Computing with Multi-Value Logic in Quantum Dot Cellular Automata E-Book

Reza Sabbaghi-Nadooshan

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 379

Veröffentlichungsjahr: 2024

Beschreibung

Meet the latest challenges in quantum computing with this cutting-edge volume

Miniaturization is one of the major forms (and drivers) of innovation in electronics and computing. In recent years, the rapid reduction in the size of semiconductors and other key elements of digital technology has created major challenges, which new technologies are being continuously mobilized to meet. Quantum dot cellular automata (QCA) is a technology with huge potential to meet these challenges, particularly if multi-value computing is brought to bear.

Computing with Multi-Value Logic in Quantum Dot Cellular Automata introduces this groundbreaking area of technology and its major applications. Using MATLAB^® software and a novel multi-value logic simulator, the book demonstrates that multi-value circuits with a function that approximates fuzzy logic are within reach of modern engineering and design. Rigorous and clear, this book offers a crucial introduction to the processes of designing multi-value logic circuits with QCA technology.

Readers will also find:

• The tools required to design fuzzy-quantum controllers with high processing speed
• Detailed discussion of topics including basic gate function, the energy consumption of QCA multi-value cells, and much more
• Extensive MATLAB^® data and other worked-through examples

Computing with Multi-Value Logic in Quantum Dot Cellular Automata is ideal for researchers and readers who are looking for an explanation of the basic concepts required to design multi-value circuits in this field.

Leseprobe

Table of Contents

Cover

Table of Contents

Title Page

Copyright

List of Figures

List of Tables

About the Authors

Preface

Introduction

1 Quantum Dots

1.1 Introduction to Quantum Dots

1.2 Physical Characteristics of Semiconductor Quantum Dots

1.3 Quantum Dots Structure

1.4 Surface Structure of Quantum Dots

1.5 Properties of Quantum Dots

2 Synthesis Methods of Quantum Dots and Applications

2.1 Synthesis Processes

2.2 Top-Down Synthesis Processes

2.3 Bottom-Up Synthesis Processes

2.4 Applications of Quantum Dots

3 Overview of QCA

3.1 Introduction to QCA Technology

3.2 Binary QCA Concept

3.3 Ternary QCA Cell Structure

3.4 Clock in QCA Technology

3.5 Manufacturing and Implementation of QCA

3.6 Overview of Quantum Gates

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

4.1 Introduction

4.2 Polarization and Calculation of Hamiltonian Matrix in QCA

5 Multi-Valued Cells Based on Polarization Calculations

5.1 Ternary QCA

5.2 Quaternary QCA

5.3 Quinary QCA

5.4 Hypothesis Based on

n

-Value QCA Cell

5.5 Fuzzy Logic Design Using MIN and MAX Functions

5.6 Quantum Information

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

6.1 Effect of Two Adjacent Cells in Terms of Polarization

6.2 Power Consumption in QCA Technology

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

7.1 Structure of Basic Gates Using TQCA

7.2 Structure of Basic QQCA Gates

7.3 Structure of Basic Gates Using QuQCA

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

8.1 TQCA Simulator

8.2 QQCA Simulator for QQCA Circuit Simulation

9 A Review of Literature on Memory Structures

9.1 Introduction

9.2 A Review of Basic Memory Structures

9.3 Review of Literature on Memory Design

10 Proposed PIM Cells and Their Fault Analysis in Binary QCA

10.1 Introduction

10.2 Binary QCA-Based Structures

10.3 Fault Analysis

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

11.1 Introduction

11.2 Basic-Extended Hypothesis

11.3 Designing Logic Gates with Binary QCA-Based PIM Capability

12 Proposed PIM Cells in Ternary QCA and Their Fault Analysis

12.1 Introduction

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

12.3 Structures in Ternary QCA

12.4 Fault Analysis

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

13.1 Introduction

13.2 Designing Logic Gates With Ternary QCA-Based PIM Capability

13.3 Evaluation, Analysis, and Comparison of Results

14 Conclusions and Suggestions

14.1 Introduction

14.2 Summary and Conclusion

14.3 Suggestions

References

A Matrices

A.1 Particle State Matrix in QQCA

A.2 Particle State Matrix in QQCA

B Electrostatic Energy Calculation

Index

End User License Agreement

List of Tables

Chapter 3

Table 3.1 Binary NOT gate response for different polarizations.

