量子计算与量子计算机

量子计算的强大运算能力使得量子计算机具有广阔的应用前景。该文简要介绍了量子计算的发展现状和基本原理,列举了典型的量子算法,阐明了量子计算机的优越性,最后预测了量子计算及量子计算机的应用方向。     

Quantum Algorithms for Highly Structured Search Problems

We consider the problem of identifying a base k string given an oracle which returns information about the number of correct components in a query, specifically, the Hamming distance between the query and the solution, modulo r = max{2, 6 – k}. Classically this problem requires (nlog _r k) queries. For k {2, 3, 4}, we construct quantum algorithms requiring only a single quantum query. For k > 4, we show that O(k) quantum queries suffice. In both cases the quantum algorithms are optimal. PACS: 03.67.Lx     

求最优装载的量子算法

随着Grover量子搜索算法的不断发展,它的实际应用价值也在逐渐体现.通过介绍量子并行计算和量子算法的基本思想以及对改进的Grover搜索算法进行研究的基础上,分析给出了一个时间复杂度为O(√N)的求解最优装载问题的量子算法.对于最优装载问题,分别用经典计算机上的贪心算法和量子算法来求解,得出了这两种算法的时间复杂度,从而可以看出量子算法相对于经典算法具有更快的搜索速度.     

Visualization of the Quantum Fourier Transform Using a Quantum Computer Simulator

The quantum Fourier transform (QFT) is a key subroutine of quantum algorithms for factoring and simulation and is the heart of the hidden-subgroup problem, the solution of which is expected to lead to the development of new quantum algorithms. The QFT acts on the Hilbert space and alters the quantum mechanical phases and probability amplitudes. Unlike its classical counterpart its schematic representation and visualization are very dif.cult. The aim of this work is to develop a schematic representation and visualization of the QFT by running it on a quantum computer simulator which has been constructed in the framework of this research. Base states, superpositions of base states and entangled states are transformed and the corresponding schematic representations are presented. The visualization of the QFT presented here and the quantum computer simulator developed for this purpose may become a useful tool for introducing the QFT to students and researches without a strong background in quantum mechanics or Fourier analysis. PACS: 03.67.-a, 03.67.Lx     

Deep Web查询优化算法研究

Deep Web查询是在指分析接口属性及其丰富的语义信息后构造的用于向数据源请求特定数据的语句,其质量将影响查询结果相关度的高低和查询代价的大小.为优化查询,提出一种基于量子遗传算法的优化算法,以Deep Web查询的实数二进制串为输入进行量子编码,引入了球面解空间多子群并行寻优机制、群间染色体置换操作和量子变异算子以丰富种群多样性、提高算法的寻优效率.实验结果表明,该算法在R-Precision、覆盖率上具有一定的优势,能够有效地减少查询次数.     

基于二进制量子微粒群算法的二维熵图像分割

分析量子计算的特点,对量子旋转门进行研究,给出了新的量子旋转门调整策略,并与离散二进制粒子群优化算法进行组合,提出了二进制量子粒子群优化算法。该算法具有收敛速度快、全局寻优能力强的特点。用典型复杂函数对其进行测试,测试结果表明,算法的优化质量和效率都优于离散二进制粒子群优化算法。将二进制量子粒子群优化算法与阈值法相结合应用于图像分割,结果表明了基于二进制量子粒子群优化算法的二维熵图像分割法用于阈值寻优具有更快的收敛速度和更好的全局寻优能力。     

The Quantum Black-Box Complexity of Majority

   Abstract. We describe a quantum black-box network computing the majority of N bits with zero-sided error ɛ using only

一种基于量子遗传算法的分布式异构数据库查询优化方法

对于分布式异构数据库,查询优化既是非常复杂的问题,又是影响系统性能的关键因素。该文结合遗传算法和量子计算的优点,提出了基于量子遗传算法的分布式异构数据库查询优化方法。仿真实验表明,该方法有效地提高了分布式异构数据库的查询优化效率。     

