻辑电路,并且电路中门的数量有所减少。     

基于快速Jacket变换的量子纠错码*

受到基于Pauli矩阵的快速Jacket变换的启发,提出一种利用分块Jacket矩阵简化量子纠错码编码方案的方法。与已有的量子纠错码构造法相比,在构造量子Jacket码的稳定子的时候,不需要检验经典纠错码的“自对偶”条件,因此,它能促使高效地利用由分块Jacket矩阵产生的Pauli矩阵群的交换子群直接生成辛内积为零的独立向量,在此基础上构造出码长较大、参数较好的量子纠错码。该量子Jacket码具有构造快速、纠错行为渐进好的优点。     

数字图像的小波算法及快速小波变换

小波变换是近几年来兴起的一种新的变换方法 ,主要特点是通过变换能够充分突出问题某些方面的特征 ,因此 ,小波变换在许多领域都得到了成功的应用 ,特别是其离散数字算法在图像分析领域取得了重大突破。但是 ,小波变换的算法一般相对来说比较复杂 ,而其处理速度往往也成为制约其发展的瓶颈。该文从小波变换的基础出发 ,给出了一种针对数字图像的小波矩阵算法 ,并实现了快速小波变换的算法和流程 ,为实际应用编程提供了有效的理论依据     

三值量子基本门及其对量子Fourier变换的电路实现

理论上可以把量子基本门组合在一起来实现任何量子电路和构建可伸缩的量子计算机。但由于构建量子线路的量子基本门数量庞大,要正确控制这些量子门十分困难。因此,如何减少构建量子线路的基本门数量是一个非常重要和非常有意义的课题。提出采用三值量子态系统构建量子计算机,并给出了一组三值量子基本门的功能定义、算子矩阵和量子线路图。定义的基本门主要包括三值量子非门、三值控制非门、三值Hadamard门、三值量子交换门和三值控制CR_k门等。通过把量子Fourier变换推广到三值量子态,成功运用部分三值量子基本门构建出能实现量子Fourier变换的量子线路。通过定量分析发现,三值量子Fourier变换的线路复杂度比二值情况降低了至少50%,表明三值量子基本门在降低量子计算线路复杂度方面具有巨大优势。     

Three-dimensional quantum wavelet transforms

Wavelet transform is being widely used in the field of information processing. One-dimension and two-dimension quantum wavelet transforms have been investigated as important tool algorithms. However, three-dimensional quantum wavelet transforms have not been reported. This paper proposes a multi-level three-dimensional quantum wavelet transform theory to implement the wavelet transform for quantum videos. Then, we construct the iterative formulas for the multi-level three-dimensional Haar and Daubechies D4 quantum wavelet transforms, respectively. Next, we design quantum circuits of the two wavelet transforms using iterative methods. Complexity analysis shows that the proposed wavelet transforms offer exponential speed-up over their classical counterparts. Finally, the proposed quantum wavelet transforms are selected to realize quantum video compression as a primary application. Simulation results reveal that the proposed wavelet transforms have better compression performance for quantum videos than two-dimension quantum wavelet transforms.     

A quantum Jensen–Shannon graph kernel for unattributed graphs

In this paper, we use the quantum Jensen–Shannon divergence as a means of measuring the information theoretic dissimilarity of graphs and thus develop a novel graph kernel. In quantum mechanics, the quantum Jensen–Shannon divergence can be used to measure the dissimilarity of quantum systems specified in terms of their density matrices. We commence by computing the density matrix associated with a continuous-time quantum walk over each graph being compared. In particular, we adopt the closed form solution of the density matrix introduced in Rossi et al. (2013) 27 and 28 to reduce the computational complexity and to avoid the cumbersome task of simulating the quantum walk evolution explicitly. Next, we compare the mixed states represented by the density matrices using the quantum Jensen–Shannon divergence. With the quantum states for a pair of graphs described by their density matrices to hand, the quantum graph kernel between the pair of graphs is defined using the quantum Jensen–Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets from both bioinformatics and computer vision. The experimental results demonstrate the effectiveness of the proposed quantum graph kernel.     