Table 3.2 Binary AND gate truth table in QCA technology.

Table 3.3 Binary gate truth table in QCA technology.

Chapter 4

Table 4.1 Spin state of two electrons.

Table 4.2 Spin states of a three-particle system (with electrons).

Table 4.3 Vectors of quaternary input states.

Table 4.4 Polarization of a three-particle system in QQCA.

Table 4.5 Spin states of a four-electron system.

Table 4.6 Input states of the quinary system.

Table 4.7 Polarizations of the quinary system.

Chapter 5

Table 5.1 QQCA cell polarizations.

Table 5.2 Truth table for the quaternary input drive.

Table 5.3 Truth table of the first structure of the quaternary output drive....

Table 5.4 The truth table of the second structure of the quaternary input dr...

Table 5.5 The truth table for determination of quaternary output using bQCA ...

Table 5.6 Polarizations in QuQCA.

Table 5.7 Truth table of five-value input drive.

Table 5.8 Input states for the simplified output model in the quinary system...

Table 5.9 Truth table of the second input drive in QuQCA.

Table 5.10 QuQCA output truth table.

Table 5.11 Specifications of

n

-valued cell structures.

Table 5.12 Truth table of the proposed fuzzy pressure control system.

Chapter 7

Table 7.1 Output of ternary NOT gate.

Table 7.2 Outputs of the ternary inverter gate for all polarization states....

Table 7.3 Interactions of two adjacent ternary cells (TQCA quantum wire).

Table 7.4 Outputs of the interactions of two adjacent ternary cells for all ...

Table 7.5 Majority ternary gate output.

Table 7.6 Results of AND and OR gates with three values.

Table 7.7 Output of the QQCA-based NOT gate.

Table 7.8 Results of the QQCA-based NOT gate in different states and corresp...

Table 7.9 Effect of two adjacent four-valued cells (QQCA-based wire).

Table 7.10 Output states of the interactions of two quaternary cells and the...

Table 7.11 QQCA majority gate output.

Table 7.12 Validity of QQCA-based AND and OR gates.

Table 7.13 Quaternary AND and OR gate truth table.

Table 7.14 NOT gate states in QuQCA.

Table 7.15 QuQCA NOT gate for all states and determining the...

Table 7.16 QuQCA-based wire truth table.

Table 7.17 Output states of the interactions of two QuQCA cells and final re...

Table 7.18 Majority gate truth table in QuQCA.

Table 7.19 Truth tables of the quinary AND and OR gates.

Chapter 10

Table 10.1 Parameters used in QCADesigner.

Table 10.2 Outputs of different inputs applied to BPIM3188.

Table 10.3 Cell omission fault evaluation in BPIM1.

Table 10.4 Extra-cell deposition fault evaluation in BPIM1187.

Table 10.5 Cell omission fault evaluation in BPIM2.

Table 10.6 Extra-cell deposition fault evaluation in BPIM2.

Table 10.7 Cell omission fault evaluation in BPIM3.

Table 10.8 Extra-cell deposition fault evaluation in BPIM3.

Table 10.9 Cell omission fault evaluation in BPIM4.

Table 10.10 Extra-cell deposition fault evaluation in BPIM4.

Chapter 12

Table 12.1 Cell omission defect analysis for TPIM1.

Table 12.2 Extra-cell deposition defect analysis for TPIM1.

Table 12.3 Cell omission defect analysis for TPIM2.

Table 12.4 Extra-cell deposition defect analysis for TPIM2.

