Quantum search for unknown number of target items by hybridizing fixed-point method with trail-and-error method

For the unsorted database quantum search with the unknown fraction λ of target items, there are mainly two kinds of methods, i.e., fixed-point and trail-and-error.(i) In terms of the fixed-point method, Yoder et al. [Phys. Rev. Lett.113 210501(2014)] claimed that the quadratic speedup over classical algorithms has been achieved. However, in this paper, we point out that this is not the case, because the query complexity of Yoder’s algorithm is actually in O(1/λ01/2)rather than O(1/λ1/2), where λ0 is a known lower bound of λ.(ii) In terms of the trail-and-error method, currently the algorithm without randomness has to take more than 1 times queries or iterations than the algorithm with randomly selected parameters. For the above problems, we provide the first hybrid quantum search algorithm based on the fixed-point and trail-and-error methods, where the matched multiphase Grover operations are trialed multiple times and the number of iterations increases exponentially along with the number of trials. The upper bound of expected queries as well as the optimal parameters are derived. Compared with Yoder’s algorithm, the query complexity of our algorithm indeed achieves the optimal scaling in λ for quantum search, which reconfirms the practicality of the fixed-point method. In addition, our algorithm also does not contain randomness, and compared with the existing deterministic algorithm, the query complexity can be reduced by about 1/3. Our work provides a new idea for the research on fixed-point and trial-and-error quantum search.

基于模糊n-cell数的非线性投入产出模型解的存在性

将混合单调以及耦合不动点的概念引入到模糊n-cell数空间中,给出此空间上的混合单调型不动点定理。考虑到模糊n-cell数具有表示n维不确定信息的特点,将非线性投入产出模型与模糊n-cell数相结合,建立模糊非线性投入产出模型并给出相应的平衡方程。最后利用本文中所给的不动点定理讨论此模型解存在的条件,验证模型的合理性。

On Perron’s Formula and the Prime Numbers

The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.

Fixed Point Theorems of the Iterated Function Systems

In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of generalized metric space, which is Mso extensively applied in topological dynamic system.

模H-Nielsen数(2)

通过研究自映射ｆ在π１（Ｘ，ｘ０）上的作用ｆπ，发现只要适当地选取π１（Ｘ，ｘ０）中子群Ｈ（ｆπ，π１）作为正则复迭空间的子群，得到模Ｈ－Ｎｉｅｌｓｅｎ数等于Ｎｉｅｌｓｅｎ数的结果，从而简化了用模Ｈ－Ｎｉｅｌｓｅｎ数计算Ｎｉｅｌｓｅｎ数的过程。

采用定点数的数字DC-DC控制器设计

提出了一种应用于数字DC-DC变换器的高精度定点数字控制器的设计方法;在数字控制器的控制率运算中,将浮点数格式的控制参数转化为定点数格式,从而达到简化硬件电路的目的;该设计方法应用于降压型数字DC-DC变换器的设计中,并完成了基于FPGA的测试和验证;在500kHz的开关频率下,输出电压纹波为14mV,对于±0.5A的负载电流跳变,控制器响应时间约为330μs。测试结果表明,该设计方法在保持控制精度的前提下,可简化硬件电路的设计复杂度,并改善系统的瞬态性能。

Fixed points of n-valued maps on surfaces and the Wecken property a configuration space approach

In this paper, we explore the fixed point theory of n-valued maps using configuration spaces and braid groups, focusing on two fundamental problems, the Wecken property, and the computation of the Nielsen number. We show that the projective plane(resp. the 2-sphere S^2) has the Wecken property for n-valued maps for all n ∈ N(resp. all n 3). In the case n = 2 and S^2, we prove a partial result about the Wecken property.We then describe the Nielsen number of a non-split n-valued map ? : X■X of an orientable, compact manifold without boundary in terms of the Nielsen coincidence numbers of a certain finite covering q : X → X with a subset of the coordinate maps of a lift of the n-valued split map ? ? q : X■X.

Least Number of Periodic Points of Self-maps of Lie Groups

There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M → M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g is continuous} and NJDn（f） = min{#Fix（gn）; g - f; g is smooth}. In general, NJDn（f） may be much greater than NFn（f）. If M is a torus, then the invariants are equal. We show that for a self-map of a nonabelian compact Lie group, with free fundamental group, the equality holds 〈=〉 all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.

基于分数表示模型的量子信号中值滤波

在过去10年里,基于量子力学的量子信号表示研究已经出现一些重要结果.然而,关于量子信号处理方面的研究却相对滞后,其中就包括量子信号的滤波处理.首先,改进了现有的数字信号的量子表示模型(quantum representation of digital signals,QRDS),使其适用于任意长度的时间信号,同时还修改了QRDS模型中二补码的编码方法,使得新的编码更符合实际问题.然后,基于改进的模型引入了中值滤波方案,该方案回避了量子计算不能直接实现卷积运算的缺陷.为了实现该滤波方案的量子电路,又给出了基本量子运算模块:比较器模块、交换模块和中值计算模块.最后,通过实例验证了文中所提滤波方案的有效性和合理性.

Realization of Fixed Point Sets

Let f: X→X be a selfmap of a compact connected polyhedron, and A a nonempty closed subset of X. In this paper, we shall deal with the question whether or not there is a map g: X→X homotopic to f such that the fixed point set Fixg of g equals A. We introduce a necessary condition for the existence of such a map g. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.

