Computing with Multi-Value Logic in Quantum Dot Cellular Automata

Reza Sabbaghi-Nadooshan, PhD, is a Professor with the Department of Electrical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran. Reza Akbari-Hasanjani, PhD, is with the Department of Electrical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran. Leila Dehbozorgi is with the Department of Electrical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran. Majid Haghparast is affiliated with the Faculty of Information Technology at the University of Jyväskylä, Jyväskylä, Finland. Hamid Reza Akbari-Hasanjani, PhD, is with the School of Chemistry, Damghan University, Damghan, Iran.

List of Figures xi

List of Tables xvii

About the Authors xxi

Preface xxiii

Introduction xxv

1 Quantum Dots 1

1.1 Introduction to Quantum Dots 1

1.2 Physical Characteristics of Semiconductor Quantum Dots 2

1.3 Quantum Dots Structure 3

1.4 Surface Structure of Quantum Dots 7

1.5 Properties of Quantum Dots 10

2 Synthesis Methods of Quantum Dots and Applications 15

2.1 Synthesis Processes 15

2.2 Top-Down Synthesis Processes 15

2.3 Bottom-Up Synthesis Processes 17

2.4 Applications of Quantum Dots 19

3 Overview of QCA 23

3.1 Introduction to QCA Technology 23

3.2 Binary QCA Concept 24

3.3 Ternary QCA Cell Structure 24

3.4 Clock in QCA Technology 25

3.5 Manufacturing and Implementation of QCA 26

3.6 Overview of Quantum Gates 26

4 Polarization and Polarization Calculations in QCA (Quantum Calculations in QCA) 33

4.1 Introduction 33

4.2 Polarization and Calculation of Hamiltonian Matrix in QCA 33

5 Multi-Valued Cells Based on Polarization Calculations 59

5.1 Ternary QCA 59

5.2 Quaternary QCA 62

5.3 Quinary QCA 72

5.4 Hypothesis Based on n-Value QCA Cell 82

5.5 Fuzzy Logic Design Using MIN and MAX Functions 84

5.6 Quantum Information 87

6 Effect of Polarization for Two Adjacent Cells and Power Consumption in Multi-Valued Cells 91

6.1 Effect of Two Adjacent Cells in Terms of Polarization 91

6.2 Power Consumption in QCA Technology 95

7 Structure of Basic Gates Using the Proposed Cells in Multi-Value QCA 101

7.1 Structure of Basic Gates Using TQCA 101

7.2 Structure of Basic QQCA Gates 105

7.3 Structure of Basic Gates Using QuQCA 111

8 Implementation of Ternary and Quaternary Basic Gates Using QQCASim and TQCASim 119

8.1 TQCA Simulator 120

8.2 QQCA Simulator for QQCA Circuit Simulation 125

9 A Review of Literature on Memory Structures 135

9.1 Introduction 135

9.2 A Review of Basic Memory Structures 136

9.3 Review of Literature on Memory Design 138

10 Proposed PIM Cells and Their Fault Analysis in Binary QCA 141

10.1 Introduction 141

10.2 Binary QCA-Based Structures 143

10.3 Fault Analysis 147

11 Design Details of Binary Boolean Operators Using Basic PIM Cells: Proposing and Analyzing Basic-Extended Hypothesis 157

11.1 Introduction 157

11.2 Basic-Extended Hypothesis 157

11.3 Designing Logic Gates with Binary QCA-Based PIM Capability 157

12 Proposed PIM Cells in Ternary QCA and Their Fault Analysis 173

12.1 Introduction 173

12.2 Simulation of a Flip-Flop in Ternary QCA Using MATLAB 173

12.3 Structures in Ternary QCA 174

12.4 Fault Analysis 181

13 Design Details of Ternary Boolean Operators Using Basic PIM Cells and Analysis of Basic-Extended Hypothesis 189

13.1 Introduction 189

13.2 Designing Logic Gates With Ternary QCA-Based PIM Capability 189

13.3 Evaluation, Analysis, and Comparison of Results 196

14 Conclusions and Suggestions 201

14.1 Introduction 201

14.2 Summary and Conclusion 201

14.3 Suggestions 203

References 205

A Matrices217

A.1 Particle State Matrix in QQCA 217

A.2 Particle State Matrix in QQCA 218

B Electrostatic Energy Calculation 223

Index 237