Table 12.5 Cell omission defect analysis for TPIM3.

Table 12.6 Extra-cell deposition defect analysis for TPIM3.

Chapter 13

Table 13.1 Parameters of proposed binary and ternary RAM and PIM cells.

Table 13.2 Design parameters of binary and ternary gates.

Table 13.3 Comparison of binary and ternary XOR structures.

B

Table B.1 Output results of the ternary AND gate in all cases.

Table B.2 Output of ternary OR gates in all cases.

Table B.3 Outputs of the quaternary AND gates in all cases.

Table B.4 Output results of quaternary OR gate.

Table B.5 Output results of Coulomb energy values in the quaternary AND gate...

Table B.6 Output results of Coulomb energy values for the quinary OR gate in...

List of Illustrations

Chapter 1

Figure 1.1 The role of energy levels in the reduction of semiconductor gaps ...

Figure 1.2 Basic structure of an uncoated QD.

Figure 1.3 The bandgap alignments.

Figure 1.4 Schematic representation of the emission mechanism in QDs.

Figure 1.5 Photoelectrochemical property of quantum dots under light irradia...

Chapter 2

Figure 2.1 Comparison of top-down and bottom-up methods.

Chapter 3

Figure 3.1 Polarizations of bQCA cells.

Figure 3.2 TQCA cell.

Figure 3.3 States of electron placement in a stable TQCA cell.

Figure 3.4 Clock in QCA in four phases.

Figure 3.5 90° wire.

Figure 3.6 45° wire.

Figure 3.7 Overlapping or plate wiring structure.

Figure 3.8 Multilayer wiring structure.

Figure 3.9 Transmission wire with two-phase clock difference.

Figure 3.10 NOT gate using two bQCA cells diagonally.

Figure 3.11 NOT gate using two diagonal NOT gates.

Figure 3.12 Inverter gate with reduced area.

Figure 3.13 Majority gate with three inputs.

Figure 3.14 The majority gate with five inputs.

Figure 3.15 AND gate structure.

Figure 3.16 OR gate structure.

Chapter 4

Figure 4.1 TQCA polarization simulation diagram.

Figure 4.2 Polarization diagram in QQCA based on calculations.

Figure 4.3 Polarization diagram in QuQCA.

Chapter 5

Figure 5.1 Polarizations of the ternary model.

Figure 5.2 TQCA cell proposed in Ref. [129].

Figure 5.3 Distance between items of two proposed TQCA cells.

Figure 5.4 Distances between two ternary cells to calculate the external ele...

Figure 5.5 Shows the proposed QQCA model.

Figure 5.6 Specifications of the used layers.

Figure 5.7 QQCA cell symbol.

Figure 5.8 Input drive block in QQCA.

Figure 5.9 The first proposed output drive.

Figure 5.10 Second structure of the input drive.

Figure 5.11 Distances between two ternary cells in the first layer.

Figure 5.12 Distances between two QQCA cells in the second layer.

Figure 5.13 Symbolic representation of two QCA cells.

Figure 5.14 Proposed QuQCA model.

Figure 5.15 Specifications of the ternary layer.

Figure 5.16 QuQCA cell symbol.

Figure 5.17 Schematic of the input drive using decoder.

Figure 5.18 Schematic of the first output drive.

Figure 5.19 Simplified output drive model [131].

Figure 5.20 Second input drive in QuQCA.

Figure 5.21 TQCA-based half-adder circuit.

Figure 5.22 Distances between electrons in the first layer.

Figure 5.23 Distances between electrons in the second layer.

Figure 5.24 Symbolic representation of two adjacent cells in QuQCA.

Figure 5.25 Block diagram of the studied fuzzy system.

Figure 5.26 Fuzzy system rule base simulation: (a) the circuit representatio...

Figure 5.27 Quantum gates.

Chapter 6

Figure 6.1 Effect of two neighboring TQCA cells at different kinetic energie...

Figure 6.2 Interactions of two cells in the ternary layer.

