Implementability of Liouville Evolution,Koopman and Banach-Lamperti Theorems in Classical and Quantum Dynamics

We extend the concept of implementability of semigroups of evolution operators associated with dynamical systems to quantum case. We show that such an extension can be properly formulated in terms of Jordan morphisms and isometries on non-commutative L ^p spaces. We focus our attention on a non-commutative analog of the Banach-Lamperti theorem.     

量子力学和量子计算机

In this paper,the relationship between computation and physics and the application of the principle of Quantum mechanics to Quantum Computing and Quantum Computers was reviewed     

论古典经济学与物理学的关系及动态系统仿真(Ⅲ)

牛顿力学是一个公认的科学理论体系,它不仅具有合理的逻辑系统,同时也经得起科学实验的检验.通过对古典经济学的劳动价值理论与物理学的牛顿力学之间的可类比性,以及相应的数学理论模型和实际案例的分析,说明古典经济学的劳动价值理论与牛顿力学在理论研究对象、基本理论假设、基本理论形式、主要的研究问题、主要理论结论等方面不仅是相同的,而且在实际上前者是后者的构成之一.与此同时,我们还依据古典经济学的数学模型建立了一个国民经济系统动态仿真模型(简称SED模型).通过反复的实验证明,SED模型能够逼真地模拟现代商品经济社会的复杂系统的实际运行状况.这一实证性的案例说明,古典经济学的劳动价值理论作为牛顿力学的构成,是一个逻辑合理和经得起实践检验的科学的理论体系.     

论古典经济学与物理学的关系及动态系统仿真(Ⅱ)

牛顿力学是一个公认的科学理论体系,它不仅具有合理的逻辑系统,同时也经得起科学实验的检验。本文通过对古典经济学的劳动价值理论与物理学的牛顿力学之间的可类比性,以及相应的数学理论模型和实际案例的分析,说明古典经济学的劳动价值理论与牛顿力学在理论研究对象、基本理论假设、基本理论形式、主要的研究问题、主要理论结论等方面不仅是相同的,而且在实际上前者是后者的构成之一。与此同时,我们还依据古典经济学的数学模型建立了一个国民经济系统动态仿真模型(简称SED模型)。通过反复的实验证明,SED模型能够逼真地模拟现代商品经济社会的复杂系统的实际运行状况。这一实证性的案例说明,古典经济学的劳动价值理论作为牛顿力学的构成,是一个逻辑合理和经得起实践检验的科学的理论体系。     

论古典经济学与物理学的关系及动态系统仿真(Ⅰ)

牛顿力学是一个公认的科学理论体系,它不仅具有合理的逻辑系统,同时也经得起科学实验的检验.通过对古典经济学的劳动价值理论与物理学的牛顿力学之间的可类比性,以及相应的数学理论模型和实际案例的分析,说明古典经济学的劳动价值理论与牛顿力学在理论研究对象、基本理论假设、基本理论形式、主要的研究问题、主要理论结论等方面不仅是相同的,而且在实际上前者是后者的构成之一.与此同时,还依据古典经济学的数学模型建立了一个国民经济系统动态仿真模型(简称SED模型).通过反复的实验证明,SED模型能够逼真地模拟现代商品经济社会的复杂系统的实际运行状况.这一实证性的案例说明,古典经济学的劳动价值理论作为牛顿力学的构成,是一个逻辑合理和经得起实践检验的科学的理论体系.     

对称不变形状上下文特征提取与匹配

形状上下文是一种广泛应用的图像形状特征提取与匹配算法,针对其特征不具有对 称不变性,无法对互相对称的相似图像建立匹配的问题,提出了一种具有对称不变性的改进形状 上下文特征提取与匹配算法。在形状边缘采样点上计算形状上下文中的角度关系描述时,令该点 的梯度方向为极坐标系的0°,并比较特征0 到π 与π 到2π 两个角度区间内其他边缘点的数量大 小,根据比较结果,调整极坐标系中角度增加的方向,从而使特征具备对称不变性。在迭代变形 与计算形状上下文时,仅在第一次迭代中使用改进的形状上下文特征,从而使匹配更加稳定。仿 真实验证明,该算法能够有效地在互相对称的相似图像间建立匹配,提高检索精度。     

Douglas Hartree and Early Computations in Quantum Mechanics

Douglas Hartree, who was a mathematical physicist at the University of Manchester and the University of Cambridge during the first half of this century, examined the possibilities for numerical solutions of the many-body problem in quantum mechanics which did not permit analytic, closed-form results. In an attempt to surmount the mathematical complexities associated with multi-electron atoms, Hartree proposed the method of self-consistent fields as an approximation scheme which would give numerical forms of atomic wave functions via iterative solution of the Schrödinger equation. Hartree was quick to recognize the need for automatic computation, both analog and digital, for the practical implementation of the technique. To this end, he investigated the application of analog differential analyzers to the problem before realizing the superiority of digital computation. The question of the first self-consistent field calculations to be run on an electronic digital machine is addressed in an effort to clarify misinformation in the existing literature about the use of early computers to perform Hartree computations.     

