Note on Implementation of Three-Qubit SWAP Gate

In this paper, the synthesis and implementation of three-qubit SWAP gate is discussed. The three-qubit SWAP gate can be decomposed into product of 2 two-qubit SWAP gates, and it can be realized by 6 CNOT gates. Research illustrated that although the result is very simple, the current methods of matrix decomposition for multi-qubit gate can not get that. Then the implementation of three-qubit SWAP gate in the three spin system with Ising interaction is investigated and the sequence of control pulse and drift process to implement the gate is given. It needs 23 control pulses and 12 drift processes. Since the interaction can not be switched on and off at will, the realization of three-qubit SWAP gate in specific quantum system also can not simply come down to 2 two-qubit SWAP gates.     

A new domain decomposition method with overlapping patches for ultrascale simulations: Application to biological flows

We address the failure in scalability of large-scale parallel simulations that are based on (semi-)implicit time-stepping and hence on the solution of linear systems on thousands of processors. We develop a general algorithmic framework based on domain decomposition that removes the scalability limitations and leads to optimal allocation of available computational resources. It is a non-intrusive approach as it does not require modification of existing codes. Specifically, we present here a two-stage domain decomposition method for the Navier–Stokes equations that combines features of discontinuous and continuous Galerkin formulations. At the first stage the domain is subdivided into overlapping patches and within each patch a C⁰ spectral element discretization (second stage) is employed. Solution within each patch is obtained separately by applying an efficient parallel solver. Proper inter-patch boundary conditions are developed to provide solution continuity, while a Multilevel Communicating Interface (MCI) is developed to provide efficient communication between the non-overlapping groups of processors of each patch. The overall strong scaling of the method depends on the number of patches and on the scalability of the standard solver within each patch. This dual path to scalability provides great flexibility in balancing accuracy with parallel efficiency. The accuracy of the method has been evaluated in solutions of steady and unsteady 3D flow problems including blood flow in the human intracranial arterial tree. Benchmarks on BlueGene/P, CRAY XT5 and Sun Constellation Linux Cluster have demonstrated good performance on up to 96,000 cores, solving up to 8.21B degrees of freedom in unsteady flow problem. The proposed method is general and can be potentially used with other discretization methods or in other applications.     

Fast algorithms for spherical harmonic expansions,III

We accelerate the computation of spherical harmonic transforms, using what is known as the butterfly scheme. This provides a convenient alternative to the approach taken in the second paper from this series on “Fast algorithms for spherical harmonic expansions”. The requisite precomputations become manageable when organized as a “depth-first traversal” of the program’s control-flow graph, rather than as the perhaps more natural “breadth-first traversal” that processes one-by-one each level of the multilevel procedure. We illustrate the results via several numerical examples.     

Numerical Complexiton Solutions of Complex KdV Equation

In this paper, we directly extend the applications of the Adomian decomposition method to investigate the complex KdV equation. By choosing different forms of wave functions as the initial values, three new types of realistic numerical solutions： numerical positon, negaton solution, and particularly the numerical analytical complexiton solution are obtained, which can rapidly converge to the exact ones obtained by Lou et al. Numerical simulation figures are used to illustrate the efficiency and accuracy of the proposed method.     

近红外漫反射光谱信息分解的数量分析

近红外漫反射光谱分析中,一直认为近红外光可获取样品内部的物质信息,但近红外漫反射光谱包含样品内部信息量究竟是多少,一直未给出准确的数量描述。该研究以烤烟样品为实验材料设计样品,每个实验样品分别由表层片状烤烟与内部烤烟粉末两部分组合而成,测定样品近红外漫反射光谱,提取光谱主成分信息(principal component, PC),将所提取的各主成分的不同组合作为统计指标,对样品进行聚类分析,结合各主成分方差贡献率,初步给出了样品不同深度光谱信息分解量的描述。实验结果表明,近红外漫反射光谱第1和第2主成分包含的信息量约占总信息的98%,反映样品表层信息;第3和第4主成分约占1.5%,表征样品内部信息。这一结果将有助于我们对近红外光谱定性定量分析时主成分信息的选择有一个更深刻的理解。     

GRCA(1)模型中误差方差自加权估计的渐近分布

考虑随机系数自回归模型Y_t =Φ_ty_t-1+ u_t,其中 Φ_t为随机系数,u_t为随机误差。在允许Φ_t与u_t相依以及Eu_t无穷的条件下,构造了误差方差的自加权估计,并证明了该估计的渐近正态性。最后通过数值模拟,说明 自加权估计的稳健和有效性。     

正交饱和效应模型及其统计分析

文\cite{14}讨论了2水平正交饱和设计的一种统计分析方法---零效应搜索法, 本文将此方法推广到一般的饱和模型---正交饱和效应模型. 首先给出正交饱和效应模型的定义及其相关的参数估计和平方和分解, 然后用零效应搜索法对显著效应的检验问题进行分析, 模拟结果显示效果很好.     