Path Integration on a Quantum Computer

We study path integration on a quantum computer that performs quantum summation. We assume that the measure of path integration is Gaussian, with the eigenvalues of its covariance operator of order j^-k with k>1. For the Wiener measure occurring in many applications we have k=2. We want to compute an -approximation to path integrals whose integrands are at least Lipschitz. We prove: Path integration on a quantum computer is tractable. Path integration on a quantum computer can be solved roughly ^-1 times faster than on a classical computer using randomization, and exponentially faster than on a classical computer with a worst case assurance. The number of quantum queries needed to solve path integration is roughly the square root of the number of function values needed on a classical computer using randomization. More precisely, the number of quantum queries is at most 4.46 ^-1. Furthermore, a lower bound is obtained for the minimal number of quantum queries which shows that this bound cannot be significantly improved. The number of qubits is polynomial in ^-1. Furthermore, for the Wiener measure the degree is 2 for Lipschitz functions, and the degree is 1 for smoother integrands. PACS: 03.67.Lx; 31.15Kb; 31.15.-p; 02.70.-c     

量子计算与量子计算机展望

量子计算和量子计算机的研究是当代信息科学所面临的一个重大科学课题。阐述了量子计算、量子逻辑门的基本概念和Shor算法,指出了当前实现大规模量子计算所遇到的困难和可能的解决办法。     

On the complexity of a two-point boundary value problem in different settings

We study the complexity of a two-point boundary value problem. We concentrate on the linear problem of order k with separated boundary conditions. Right-hand side functions are assumed to be r times differentiable with all derivatives bounded by a constant. We consider three models of computation: deterministic with standard and linear information, randomized and quantum. In each setting, we construct an algorithm for solving the problem, which allows us to establish upper complexity bounds. In the deterministic setting, we show that the use of linear information gives us a speed-up of at least one order of magnitude compared with the standard information. For randomized algorithms, we show that the speed-up over standard deterministic algorithms is by 1/2 in the exponent. For quantum algorithms, we can achieve a speed-up by one order of magnitude. We also provide lower complexity bounds. They match upper bounds in the deterministic setting with the standard information, and almost match upper bounds in the randomized and quantum settings. In the deterministic setting with the linear information, a gap still remains between the upper and lower complexity bounds.     

Quantum lower bounds for the Goldreich-Levin problem

At the heart of the Goldreich-Levin theorem is the problem of determining an n-bit string a by making queries to two oracles, referred to as IP (inner product) and EQ (equivalence). The IP oracle, on input x, returns a bit that is biased towards a⋅x (the modulo two inner product of a with x) in the following sense. For a random x, the probability that IP(x)=a⋅x is at least . The EQ oracle, on input x, returns a bit specifying whether or not x=a. It has been shown that a quantum algorithm can solve this problem with O(1/?) IP and EQ queries, whereas any classical algorithm requires Ω(n/?²) such queries. Also, the quantum algorithm requires only O(n/?) auxiliary one- and two-qubit gates in addition to its queries. We show that the above quantum algorithm is optimal in terms of both EQ and IP queries. Specifically, Ω(1/?) EQ queries are necessary, and Ω(1/?) IP queries are necessary if the number of EQ queries is .     

基于量子遗传算法的知识分布优化研究

研究了智能考试系统的知识分布问题,基于量子计算理论,提出采用量子遗传算法,对知识分布优化策略进行改进,提高了试卷知识分布的覆盖率和效率。     

基于量子遗传算法的路由选择

网络中存在许多设计和优化问题,其中相当一部分属于NP类型。传统的解法由于计算复杂度过大而失效。文中探讨了该类问题中路由选择问题的一种新的解决方法:量子遗传算法。就路由选择问题的数学模型进行了简单的介绍,并深入研究了量子遗传算法及其在路由选择优化问题中的应用,最后在计算机上进行了模拟分析实验。仿真实验的结果表明,量子遗传算法在性能上优于常规遗传算法。该算法搜索速度快、效率高,并且具有较强的实用性和鲁棒性。     