When a smooth self-map of a semi-simple Lie group can realize the least number of periodic points

There are two algebraic lower bounds of the number of n-periodic points of a self-map f : M → M of a compact smooth manifold of dimension at least 3: NF_n(f) = min{#Fix(g^n); g ～ f; g continuous} and NJD_n(f) = min{#Fix(g^n); g ～ f; g smooth}. In general, NJD_n(f) may be much greater than NF_n(f). We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism,the equality NF_n(f) = NJD_n(f) holds for all n ? all eigenvalues of a quotient cohomology homomorphism induced by f have moduli 1.

定点发车模式中最小编成辆数的研究

铁路编组站有定编发车和定点发车两种货物列车发车模式。为确定定点发车模式中最小编成辆数的模型,对发车模式的条件进行了一定的假设,研究了两种模式的相关运行指标,找出了其基本变化规律。提出定点发车模式中有利最小编成辆数、效益最小编成辆数、成本最小编成辆数、能力最小编成辆数和模型最小编成辆数5个概念,并给出了相应变量的确定方法。研究表明,定点发车模式适宜于车流量小、运行区间距离短的车流方向。

闭轨线上模映射的不动点类与拓扑熵下界估计

本文在自治系统dx/dt=f(x),f∈C(DRn,Rn)的闭轨线Γ上定义了模映射,并利用闭轨线Γ与单位圆周S1的同胚关系,给出了模映射的Reidemeister数、Nielsen数,以及模映射的拓扑熵下界估计.

不动点大类与Nielsen数

通过引进 π１ （ Ｘ，ｘ０ ） 的同态 ｆπ 的不动子群 Ｆｉｘｆπ，在 Ｈ ＝ Ｆｉｘｆπ ·ｋｅｒｆ π为π１ （ Ｘ，ｘ０ ） 的正规子群时定义了不动点大类，得到不动点大类数是有限的．在曲面 Ｘ的正则复迭空间 Ｘ Ｈ 为有限叶时只要姜子 群相对于 Ｈ 极大，ｆ 的 Ｎｉｅｌｓｅｎ

有界闭模糊复数集上映射的几个不动点性质

首先介绍了模糊复集与模糊复数的相关概念,根据复模糊集的多元扩张原理给出有界闭模糊复数的一般运算。其次,给出模糊复数序列依度量收敛的概念,在有界闭模糊复数构成的度量空间上给出模糊复数值映射的连续性和压缩映射概念。再次,重点研究了此度量空间上模糊复数值映射的不动点问题,得到了有关此映射不动点、最大不动点和最小不动点存在性的一些新结果,为进一步在经济和工程技术领域的应用奠定了理论基础。

高精度定点数平方根汇编子程序的实现原理

在8/16位单片机或32位定点DSP实时测控系统中,汇编应用程序仍占主导地位。介绍一种用定点实数格式实现平方根汇编子程序的方法,并通过与3字节浮点数平方根汇编子程序运算结果比较发现:前者比后者的精度更高,在保持精度不变时,开平方根数的范围更大。

压缩查找表的高精度CORDIC算法设计

目前16位精度的坐标旋转数字计算机(CORDIC)算法设计存在输出时延长、硬件消耗大等问题,而在数字加密和信息安全等领域需要32位乃至更高精度的输出.文中提出了一种基于压缩查找表的32位精度CORDIC算法,根据内在迭代规律分解并压缩查找表,还采用区间折叠、角度重编码和合并迭代等,实现了一种电路资源消耗不大,输出时延仅需3个时钟周期,基于定点数格式的算法设计.仿真结果表明,查找表容量压缩到常规方法所需容量的1. 78%,输出时延从常规方法所需的8个时钟周期降低至3个时钟周期,输出平均误差为2. 3048×10-10.本设计具有电路资源消耗少、精度高、输出时延低等优点,更适合实时性强、硬件资源紧凑的现代通信应用场合.

一种定点数权值神经网络的优化方法及其应用

为了使得神经网络的应用符合嵌入式系统快速计算、存储量精简的要求,提出了一种定点数权值神经网络的优化方法。采用精度可调的比例数格式定点数表示神经网络的权值和阈值,用遗传算法对神经网络进行训练,并用最小二乘法对网络的非线性连续节点激励函数进行了线性离散化。将这种优化的神经网络应用于触摸屏校准。实验表明,采用该方法进行触摸屏校准比传统的校准方法具有更高的准确率。

基于Simulink的绝对位置传感器的FPGA实现

针对传统图像处理FPGA设计的设计周期长,仿真验证复杂等问题,提出了采用Simulink的硬件设计方法。该方法以具有强大图像处理能力、操作简便、灵活性高,并以便于仿真的Simulink为基础,进行了功能模型的设计,再将其转换为定点模型及HDL模型。该方法由于前期图像可视化的仿真,大幅缩减了功能模型设计周期,并在允许误差范围内(0.01 mm)完成了对绝对位置传感器的FPGA实现。

Fuzzy度量空间的度量性质及其集值映射的不动点定理

研究Fuzzy度量空间的一些性质,给出了几个集值映射的不动点定理.