高温下HBT晶体热分解过程的理论模拟

基于自洽电荷密度泛函紧束缚(SCC-DFTB)方法研究了富氮含能材料5, 5’-双四唑肼(C₂H₄N₁₀, HBT)晶体在高温下的热分解反应过程.结果表明,结构优化参数与实验误差在5%以内.在2000 K, 2500 K,和3000 K不同温度下,HBT晶体热分解路径和产物表现出相似性.通过过渡态理论和分子动力学两种方法,研究了分解反应C₂H₄N₁₀→C₂H₃N₇+HN₃,发现HBT晶体分解产物中存在叠氮酸(HN₃)分子,化学反应势垒高度为222.85 kJ·mol^-1.研究结果为进一步理解高温下HBT晶体热分解特征提供理论参考.     

Integrating modeling,algorithm design,and computational implementation to solve a large-scale nonlinear mixed integer programming problem

This paper describes the formulation of a nonlinear mixed integer programming model for a large-scale product development and distribution problem and the design and computational implementation of a special purpose algorithm to solve the model. The results described demonstrate that integrating the art of modeling with the sciences of solution methodology and computer implementation provides a powerful approach for attacking difficult problems. The efforts described here were successful because they capitalized on the wealth of existing modeling technology and algorithm technology, the availability of efficient and reliable optimization, matrix generation and graphics software, and the speed of large-scale computer hardware. The model permitted the combined use of decomposition, general linear programming and network optimization within a branch and bound algorithm to overcome mathematical complexity. The computer system reliably found solutions with considerably better objective function values 30 to 50 times faster than had been achieved using general purpose optimization software alone. Throughout twenty months of daily use, the system was credited with providing insights and suggesting strategies that led to very large dollar savings. This research was supported in part by the Office of Naval Research Contract N00014-78-C-0222, by the Center for Business Decision Analysis*, by the University of Texas at Austin, and by the David Bruton, Jr., Centennial Chair in Business Decision Support Systems. Reproduction in whole or in part is permitted for any purpose of the U.S. Government. Center for Business Decision Analysis, Graduate School of Business — GSB 3.126, University of Texas, Austin, Texas 78712, USA.     

H2S splitting on Cu(110): Insight from combined periodic density functional theory calculations and microkinetic simulation

Practical copper (Cu)‐based catalysts for the water–gas shift (WGS) reaction was long believed to expose a large proportion of Cu(110) planes. In this work, as an important first step toward addressing sulfur poisoning of these catalysts, the detailed mechanism for the splitting of hydrogen sulfide (H₂S) on the open Cu(110) facet has been investigated in the framework of periodic, self‐consistent density functional theory (DFT‐GGA). The microkinetic model based on the first‐principles calculations has also been developed to quantitatively evaluate the two considered decomposition routes for yielding surface atomic sulfur (S*): (1) H₂S → H₂S* → SH* → S* and (2) 2H₂S → 2H₂S* → 2SH* → S* + H₂S* → S* + H₂S. The first pathway proceeding through unimolecular SH* dissociation was identified to be feasible, whereas the second pathway involving bimolecular SH* disproportionation made no contribution to S* formation. The molecular adsorption of H₂S is the slowest elementary step of its full decomposition, being related with the large entropy term of the gas‐phase reactant under realistic reaction conditions. A comparison of thermodynamic and kinetic reactivity between the substrate and the close‐packed Cu(111) surface further shows that a loosely packed facet can promote the S* formation from H₂S on Cu, thus revealing that the reaction process is structure sensitive. The present DFT and microkinetic modeling results provide a reasonably complete picture for the chemistry of H₂S on the Cu(110) surface, which is a necessary basis for the design of new sulfur‐tolerant WGS catalysts. © 2013 Wiley Periodicals, Inc.