Figure 6.3 Interactions of two cells in the binary layer.

Figure 6.4 Interactions of two neighboring cells in the ternary layers of Qu...

Figure 6.5 Power consumption in TQCA as per polarization set {−2, 0, 2}.

Figure 6.6 Energy consumption in QQCA using quantum computation.

Figure 6.7 Power consumption in the proposed QQCA cell.

Figure 6.8 Power consumption using QuQCA quantum calculations.

Figure 6.9 Power consumption in the proposed QuQCA cell.

Chapter 7

Figure 7.1 Ternary NOT gate.

Figure 7.2 Two adjacent TQCA cells (wire).

Figure 7.3 Majority ternary gate.

Figure 7.4 (a) AND gate structure with a fixed input in state A and (b) OR g...

Figure 7.5 QQCA-based NOT gate.

Figure 7.6 Two QQCA cells (QQCA-based wire).

Figure 7.7 QQCA majority gates: (a) standard majority gate and (b) diagonal ...

Figure 7.8 AND and OR gates with two inputs and one fixed input (a) AND gate...

Figure 7.9 Representation of a NOT gate using the QuQCA-based symbolic model...

Figure 7.10 Two neighboring cells using the QuQCA symbolic model.

Figure 7.11 QuQCA majority gate.

Figure 7.12 QQCA-based AND and OR gate structures: (a) AND gate structure wi...

Chapter 8

Figure 8.1 Environment of TQCASim software version 1.0.11.1.

Figure 8.2 TQCA cell options.

Figure 8.3 Simulation of a three-value majority gate: (a) majority gate desi...

Figure 8.4 Simulation of ternary AND gates; (a) AND gates designed with TQCA...

Figure 8.5 Simulation of the ternary OR gate: (a) OR gate designed by TQCASi...

Figure 8.6 Simulation of two TQCA cells: (a) the two cells simulated in TQCA...

Figure 8.7 Simulation of a ternary wire with an odd number of cells: (a) odd...

Figure 8.8 Simulation of a ternary wire with an even number of cells: (a) te...

Figure 8.9 Environment of QQCASim software version 1.0.0.1.

Figure 8.10 Specifications of QQCA cells.

Figure 8.11 Simulation of a quaternary majority gate: (a) majority gate desi...

Figure 8.12 Simulation of the quaternary AND gate: (a) AND gate designed usi...

Figure 8.13 Simulation of the quaternary OR gate: (a) OR gate designed in QQ...

Figure 8.14 Quaternary NOT gate simulation: (a) NOT gate in QQCASim, (b) NOT...

Figure 8.15 A quaternary quantum wire: (a) quantum wire, (b) quantum wire ou...

Chapter 9

Figure 9.1 (a) Comparison of von Neumann and PIM structures, (b) representat...

Figure 9.2 Three different fault-tolerant three-input majority gates.

Chapter 10

Figure 10.1 BPIM1: (a) implementation in binary QCA and (b) simulation resul...

Figure 10.2 BPIM2: (a) implementation in binary QCA and (b) simulation resul...

Figure 10.3 BPIM3: (a) block diagram of the proposed model, (b) implementati...

Figure 10.4 BPIM4: (a) block diagram, (b) implementation in binary QCA, and ...

Figure 10.5 Cell numbering in BPIM1.

Figure 10.6 Cell numbering in BPIM2.

Figure 10.7 Cell numbering in BPIM3.

Figure 10.8 Cell numbering in BPIM4.

Chapter 11

Figure 11.1 Block diagram of two-input AND gate using Akers array.

Figure 11.2 Two-input AND gate using PIM structure in binary QCA: (a) BAND1 ...

Figure 11.3 AND gate simulation results using binary QCA-based PIM structure...

Figure 11.4 Block diagram of two-input OR gate using Akers array.

Figure 11.5 Two-input OR gate using binary QCA-based PIM structure: (a) BOR1...