Moment quantization of inhomogeneous spin ensembles

Robust excitation of a large spin ensemble is a long-standing problem in the field of quantum information science and engineering and presents a grand challenge in quantum control. A formal theoretical treatment of this task is to formulate it as an ensemble control problem defined on an infinite-dimensional space. In this paper, we present a distinct perspective to understand and control quantum ensemble systems. Instead of directly analyzing spin ensemble systems defined on a Hilbert space, we transform them to a space where the systems have reduced dimensions with distinctive network structures through the introduction of moment representations. In particular, we illustrate the idea of moment quantization for a spin ensemble and illuminate how this technique leads to a dynamically equivalent control system of moments. This equivalence enables the control of spin ensembles through the control of their moment systems, which in turn creates a new control analysis and design paradigm for quantum ensemble systems based on the use of truncated moment systems.     

The quantum realization of Arnold and Fibonacci image scrambling

The quantum Fourier transform, the quantum wavelet transform, etc., have been shown to be a powerful tool in developing quantum algorithms. However, in classical computing, there is another kind of transforms, image scrambling, which are as useful as Fourier transform, wavelet transform, etc. The main aim of image scrambling, which is generally used as the preprocessing or postprocessing in the confidentiality storage and transmission, and image information hiding, was to transform a meaningful image into a meaningless or disordered image in order to enhance the image security. In classical image processing, Arnold and Fibonacci image scrambling are often used. In order to realize these two image scrambling in quantum computers, this paper proposes the scrambling quantum circuits based on the flexible representation for quantum images. The circuits take advantage of the plain adder and adder modulo $N$ to factor the classical transformations into basic unitary operators such as Control-NOT gates and Toffoli gates. Theoretical analysis indicates that the network complexity grows linearly with the size of the number to be operated.     

CUGatesDensity—Quantum circuit analyser extended to density matrices

CUGatesDensity is an extension of the original quantum circuit analyser CUGates (Loke and Wang, 2011) [7] to provide explicit support for the use of density matrices. The new package enables simulation of quantum circuits involving statistical ensemble of mixed quantum states. Such analysis is of vital importance in dealing with quantum decoherence, measurements, noise and error correction, and fault tolerant computation. Several examples involving mixed state quantum computation are presented to illustrate the use of this package.     

小波域音频水印综述

该文对基于小波变换的数字音频水印算法做了概要性的介绍,由于其良好的局部性时频分析特性和多分辨率分析,小波变换在数字音频版权保护领域有很好的应用效果。对基于小波变换的数字水印技术的相关概念和现有方法进行了描述与分析,另外,对基于小波变换的数字音频水印技术的未来发展方向和前景进行了预测。     

边界镜像对称延拓双正交小波变换矩阵的构造

计算小波变换的Mallat算法需要进行逐级分解和重构,对于有限长信号的小波变换来说,为了保证其完全重构,有必要对其进行边界延拓。基于边界周期延拓的小波变换算法极易实现,也常见于文献,而边界对称延拓较周期延拓则更适合用于信号和图像的处理,但基于边界对称延拓的小波变换矩阵实现方法却很少出现在文献中。为了用矩阵-向量乘积实现信号的小波变换,给出了一种在信号镜像对称延拓方式下,任意深度小波变换矩阵的构造方法,并证明了该延拓方式下实现Mallat算法的完全重构条件。作为实例,绘出了B ior3.3小波的分解和重构矩阵的基向量及波形图。将构造的变换矩阵用于基于小波的图像处理中,不仅可以避免逐级迭代,大大简化运算量,而且边界效应也明显减少。     

一种基于[7,1]CSS纠错码的量子密钥分配协议

量子密钥分配协议具有可证明的绝对安全性,但是由于量子信道噪声的作用,量子比特在传输过程中容易产生错误,从而降低量子密钥分配的效率。对此,根据量子纠错理论,利用Hamming码构造一种[7,1]CSS纠错码,并结合BB84协议,提出一种改进的量子密钥分配协议。通过理论分析与数值计算,对比改进协议与BB84协议在含噪声量子信道中的传输错误率,结果表明改进的量子密钥分配协议相比于BB84协议提高了对信道噪声的抵抗能力。