### 计算机代写|量子计算代写Quantum computing代考|New Three-Valued Families

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|Davio Lattice Structures

The concept of binary two-dimensional Shannon and Davio lattice structures that was presented in Sect. $4.2$ can be generalized to include the case of three-dimensional Shannon and Davio lattice structures with function expansions that implement the fundamental multi-valued Shannon and Davio decompositions, as well as the new invariant set of multi-valued Shannon and Davio decompositions from Sect. 2.2. Since the most natural way to think about binary lattice structures is the two-dimensional 4-neighbor lattice structure that was shown in Fig. 4.4a, one can extend the same idea to utilize the full three-dimensional space in the case of ternary lattices. Such lattices represent three-dimensional 6-neighbor lattice structures. Although regular lattices can be realizable in the three-dimensional space for radix three while maintaining their full regularity, they are unrealizable for radices higher than three (i.e., 4 , 5, etc). Higher dimensionality lattices can be implemented in 3-D space but at the expense of losing the full regularity. This is because the circuit realization for the ternary case produces a regular structure in three dimensions that is fully regular in terms of connections; all connections are of the same length. Realizing the higher dimensionality lattices in lower dimensionality space is possible but

at the expense of regularity; the lattices will not be fully regular due to the uneven length of the inter-connections between nodes.

As a topological concept, and as stated previously, lattice structures can be created for two, three, four, and any higher radix. However, because our physical space is three-dimensional, lattice structures, as a geometrical concept, can be realized in solid material, with all the inter-connections between the cells of the same length, only for radix two (2-D space) or radix three (3-D space). It is thus interesting to observe that the characteristic geometric regularity of the lattice structure realization which is observed for binary and ternary symmetric functions will be no longer observable for quaternary functions. Thus, the ternary lattice structures have a unique position as structures that make the best use of threedimensional space (we do not claim here that a regular structure that would use 3-D space better than 3-D lattice structures can not be invented, and the statement is restricted only to lattice-type structures). The following Sect. will introduce the proposed general three-dimensional logic circuit of ternary lattice structures. The new 3-D lattice structures that realize ternary functions, which will be presented in the next Sects., will be further extended to the reversible case in Chapt. 6, and then mapped into quantum circuits as will be illustrated in Chapt. $10 .$

## 计算机代写|量子计算代写Quantum computing代考|Three-Dimensional Lattice Structures

In general, to reserve the fully regular realization of expansions over $\mathrm{n}^{\text {th }}$ radix, it is sufficient to join $\mathrm{n}$ nodes in $\mathrm{n}$-dimensional space to obtain the corresponding lattice structures. For instance, as was shown in Fig. 4.4, it is sufficient in the binary case to join two nodes. Analogously, it is sufficient in the ternary case to join three nodes to form the corresponding 3-D lattice structures $[5,13,18]$. Analogously to the work presented previously, fully symmetric ternary functions do not need any joining operations to repeat variables in order to realize them in three-dimensional lattice structures. Because three-dimensional lattice structures exist in a three-dimensional space, a geometrical reference of coordinate systems is needed in order to be systematic in the realizations of the corresponding logic circuits. Consequently, the right-hand rule of the Cartesian coordinate system is adopted. Example $4.6$ illustrates lattice realizations for such fully symmetric ternary functions.

## 计算机代写|量子计算代写Quantum computing代考|Three-Dimensional Invariant Shannon

In the following derivation, two correction functions for the case of ternary logic are implemented. In general, for $n^{\text {th }}$ radix Galois logic, no correction functions are needed for lattice structures with $n$ valued invariant Shannon nodes as will be shown in Theorem 4.1. So, for instance, for the case of binary Shannon, no correction functions are needed, due to the fact that all of the Shannon cofactors are disjoint, as was shown in Fig. 4.4b.

Theorem 4.1. For lattice structures with all invariant ternary Shannon nodes, the following is one possible joining rule:
$$J={ }^{0} a J_{0}+{ }^{I} a J_{l}+{ }^{2} a J_{2} .$$
Proof. Utilizing Eq. (2.61), and by joining in Fig. $4.22$ the following invariant Shannon nodes:
$$\left[\begin{array}{ccc} \alpha_{1} & 0 & 0 \ 0 & \beta_{1} & 0 \ 0 & 0 & \gamma_{1} \end{array}\right],\left[\begin{array}{ccc} \alpha_{2} & 0 & 0 \ 0 & \beta_{2} & 0 \ 0 & 0 & \gamma_{2} \end{array}\right],\left[\begin{array}{ccc} \alpha_{3} & 0 & 0 \ 0 & \beta_{3} & 0 \ 0 & 0 & \gamma_{3} \end{array}\right] .$$
And by assigning the following values for the set of edges ${\mathrm{r}, \mathrm{s}, \mathrm{t}, \mathrm{u}$, $\mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{y}, \mathrm{z}}$ in Fig. 4.22:
\begin{aligned} &t=\hat{\alpha}{1}{ }^{0} a, v=\hat{\alpha}{2}{ }^{0} a, y=\hat{\alpha}{3}{ }^{0} a . \ &r=\hat{\beta}{1}{ }^{l} a, u=\hat{\beta}{2}{ }^{l} a, x=\hat{\beta}{3}{ }^{I} a . \ &s=\hat{\gamma}{1}{ }^{2} a, w=\hat{\gamma}{2}{ }^{2} a, z=\hat{\gamma}{3}{ }^{2} a . \end{aligned} One obtains the following set of Eqs. before and after joining the three nodes $\mathrm{J}{0}, \mathrm{~J}{1}$, and $\mathrm{J}{2}$ in Fig. $4.22$ (where: $\left{\mathrm{A}, \mathrm{C}, \mathrm{J}{0}\right}$ are the set of functions for node $B,\left{E, F, J{1}\right}$ are the set of functions for node $D$, and $\left{\mathrm{I}, \mathrm{G}, \mathrm{J}_{2}\right}$ are the set of functions for node $\mathrm{H}$, respectively).

## 计算机代写|量子计算代写Quantum computing代考|Three-Dimensional Invariant Shannon

Ĵ=0一种Ĵ0+一世一种Ĵl+2一种Ĵ2.

[一种100 0b10 00C1],[一种200 0b20 00C2],[一种300 0b30 00C3].

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。