Figure 11.6 OR gate simulation results using binary QCA-based PIM: (a) BOR1 ...

Figure 11.7 Block diagram of two-input NAND gate in Akers array.

Figure 11.8 Two-input NAND gate based on PIM structure in binary QCA: (a) BN...

Figure 11.9 NAND simulation results based on PIM structure in binary QCA: (a...

Figure 11.10 Block diagram of two-input NOR gate using Akers array.

Figure 11.11 Two-input NOR gate using PIM structure in binary QCA: (a) BNOR1...

Figure 11.12 NOR simulation results based on PIM structure in binary QCA: (a...

Figure 11.13 (a) structure of basic cells and their layout in Akers array an...

Figure 11.14 Two-input BXOR gate using PIM in binary QCA.

Figure 11.15 Simulation results of BXOR using PIM in binary QCA.

Chapter 12

Figure 12.1 DFF structure.

Figure 12.2 Proposed DFF implemented and simulated using MATLAB.

Figure 12.3 Output diagrams of the proposed ternary QCA-based DFF designed u...

Figure 12.4 First model of PIM cell, TPIM1: (a) implementation in ternary QC...

Figure 12.5 Second model of PIM cell, TPIM2: (a) implementation in ternary Q...

Figure 12.6 Third model of PIM cell (TPIM3): (a) implementation in ternary Q...

Figure 12.7 (a) Diagram and operating principle of switches in the QCA-based...

Figure 12.8 Numbering of cells in TPIM1.

Figure 12.9 Numbering of cells in TPIM2.

Figure 12.10 Numbering of cells in TPIM3.

Chapter 13

Figure 13.1 Two-input AND gate using PIM structure in ternary QCA: (a) TAND1...

Figure 13.2 AND gate simulation results using ternary QCA-based PIM structur...

Figure 13.3 Two-input OR gate using PIM structure in ternary QCA: (a) TOR1 m...

Figure 13.4 OR gate simulation results using ternary QCA-based PIM structure...

Figure 13.5 XOR gate using ternary QCA-based PIM: (a) TXOR model and (b) tru...

Figure 13.6 Comparison of fault tolerance against extra-cell deposition and ...

Guide

Cover

Table of Contents

Series Page

Title Page

Copyright

List of Figures

List of Tables

About the Authors

Preface

Introduction

Begin Reading

References

A Matrices

B Electrostatic Energy Calculation

Index

End User License Agreement

Pages

ii

iii

iv

xi

xii

xiii

xiv

xv

xvii

xviii

xix

xxi

xxiii

xxv

xxvi

1

2

3

4

5

6

7

8

9

10

11

12

13

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

91

92

93

94

95

96

97

98

99

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

189

190

191

192

193

194

195

196

197

198

199

201

202

203

205

206

207

208

209

210

211

212

213

214

215

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

237

238

239

240

241

242

243

IEEE Press445 Hoes LanePiscataway, NJ 08854

IEEE Press Editorial BoardSarah Spurgeon, Editor in Chief

Moeness AminJón Atli BenediktssonAdam DrobotJames Duncan

Ekram HossainBrian JohnsonHai LiJames LykeJoydeep Mitra

Desineni Subbaram NaiduTony Q. S. QuekBehzad RazaviThomas RobertazziDiomidis Spinellis

Computing with Multi-Value Logic in Quantum Dot Cellular Automata

Reza Sabbaghi-Nadooshan

Islamic Azad University

Tehran, Iran

Reza Akbari-Hasanjani

Islamic Azad University

Tehran, Iran

Leila Dehbozorgi

Islamic Azad University

Tehran, Iran

Majid Haghparast

University of Jyväskylä

Jyväskylä, Finland

Hamid Reza Akbari Hasanjani

Damghan University

Damghan, Iran

Copyright © 2024 by The Institute of Electrical and Electronics Engineers, Inc.

All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, [phone], fax [phone], or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, [phone], fax [phone], or online at http://www.wiley.com/go/permission.

