### 计算机代写|量子计算代写Quantum computing代考|Fundamentals and New Results

statistics-lab™ 为您的留学生涯保驾护航 在代写量子计算Quantum computing方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量子计算Quantum computing代写方面经验极为丰富，各种代写量子计算Quantum computing相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 计算机代写|量子计算代写Quantum computing代考|Fundamentals and New Results

Due to the anticipated failure of Moore’s law around the year 2020 , quantum computing will hopefully play an increasingly crucial role in building more compact and less power consuming computers $[93,107,167,248,253]$. Due to this fact, and because all quantum computer gates (i.e., building blocks; primitives) must be reversible $[37,38,39,73,74,75,95,97,139,150,167,203,245,246]$ reversibility in computing will have increasing importance in the future design of regular, compact, and universal structures and machines (systems). $(\mathrm{n}, \mathrm{k})$ reversible circuits are circuits that have (n) inputs and (k) outputs and are one-to-one mappings between vectors of inputs and outputs, thus the vector of input states (values) can be always uniquely reconstructed from the vector of output states (values). $(k, k)$ reversible circuits are circuits that have the same number of inputs $(\mathrm{k})$ and outputs $(\mathrm{k})$ and are one-to-one mappings between vectors of inputs and outputs, thus the vector of input states (values) can be always uniquely reconstructed from the vector of output states (values). Conservative circuits $[98,210,211,212]$ are circuits that have the same number of values in inputs and outputs (e.g., the same number of ones in inputs and outputs for binary, the same number of ones and twos in inputs and outputs for ternary, etc). Conservativeness exists naturally in physical laws where no energy is created or destroyed.

As was proven in $[37,139]$ it is a necessary but not sufficient condition for not dissipating power in any physical circuit that all system circuits must be built using fully reversible logical components. An important argument for power-free computation in a computer that “pushes information around” using reversible logic is given in [139], using the model of a particle in a bistable potential well, as follows.

## 计算机代写|量子计算代写Quantum computing代考|Fundamental Reversible Logic Primitives and Circuits

Reversible circuits which are hierarchically composed of reversible primitives have two types of outputs in general: (1) functionality outputs, and (2) outputs that are needed only to achieve reversibility which are called “garbage” [98]. Many reversible gates have been proposed as building blocks for reversible (and consequently quantum) computing. Figure $5.4$ shows some of the binary $(\mathrm{k}, \mathrm{k})$ reversible gates that are commonly used in the synthesis of reversible logic circuits $[6,14,95,126,127,128,129]$. It is noted from Fig. $5.4$ that while Wire (Buffer), Not, and Swap gates are naturally reversible, others are not, and thus “garbage” has to be added.Multiple-valued counterparts of similar reversible primitives and some of their applications were introduced in $[6,11,14,190,191,192,193]$. Figure $5.5$ illustrates the multiple-valued gate from [191]. More multiple-valued gates and the systematic methodology for their creation and classification will be introduced in Sect. 5.4.

Although most of available literature on reversible computing presents gates that are $(k, k)$ reversible, other literature has reported the conceptual need for $(\mathrm{n}, \mathrm{k})$ reversible primitives in general. The need for $(n, k)$ reversible primitives stems from the fact that the logical model must fit the physical reality of computing, and not to be disjoint from the physical laws of computing as it was in the previous abstract mathematical logics before reversible (and thus quantum) computing. For instance, the Interaction gate $[62,63,64,222]$ has been reported to be of a good fit to reversible computing in optics. Figure $5.6$ illustrates some of the $(\mathrm{n}, \mathrm{k})$ reversible gates. (It is important to note that here fan-out and feedback are not allowed in reversible computing applications using either $(\mathrm{k}, \mathrm{k})$ reversible gates or $(\mathrm{n}, \mathrm{k})$ reversible gates.)

Fredkin gate [98] is one of the most basic building blocks in reversible and quantum computing. Many propositions have been proposed to realize the Fredkin gate in various technologies: Optical, Electrical, Mechanical (nano-technology), and Quantum. The Fredkin gate belongs to a group of gates that each represents a fundamental family of logic gates in reversible computing. These families of reversible gates are Fredkin-like, Toffoli-like, and Feynman-like gates. It will be shown in Sect. $5.4$ how to formally generalize the Fredkin gate to any multiple-valued logic radix.

## 计算机代写|量子计算代写Quantum computing代考|Combinational Reversible Circuits

Reversible circuits can be synthesized using careful design methodologies where one utilizes the outputs from a previous stage as inputs to the next stage. Various reversible circuits have been synthesized using this methodology [8,200]. This Sect. introduces some of these circuits. Figure $5.15$ illustrates the creation of all of the 16 possible binary logic functions of two variables (cf. Fig. G.3 in Appendix G) using certain reversible logic primitives.

Note that such constructions are not unique, and thus the optimization criteria should be (1) minimum size and (2) have mimimum garbage used in the synthesis. Figure $5.16$ illustrates the synthesis of half-adder and full-adder using Feynman (ControlledNOT: CN) and Toffoli (Controlled-Controlled-NOT: CCN) gates.

As shifters are important in combinational and sequential logic synthesis, it is important to produce a reversible logic shifter. Figure $5.18$ illustrates a novel reversible Barrel shifter design from [8]. Figure $5.18$ represents one possible design of concurrent shift-left and shift-right reversible Barrel shifter, which shows a fundamental concept in the design of reversible logic circuits: the idea of the use of reversibility to perform multiple operations using the same design while retaining reversibility [8].

Note that by controlling the value of the variable in the first level, the Barrel shifter operates in the shift-left mode by setting the value of variable $X$ in the first level to value “0” and collecting the shifted-left outputs from the locations that are marked by $(X)$ at the outputs of Fredkin gates, or the shift-right mode by setting the value of variable $X$ in the first level to value ” 1 ” and collecting the shiftedright outputs from the locations that are marked by ( $+)$ at the outputs of Fredkin gates, respectively. The first level of the reversible Barrel shifter will shift the inputs by one location, the second level will shift the inputs by two locations, the third level will shift the inputs by three locations, and the fourth level will shift the inputs by four locations (i.e., full cycle or rotation).

Figure $5.19$ illustrates the use of MIN/MAX gate, which is synthesized from Picton gate, to realize a multiple-valued Sorter [8]. By following the paths, from the inputs to the outputs, one will obtain the sorted values of the inputs at the outputs.

## 计算机代写|量子计算代写Quantum computing代考|Fundamental Reversible Logic Primitives and Circuits

Fredkin Gate [98] 是可逆和量子计算中最基本的构建模块之一。已经提出了许多命题来在各种技术中实现 Fredkin 门：光学、电气、机械（纳米技术）和量子。Fredkin 门属于一组门，每个门都代表可逆计算中的一个基本逻辑门家族。这些可逆门家族是 Fredkin-like、Toffoli-like 和 Feynman-like gates。它将在Sect中显示。5.4如何将 Fredkin 门正式推广到任何多值逻辑基数。

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。