一种量子神经网络模型及改进学习算法

提出一种量子BP网络模型及改进学习算法,该BP网络模型首先基于量子学中一位相移门和两位受控非门的通用性,构造出一种量子神经元,然后由该量子神经元构造隐含层,采用梯度下降法进行学习。输出层采用传统神经元构造,采用基于改进的带动量自适应学习率梯度下降法学习。在UCI两个数据集上采用该模型及算法,实验结果表明该方法比传统的BP网络具有较好的收敛速度和正确率。     

Quantum Algorithms for Weighing Matrices and Quadratic Residues

Abstract. In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to devise new quantum algorithms. We show how the properties of a weighing matrix can be used to construct a problem for which the quantum query complexity is significantly lower than the classical one. It is pointed out that this scheme captures both Bernstein and Vazirani's inner-product protocol, as well as Grover's search algorithm. In the second part of the article we consider Paley's construction of Hadamard matrices, which relies on the properties of quadratic characters over finite fields. We design a query problem that uses the Legendre symbol χ (which indicates if an element of a finite field F _q is a quadratic residue or not). It is shown how for a shifted Legendre function f _s (i)=χ(i+s) , the unknown s ∈ F _q can be obtained exactly with only two quantum calls to f _s . This is in sharp contrast with the observation that any classical, probabilistic procedure requires more than log q + log ((1-ɛ )/2) queries to solve the same problem.     

Interference automata

We propose a computing model, the Two-Way Optical Interference Automata (2OIA), that makes use of the phenomenon of optical interference. We introduce this model to investigate the increase in power, in terms of language recognition, of a classical Deterministic Finite Automaton (DFA) when endowed with the facility of interference. The question is in the spirit of Two-Way Finite Automata With Quantum and Classical States (2QCFA) [A. Ambainis, J. Watrous, Two-way finite automata with quantum and classical states, Theoret. Comput. Sci. 287 (1) (2002) 299–311] wherein the classical DFA is augmented with a quantum component of constant size. We test the power of 2OIA against the languages mentioned in the above paper. We give efficient 2OIA algorithms to recognize languages for which 2QCFA machines have been shown to exist, as well as languages whose status vis-a-vis 2QCFA has been posed as open questions. Having a DFA as a component, it trivially recognizes regular languages. We show that our model can recognize all languages recognized by 1-way deterministic blind counter automata. Finally we show the existence of a language that cannot be recognized by a 2OIA but which can be recognized by an O(n³)$O\left(n^3\right)$ space Turing machine.     

Optimal computation with non-unitary quantum walks

Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times, respectively. Non-unitary quantum walks can provide a useful optimisation of these properties, producing a more uniform distribution on the line, and faster mixing times on the cycle. We investigate the interplay between quantum and random dynamics by comparing the resources required, and examining numerically how the level of quantum correlations varies during the walk. We show numerically that the optimal non-unitary quantum walk proceeds such that the quantum correlations are nearly all removed at the point of the final measurement. This requires only O(logT)$O(logT)$ random bits for a quantum walk of T$T$ steps.     

量子小波变换算法及线路实现

随着小波理论研究的深入,以及小波分析在信号分析和图像处理等领域的广泛应用,小波分析在量子计算领域中也越来越受到重视.应用置换矩阵、W-H变换矩阵和量子傅立叶变换矩阵来对Haar小波及D(4)小波变换矩阵进行分解,给出其算法,然后得出其完整的量子逻辑线路图,最后分析其复杂度.     

SHOR量子算法的优化及应用研究

Shor算法是目前最常用的算法之一.主要是基于Shor量子算法分解效率不高的问题作出的一些算法上的优化.通过对Shor算法的进一步分析,提出优化思想及对优化过程进行理论论证来论证算法分解效率的提高.最后讨论了Shor算法的现实意义以及应用研究.     

一种实数编码量子进化算法及其收敛性

基于量子计算理论和进化理论,提出一种新的量子进化算法--基于实数编码的量子进化算法(RQEA).不同于传统进化算法的单点编码和量子进化算法的量子比特编码,该算法以实数矩形区域表示基因,一条染色体携带多个个体信息,利用量子态叠加和相干机理,通过叠加、变异及自学习来完成进化过程,理论分析证明了算法具有全局收敛性,实验结果表明,该算法在函数优化上具有优异的性能.     

基于改进量子遗传算法的过程神经元网络训练

针对过程神经元网络由于模型参数较多BP算法不易收敛的问题,提出一种基于量子位Bloch坐标的量子遗传算法.将该算法融合于过程神经网络的训练.按权值参数的个数确定量子染色体上的基因数并完成种群编码,通过新的量子旋转门完成个体的更新.算法中的每条染色体携带3条基因链,因此可扩展对解空间的遍历性,加速优化进程.以两组二维三角函数的模式分类问题为例,仿真结果表明该方法不仅收敛速度快,而且寻优能力强.     

基于量子粒子群优化的在线航迹规划

现代战场中,环境信息是变化的,飞行器很难预先获得精确的全局环境信息,因此要求无人飞行器具有实时的航迹规划能力,采用量子粒子群优化算法,将约束条件和搜索算法相结合,有效解决了简单粒子群算法在高维空间中易陷入局部最优点的问题;同时,根据地形障碍、敌方防御雷达、防空火力等威胁以及禁飞区的分布情况,引入最小威胁面的概念,利用B-Spline插值逼近最小威胁面中的三维航迹在二维水平面内的投影,从而将三维曲线的规划问题简化为二维平面中控制点的寻优问题,简化了问题复杂度,提高了计算效率.仿真结果表明该方法可以满足在线航迹规划的要求.     

抗量子计算公钥密码需求分析与技术路线

本文对国外量子计算机研究进展情况进行了分析,并针对量子计算机对于信息安全的挑战,讨论了国内下一代公钥密码技术的需求、发展思路和技术路线。