Trademarks: Wiley and the Wiley logo are trademarks or registered trademarks of John Wiley & Sons, Inc. and/or its affiliates in the United States and other countries and may not be used without written permission. All other trademarks are the property of their respective owners. John Wiley & Sons, Inc. is not associated with any product or vendor mentioned in this book

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at [phone], outside the United States at [phone] or fax [phone].

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com.

Library of Congress Cataloging-in-Publication Data:

Names: Sabbaghi-Nadooshan, Reza, author.

Title: Computing with multi-value logic in quantum dot cellular automata / Reza Sabbaghi-Nadooshan, Reza Akbari-Hasanjani, Leila Dehbozorgi, Majid Haghparast, and Hamid Reza Akbari-Hasanjani.

Description: Hoboken, New Jersey : Wiley, [2024] | Includes index.

Identifiers: LCCN 2024023397 (print) | LCCN 2024023398 (ebook) | ISBN 9781394253944 (hardback) | ISBN 9781394253968 (adobe pdf) | ISBN 9781394253951 (epub)

Subjects: LCSH: Quantum dots. | Cellular automata. | Many-valued logic.

Classification: LCC TK7874.88 .S23 2017 (print) | LCC TK7874.88 (ebook) | DDC 621.39/5–dc23/eng/20240629

LC record available at https://lccn.loc.gov/2024023397

LC ebook record available at https://lccn.loc.gov/2024023398

Cover Design: WileyCover Image: © Eugene Mymrin/Getty Images

List of Figures

Figure 1.1

The role of energy levels in the reduction of semiconductor gaps with the increase in nanocrystal size.

Figure 1.2

Basic structure of an uncoated QD.

Figure 1.3

The bandgap alignments.

Figure 1.4

Schematic representation of the emission mechanism in QDs.

Figure 1.5

Photoelectrochemical property of quantum dots under light irradiation: (a) generation of anodic current in the presence of electron donor compound and (b) generation of cathodic current in the presence of electron acceptor compound.

Figure 2.1

Comparison of top-down and bottom-up methods.

Figure 3.1

Polarizations of bQCA cells.

Figure 3.2

TQCA cell.

Figure 3.3

States of electron placement in a stable TQCA cell.

Figure 3.4

Clock in QCA in four phases.

Figure 3.5

90° wire.

Figure 3.6

45° wire.

Figure 3.7

Overlapping or plate wiring structure.

Figure 3.8

Multilayer wiring structure.

Figure 3.9

Transmission wire with two-phase clock difference.

Figure 3.10

NOT gate using two bQCA cells diagonally.

Figure 3.11

NOT gate using two diagonal NOT gates.

Figure 3.12

Inverter gate with reduced area.

Figure 3.13

Majority gate with three inputs.

Figure 3.14

The majority gate with five inputs.

Figure 3.15

AND gate structure.

Figure 3.16

OR gate structure.

Figure 4.1

TQCA polarization simulation diagram.

Figure 4.2

Polarization diagram in QQCA based on calculations.

Figure 4.3

Polarization diagram in QuQCA.

Figure 5.1

Polarizations of the ternary model.

Figure 5.2

TQCA cell proposed in Ref. [129].

Figure 5.3

Distance between items of two proposed TQCA cells.

Figure 5.4

Distances between two ternary cells to calculate the external electrostatic energy.

Figure 5.5

Shows the proposed QQCA model.

Figure 5.6

Specifications of the used layers.

Figure 5.7

QQCA cell symbol.

Figure 5.8

Input drive block in QQCA.

Figure 5.9

The first proposed output drive.

Figure 5.10

Second structure of the input drive.

Figure 5.11

Distances between two ternary cells in the first layer.

Figure 5.12

Distances between two QQCA cells in the second layer.

Figure 5.13

Symbolic representation of two QCA cells.

Figure 5.14

Proposed QuQCA model.

Figure 5.15

Specifications of the ternary layer.

Figure 5.16

QuQCA cell symbol.