基于量子免疫克隆算法的入侵检测系统

该文针对现行入侵检测系统的特点,提出了一种基于量子遗传克隆的入侵检测算法。通过实验结果分析得出,该方法比遗传算法具有更高的准确率和更好的收敛性。     

求解TSP的量子遗传算法

量子遗传算法(QGA)在求解数值和组合优化问题时效率明显优于传统进化算法,但目前较多被用于求解组合优化的背包问题,为了充分发挥QGA的优点,文中用其求解TSP这一经典的NP难问题.首先,文中设计了一种利用几率幅值编码的新的编码方式,即利用几率幅值编码的量子个体与一组向量对应,而此向量又与一条可行路径一一对应.这样的编码方式不仅缩小了种群规模,占用较少内存,所得的解均可行,而且有效地增强了种群的多样性;其次,在量子个体上实施量子杂交,这一操作有利于保留相对较好的基因段;最后,为了加快算法的收敛速度,引入两阶段局部搜索,第一阶段主要针对实例中排列稀疏处的城市进行优化,第二阶段在第一阶段的基础上着重对排列密集处的城市优化.据此,设计了解TSP的一个新的高效的QGA,并证明了其以概率1收敛到全局最优解;测定算法性能的数值实验数据表明,该算法在种群规模较小,迭代次数较少的情况下就可以收敛到已知最优解.     

基于量子遗传退火策略的多播路由优化模型及其算法

针对网络通信中带时延约束的多播路由问题,提出了一种基于量子遗传退火策略的路由算法。文中对路由选择问题的优化模型进行了描述,并深入研究了量子遗传退火及其在多播路由选择优化问题中的应用。仿真实验表明,与基于遗传算法的多播路由算法相比,该算法具有更快的收敛速度和更好的全局寻优能力。     

Learning-Based Complexity Evaluation of Radial Basis Function Networks

Recently, the complexity control of dynamic neural models has gained significant attention. The performance of such a process depends highly on the applied definition of model complexity. On the other hand, the learning theory creates a framework to assess the learning properties of models. These properties include the required size of the training samples as well as the statistical confidence over the model. In this Letter, we apply the learning properties of two families of Radial Basis Function Networks (RBFN's) to introduce new complexity measures that reflect the learning properties of such neural model. Then, based on these complexity terms we define cost functions, which provide a balance between the training and testing performances of the model.     

On the Interpretation of Energy as the Rate of Quantum Computation

Over the last few decades, developments in the physical limits of computing and quantum computing have increasingly taught us that it can be helpful to think about physics itself in computational terms. For example, work over the last decade has shown that the energy of a quantum system limits the rate at which it can perform significant computational operations, and suggests that we might validly interpret energy as in fact being the speed at which a physical system is “computing,” in some appropriate sense of the word. In this paper, we explore the precise nature of this connection. Elementary results in quantum theory show that the Hamiltonian energy of any quantum system corresponds exactly to the angular velocity of state-vector rotation (defined in a certain natural way) in Hilbert space, and also to the rate at which the state-vector’s components (in any basis) sweep out area in the complex plane. The total angle traversed (or area swept out) corresponds to the action of the Hamiltonian operator along the trajectory, and we can also consider it to be a measure of the “amount of computational effort exerted” by the system, or effort for short. For any specific quantum or classical computational operation, we can (at least in principle) calculate its difficulty, defined as the minimum effort required to perform that operation on a worst-case input state, and this in turn determines the minimum time required for quantum systems to carry out that operation on worst-case input states of a given energy. As examples, we calculate the difficulty of some basic 1-bit and n-bit quantum and classical operations in an simple unconstrained scenario     

基于经典存储器的量子计算机存储系统

量子计算机具有许多与经典计算机不同的量子特性,其性能远远优于经典计算机,但量子力学特有的性质也使得量子计算机的设计方法不同于经典计算机。在量子计算机中应用经典计算机的存储层次将会遇到一些前所未有的困难,文章提出了一种解决方案,以便能够在量子计算机的存储系统中应用与经典计算机类似的层次结构来提高访存性能。最后,文章给出了这种层次结构下访存性能的分析结果,指出了在何种条件下才能最大程度地发挥层次结构的性能。