Quantum Markovian Subsystems: Invariance, Attractivity, and Control

We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem of interest. Markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing, subsystem encodings offering a general pathway to faithfully represent quantum information. We provide explicit linear-algebraic characterizations of the notion of invariant and noiseless subsystem for Markovian master equations, under different robustness assumptions for model-parameter and initial-state variations. The stronger concept of an attractive quantum subsystem is introduced, and sufficient existence conditions are identified based on Lyapunov's stability techniques. As a main control application, we address the potential of output-feedback Markovian control strategies for quantum pure state-stabilization and noiseless-subspace generation. In particular, explicit results for the synthesis of stabilizing semigroups and noiseless subspaces in finite-dimensional Markovian systems are obtained.     

The Representation of Numbers in Quantum Mechanics

Abstract. Earlier work on modular arithmetic of k-ary representations of length L of the natural numbers in quantum mechanics is extended here to k-ary representations of all natural numbers, and to integers and rational numbers. Since the length L is indeterminate, representations of states and operators using creation and annihilation operators for bosons and fermions are defined. Emphasis is on definitions and properties of operators corresponding to the basic operations whose properties are given by the axioms for each type of number. The importance of the requirement of efficient implementability for physical models of the axioms is emphasized. Based on this, successor operations for each value of j corresponding to +k ^j-1 are defined. It follows from the efficient implementability of these successors, which is the case for all computers, that implementation of the addition and multiplication operators, which are defined in terms of polynomially many iterations of the successors, should be efficient. This is not the case for definitions based on just the successor for j=1 . This is the only successor defined in the usual axioms of arithmetic.     

射影不变性在旋转对称形状描述中的一种应用

旋转对称性是计算机视觉形状分析中的一类重要结构属性。自动检测该类目标的旋转特性以及提取目标的旋转中心（轴）,是描述和分析旋转对称目标的关键步骤。旋转对称的形状经过透视成像后,其成像特点不再具有对称性甚至扭对称性,但对称的结构单元之间仍然存在内在的对应不变特性。该文以简单连通的平面多边形目标为研究模型,利用射影几何中的交比不变量定义了目标轮廓上关键点的结构参数和结构参数的相似性度量,用于自动检验目标上的旋转对称点对;并利用正多边形顶点与形心的关系约束形成射影不变性,用来自动检测目标的旋转中心。实验结果验证了方法的有效性。     

Quantum and Classical Correlations of Spatial and Spin Degrees of Freedom in Quantum Rings

A one-dimensional mesoscopic ring with one input and two output leads acts as a spintronic beam splitter. The spatial degree of freedom, i.e., the presence of two different possible output channels, gets intertwined with the spin direction as a consequence of quantum interference and spin-orbit interaction. We investigate this kind of spatial-spin correlation, and show that the output density operator contains no quantum entanglement in the important special case when the device polarizes a perfectly random input spin state. However, the correlations are in general not purely classical, we also present specific input states with maximal spatial-spin entanglement after the ring.     

基于经典力学的树木摆动断裂模型

为建立逼真的树木模型,提出将树木模型分为静态和动态2种类型。采用拓展二维半建模方法和碰撞面算法建立树木静态模型。利用经典物理学中的动量定理计算对象在风场中所受的冲力,且与杨氏模量中的断裂极限值相比较,确定对象断裂或摆动等情况,以此构建树木动态模型。仿真结果证明,该方法能够快速高效地建立树木模型。     

Sharp Quantum versus Classical Query Complexity Separations

Abstract. We obtain the strongest separation between quantum and classical query complexity known to date—specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved exactly in the quantum case with a single query (and a polynomial number of auxiliary operations). The problem is simple to define and the quantum algorithm solving it is also simple when described in terms of certain quantum Fourier transforms (QFTs) that have natural properties with respect to the algebraic structures of finite fields. These QFTs may be of independent interest, and we also investigate generalizations of them to noncommutative finite rings.     

Exponential Separation of Quantum and Classical Online Space Complexity

Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we study, for the first time explicitly, space-bounded quantum algorithms for computational problems where the input is given not as a whole, but bit by bit. We show that there exist such problems that a quantum computer can solve using exponentially less work space than a classical computer. More precisely, we introduce a very natural and simple model of a space-bounded quantum online machine and prove an exponential separation of classical and quantum online space complexity, in the bounded-error setting and for a total language. The language we consider is inspired by a communication problem (the disjointness function) that Buhrman, Cleve and Wigderson used to show an almost quadratic separation of quantum and classical bounded-error communication complexity. We prove that, in the framework of online space complexity, the separation becomes exponential.     

基于量子力学和拉普拉斯金字塔的图像融合方法

针对数字图像的融合问题,研究一种基于量子力学理论的图像分解方法,并将其结合拉普拉斯金字塔变换,提出一种新的图像融合方法.先把2幅灰度图像表示成量子比特的形式,然后把每幅图像分解成4幅特征子图,根据分解后特征子图的不同含义,使用不同的融合策略分别对子图进行融合.其中一幅子图使用拉普拉斯金字塔变换进行融合,另外3幅子图使用区域梯度取大法进行融合,最后通过重构得到融合图像.仿真实验表明该方法融合效果较好,在主观视觉感受和客观评价指标上均优于传统的图像融合方法.     

Quantum Computation Violates Mirror Symmetry

The CNOT gate is asymmetric with respect to parity. It requires interaction with the environment, and cannot be realized as an isolated quantum collision.