Figure 5.17

Schematic of the input drive using decoder.

Figure 5.18

Schematic of the first output drive.

Figure 5.19

Simplified output drive model [131].

Figure 5.20

Second input drive in QuQCA.

Figure 5.21

TQCA-based half-adder circuit.

Figure 5.22

Distances between electrons in the first layer.

Figure 5.23

Distances between electrons in the second layer.

Figure 5.24

Symbolic representation of two adjacent cells in QuQCA.

Figure 5.25

Block diagram of the studied fuzzy system.

Figure 5.26

Fuzzy system rule base simulation: (a) the circuit representation and (b) the simulation results of the rule base.

Figure 5.27

Quantum gates.

Figure 6.1

Effect of two neighboring TQCA cells at different kinetic energies.

Figure 6.2

Interactions of two cells in the ternary layer.

Figure 6.3

Interactions of two cells in the binary layer.

Figure 6.4

Interactions of two neighboring cells in the ternary layers of QuQCA cells.

Figure 6.5

Power consumption in TQCA as per polarization set {−2, 0, 2}.

Figure 6.6

Energy consumption in QQCA using quantum computation.

Figure 6.7

Power consumption in the proposed QQCA cell.

Figure 6.8

Power consumption using QuQCA quantum calculations.

Figure 6.9

Power consumption in the proposed QuQCA cell.

Figure 7.1

Ternary NOT gate.

Figure 7.2

Two adjacent TQCA cells (wire).

Figure 7.3

Majority ternary gate.

Figure 7.4

(a) AND gate structure with a fixed input in state A and (b) OR gate structure with a fixed input in state B.

Figure 7.5

QQCA-based NOT gate.

Figure 7.6

Two QQCA cells (QQCA-based wire).

Figure 7.7

QQCA majority gates: (a) standard majority gate and (b) diagonal majority gate.

Figure 7.8

AND and OR gates with two inputs and one fixed input (a) AND gate structure with one fixed input in state A and (b) OR gate structure with one fixed input in state D.

Figure 7.9

Representation of a NOT gate using the QuQCA-based symbolic model.

Figure 7.10

Two neighboring cells using the QuQCA symbolic model.

Figure 7.11

QuQCA majority gate.

Figure 7.12

QQCA-based AND and OR gate structures: (a) AND gate structure with a fixed input in state A and (b) OR gate structure with a fixed input in state E.

Figure 8.1

Environment of TQCASim software version 1.0.11.1.

Figure 8.2

TQCA cell options.

Figure 8.3

Simulation of a three-value majority gate: (a) majority gate designed with TQCASim, (b) majority gate waveform, and (c) the truth table obtained from the software in TQCA.

Figure 8.4

Simulation of ternary AND gates; (a) AND gates designed with TQCASim software, (b) AND gate waveform obtained by TQCASim, and (c) AND gate truth table obtained by TQCASim.

Figure 8.5

Simulation of the ternary OR gate: (a) OR gate designed by TQCASim, (b) OR gate waveform using TQCASim, and (c) OR gate truth table obtained from TQCASim.

Figure 8.6

Simulation of two TQCA cells: (a) the two cells simulated in TQCASim, (b) two-cell interaction waveform using TQCASim, and (c) the truth table of two cells simulated in TQCASim.

Figure 8.7

Simulation of a ternary wire with an odd number of cells: (a) odd number of cells in a wire simulated in TQCASim, (b) interaction waveform of the wire in TQCASim, and (c) truth table of the wire in TQCASim.

Figure 8.8

Simulation of a ternary wire with an even number of cells: (a) ternary wire with an even number of TQCA cells, (b) interaction waveform of the wire in TQCASim, and (c) truth table of the wire simulated in TQCASim.

Figure 8.9

Environment of QQCASim software version 1.0.0.1.

Figure 8.10

Specifications of QQCA cells.

