### 计算机代写|量子计算代写Quantum computing代考| Scope of the Work

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|Scope of the Work

Since modern circuit design requires a certain level of regularity due to the fact that regular structures lead to the ease of testability $[99,124,198,199,204,218]$, ease of manufacturability, and freelibrary synthesis, one would like to design reversible structures that are regular, which will produce (1) minimal, (2) universal, (3) regular, and (4) reversible circuits. Minimal means to reduce (or if possible to eliminate) the number of garbage outputs that are needed only for the purpose of reversibility, and to reduce the number of gates used. Universal (or complete) means that the structure must be able to realize all logic functions for particular radix of logic and particular number of variables. Regular means that the structure must have a fixed number of gate types and interconnect types from which the whole structure is synthesized. Consequently, full regularity means that one type of internal nodes and one type of interconnects are used, semi regularity means that fixed number of internal node types and fixed number of interconnect types are used, and non-regularity means that arbitrary types of internal nodes and arbitrary types of interconnects are used. Synthesis methods to design minimal-size regular reversible circuits that will produce minimal size quantum registers were largely missing from previous research and literature, and this has been the driving force behind the development of reversible and quantum computing methods presented in this Book. To achieve the general goal of reversibility and regularity new reversible logic synthesis methodologies have been developed. Figure $1.4$ shows the main ideas (i.e., tree paths) that were the driving force behind the development of this work.

Since minimal size is one important design specification of reversible and consequently quantum logic structures, functional minimization techniques, which exist in the conventional design tools, can be used to produce minimal size functional expressions, and consequently algorithms can manipulate such expressions to efficiently design reversible and quantum circuits. Conventional ESOP minimizers and other minimization techniques, such as S/D trees, can be used for this purpose $[4,9,52,114,157,232,233,235]$. Another direction of area minimization of reversible structures is using multiple-valued logic, especially as multiple-valued logic has been efficiently used in conventional hardware for learning $[186,187]$, testing [124], and IC design [86,267]. Similar to the conventional case, using higher radix in multiple-valued logic will minimize the number of wiring used as compared to binary logic to achieve the same functionality of logic structure $[86,119,120,155,166,229,267]$. Multiple-valued computing becomes important especially as multiple-valued quantum computations are performed on the same atomic structures on which two-valued quantum computations are performed without the need of adding new structural elements as compared to the conventional domain. This is due to the fact that quantum computing is performed using fundamental properties of particles such as spins of electron or polarizations of light $[162,163]$, and these same physical properties are used to perform both two-valued and multiple-valued computations without the need of adding new circuit elements as in the conventional circuit design, especially the fact that multiplevalued quantum devices that perform the corresponding multiplevalued quantum computations have been created using trapped ions $[54,165]$, and tunnel diodes [220]. For example, another way to harness the functional power of performing multiple-valued quantum computations is to perform minimal number of light polarizations to execute the same functionality as compared to using only two-valued quantum computations [163]. (One objective of this Book is to develop a theory for multiple-valued quantum computing that includes the binary case as a special case.) Consequently, the core stream of this Book follows the diagram shown in Fig. 1.5.

## 计算机代写|量子计算代写Quantum computing代考|Organization of the Book

To reach the objective shown in Fig. 1.5, this Book is divided into several intermediate steps that include the general components of: (1) reversibility, (2) multiple-valued logic, (3) minimization, (4) regularity, and (5) quantum computing. These elements of the Book are illustrated using the lattice diagram in Fig. 1.6.

Chapter 2 includes fundamentals and mathematical background that are needed to construct various important reversibility theorems in the next Chapts. This include binary and multiple-valued normal Galois forms, and new types of expansions which constitute a generalization of some basic decompositions that play classically a central role in modern logic synthesis tools.

Chapter 3 presents new types of families of multiple-valued trees, their associated properties, and their corresponding canonical forms and hierarchies. These new forms serve as an intermediate step to produce one important minimization methodology of multiple-valued Galois functions that uses the polarity of multiplevalued Inclusive Forms (IFs) which are generated from Shannon/Davio (S/D) trees. The new multiple-valued minimizer will be used for functional minimization in order to realize logic functions in minimal size reversible structures such as reversible Cascades that will be presented in Chapt. 8 .

An important class of regular structures that will be used in Chapt. 6 to reversibly realize Boolean and multiple-valued logic functions, which is called lattice structure, is presented in Chapt. 4 . New three-dimensional lattices, that are built using the new spectral transforms from Chapt. 2, are introduced. An important methodology that restricts the realization of lattice structures to specific structural boundaries, called Iterative Symmetry Indices Decomposition (ISID), is also introduced.

## 计算机代写|量子计算代写Quantum computing代考|Appendix A introduces

Appendix A introduces count results to count the various classes of the new binary and multiple-valued invariant Shannon and Davio expansions from Chapt. 2. Circuits that implement the quaternary Galois field Sum-Of-Products (GFSOP) expressions, which are discussed in Chapt. 2, are introduced in Appendix B. Two novel count results for the count of S/D trees and the corresponding Inclusive Forms, that were the main result of Chapt. 3, are presented in Appendix C. Circuit realizations of multiple-valued S/D trees are introduced in the form of Universal Logic Modules (ULMs) in Appendix D. Background on Evolutionary Computing, which is used in various algorithms in different locations in Chapt. 3, Chapt. 8 , and Chapt. 11, is presented in Appendix E. The count of all possible families of binary and multiple-valued reversible Shannon and Davio decompositions that result from Chapt. 5 is introduced in Appendix F. Appendix G presents the NPN classification method of Boolean functions and the complexity measures that are used in Chapt. 7 and Appendix $\mathrm{H}$ of this Book. New evaluation results that compare the new Modified Reconstructability Analysis (MRA) structure from Chapt. 7 and Ashenhurst-Curtis and BiDecomposition are presented in Appendix H. Appendix I introduces the count for reversible Nets that were introduced in Chapt. 8. Novel optical realizations of two-valued and multiple-valued classical and reversible logics are presented in Appendix J. Appendix $\mathrm{K}$ utilizes results in multiple-valued quantum computing from Chapt. 11 to introduce new results in multiple-valued quantum implementation of discrete Artificial Neural Networks.

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## MATLAB代写

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