Reversible Logic Synthesis Methodologies with Application to Quantum Computing 1st Edition by Saleem Mohammed Ridha Taha 3319234793 9783319234793

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ISBN-10 :  3319234793 

ISBN-13 :  9783319234793

Author:  Saleem Mohammed Ridha Taha 

This book opens the door to a new interesting and ambitious world of reversible and quantum computing research. It presents the state of the art required to travel around that world safely. Top world universities, companies and government institutions are in a race of developing new methodologies, algorithms and circuits on reversible logic, quantum logic, reversible and quantum computing and nano-technologies. In this book, twelve reversible logic synthesis methodologies are presented for the first time in a single literature with some new proposals. Also, the sequential reversible logic circuitries are discussed for the first time in a book. Reversible logic plays an important role in quantum computing. Any progress in the domain of reversible logic can be directly applied to quantum logic. One of the goals of this book is to show the application of reversible logic in quantum computing. A new implementation of wavelet and multiwavelet transforms using quantum computing is performed for this purpose. Researchers in academia or industry and graduate students, who work in logic synthesis, quantum computing, nano-technology, and low power VLSI circuit design, will be interested in this book.

Reversible Logic Synthesis Methodologies with Application to Quantum Computing 1st Table of contents:

1 Introduction
1.1 Background
1.2 What This Book Is About
1.3 Motivation
1.4 Major Contributions of This Book
1.5 Overview of the Book Chapters
1.6 Overall Message of the Book
References
2 Fundamentals of Reversible Logic
2.1 Preliminaries
2.2 Basic Definitions
2.3 Reversible Logic Gates
2.3.1 Feynman Gate
2.3.2 Toffoli Gate
2.3.3 Fredkin Gate
2.4 Reversible Logic Synthesis
2.5 Overview of Reversible Logic Synthesis Methods
2.6 The Elimination of Garbage in Binary Reversible Circuits
References
3 Methods of Reversible Logic Synthesis
3.1 Reversible Expansions and Reversible Spectral Transforms
3.1.1 Reversible Ternary Shannon and Davio Expansions
3.1.2 Reversible Shannon Spectral Transforms
3.1.3 Reversible Davio Spectral Transforms
3.2 The Elimination of Garbage in Ternary Reversible Circuits
3.3 Reversible Decision Trees (RDTs)
3.4 Reversible Decision Diagrams (RDDs)
3.5 Reversible Lattice Circuits
3.5.1 Symmetric and Non-symmetric Functions
3.5.2 Two-Dimensional Lattice Circuits
3.5.3 Three-Dimensional Lattice Circuits
3.5.4 Algorithms for Realizing the Shannon/Davio Expansions of Ternary Functions into 3D Lattice Cir
3.5.4.1 An Algorithm for the Shannon Expansion
3.5.4.2 An Algorithm for the Davio0 Expansion
3.5.4.3 New Algorithms for the Shannon/Davio Hybrid Expansions
3.5.5 Complete Example for the Implementation of Ternary Functions Using 3D Lattice Circuits
3.5.6 New Minimal Realization Method for 3D Lattice Circuits
3.5.7 Lattice Circuit Synthesis Using ISID
3.5.8 The Creation of Reversible Lattice Structures
3.5.9 3D Ternary Davio Reversible Lattice Structures
3.6 Reversible Fast Transform Circuits
3.7 Group-Theoretic Representations
3.8 Reversible Reconstructability Analysis Circuits
3.8.1 Ternary MRA
3.8.2 Reversible MRA (RMRA)
3.9 Reversible Programmable Gate Array (RPGA)
3.9.1 Definitions
3.9.2 (2 * 2) Net Structures and RPGAs
3.9.3 The New Reversible Gate (SALEEM)
3.9.4 Novel Design of RPGA Based on the SALEEM Reversible Gate
3.10 Reversible Cascade Circuits
3.11 Spectral-Based Synthesis Method
3.12 Transformation-Based Network Synthesis of Fredkin-Toffoli Cascade Gates
3.13 Heuristic Algorithm for Reversible Logic Synthesis
3.14 Constructive Synthesis of Reversible Circuits by NOT and (n 2212 1)-CNOT Gates
3.15 Summary
References
4 Evaluation of the Reversible Logic Synthesis Methodologies
4.1 NPN-Classification of Logic Functions
4.2 New Evaluation Procedure of Reversible Synthesis Methods
4.3 Comparison Between the Various Reversible Synthesis Methodologies
4.4 Summary
References
5 Reversible Sequential Logic Circuits
5.1 Reversible Flip Flops
5.1.1 Reversible RS Flip Flop
5.1.2 Reversible Clocked RS Flip Flop
5.1.3 Reversible D Flip Flop
5.1.4 Reversible JK Flip Flop
5.1.5 Reversible T Flip Flop
5.1.6 Reversible Master-Slave Flip Flop
5.1.7 The Superiority of Using the SALEEM Gate in Reversible Flip Flops Design
5.2 Complex Reversible Sequential Circuits
5.3 Novel Reversible Sequential Elements
5.3.1 New Design of Reversible T Flip Flop
5.3.2 New Design of Reversible D Flip Flop
5.3.3 New Design of Reversible JK Flip Flop
5.3.4 New Design of Reversible Master-Slave Flip Flops
5.3.5 Evaluation of the New Reversible Flip Flops
5.4 Multiple-Valued Reversible Sequential Circuits
5.5 Summary
References
6 Quantum Logic Circuits and Quantum Computing
6.1 Background
6.2 Quantum Bits and Superposition
6.3 Qubit Registers
6.4 Quantum Logic Gates
6.5 Quantum Logic Circuits
6.6 Synthesis of Quantum Logic Circuits
6.7 Binary Quantum Decision Trees and Diagrams
6.8 Fundamentals of Ternary Quantum Computing
6.9 Quantum Computing for the Reversible Structures
References
7 Wavelets and Multiwavelets Implementation Using Quantum Computing
7.1 Introduction
7.2 Quantum Circuits for Perfect Shuffle Permutation Matrices
7.3 Quantum Wavelet Algorithms
7.3.1 Wavelet Pyramidal and Packet Algorithms
7.3.2 Daubechies D(4) Wavelet Factorization
7.4 Quantum Implementation of Daubechies D(4) Wavelet
7.5 Quantum Implementation of Daubechies D(4) Multiwavelet
7.5.1 Computation of Discrete Multiwavelet Transform
7.5.2 Computation of Inverse Discrete Multiwavelet Transform
7.5.3 A New Quantum Implementation of Daubechies D(4) Multiwavelet Transform
7.5.4 A New Quantum Implementation of Inverse Daubechies D(4) Multiwavelet Transform
References
8 Conclusions and Future Researches
8.1 Conclusions
8.2 Promising Areas of Further Researches

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Tags: Reversible Logic, Methodologies, Application, Quantum Computing, Saleem Mohammed Ridha Taha