Figure 8.11

Simulation of a quaternary majority gate: (a) majority gate designed with QQCASim, (b) the majority gate waveform, and (c) truth table obtained from the software.

Figure 8.12

Simulation of the quaternary AND gate: (a) AND gate designed using QQCASim, (b) AND gate waveform in QQCASim, and (c) AND gate truth table obtained by QQCASim.

Figure 8.13

Simulation of the quaternary OR gate: (a) OR gate designed in QQCASim, (b) OR gate waveform using QQCASim, and (c) OR gate truth table obtained using QQCASim.

Figure 8.14

Quaternary NOT gate simulation: (a) NOT gate in QQCASim, (b) NOT gate output waveform, and (c) NOT gate truth table simulation using QQCASim.

Figure 8.15

A quaternary quantum wire: (a) quantum wire, (b) quantum wire output waveform, and (c) quantum wire truth table, all obtained using QQCASim.

Figure 9.1

(a) Comparison of von Neumann and PIM structures, (b) representation of Akers array and a logic cell with three inputs

X

,

Y

, and

Z

and two identical outputs, and (c) stripping process in Akers array to obtain output.

Figure 9.2

Three different fault-tolerant three-input majority gates.

Figure 10.1

BPIM1: (a) implementation in binary QCA and (b) simulation results.

Figure 10.2

BPIM2: (a) implementation in binary QCA and (b) simulation results.

Figure 10.3

BPIM3: (a) block diagram of the proposed model, (b) implementation in binary QCA, and (c) simulation results.

Figure 10.4

BPIM4: (a) block diagram, (b) implementation in binary QCA, and (c) simulation results.

Figure 10.5

Cell numbering in BPIM1.

Figure 10.6

Cell numbering in BPIM2.

Figure 10.7

Cell numbering in BPIM3.

Figure 10.8

Cell numbering in BPIM4.

Figure 11.1

Block diagram of two-input AND gate using Akers array.

Figure 11.2

Two-input AND gate using PIM structure in binary QCA: (a) BAND1 and (b) BAND2.

Figure 11.3

AND gate simulation results using binary QCA-based PIM structure for (a) BAND1 and (b) BAND2.

Figure 11.4

Block diagram of two-input OR gate using Akers array.

Figure 11.5

Two-input OR gate using binary QCA-based PIM structure: (a) BOR1 and (b) BOR2.

Figure 11.6

OR gate simulation results using binary QCA-based PIM: (a) BOR1 and (b) BOR2.

Figure 11.7

Block diagram of two-input NAND gate in Akers array.

Figure 11.8

Two-input NAND gate based on PIM structure in binary QCA: (a) BNAND1 and (b) BNAND2.

Figure 11.9

NAND simulation results based on PIM structure in binary QCA: (a) BNAND1 and (b) BNAND2.

Figure 11.10

Block diagram of two-input NOR gate using Akers array.

Figure 11.11

Two-input NOR gate using PIM structure in binary QCA: (a) BNOR1 and (b) BNOR2.

Figure 11.12

NOR simulation results based on PIM structure in binary QCA: (a) BNOR1 and (b) BNOR2.

Figure 11.13

(a) structure of basic cells and their layout in Akers array and (b) block diagram of two-input XOR gate in Akers array.

Figure 11.14

Two-input BXOR gate using PIM in binary QCA.

Figure 11.15

Simulation results of BXOR using PIM in binary QCA.

Figure 12.1

DFF structure.

Figure 12.2

Proposed DFF implemented and simulated using MATLAB.

Figure 12.3

Output diagrams of the proposed ternary QCA-based DFF designed using MATLAB for (a) AND1, (b) NOT, (c) AND2, and (d) OR1 structures.

Figure 12.4

First model of PIM cell, TPIM1: (a) implementation in ternary QCA and (b) simulation results.

Figure 12.5

Second model of PIM cell, TPIM2: (a) implementation in ternary QCA and (b) simulation results.

Figure 12.6

Third model of PIM cell (TPIM3): (a) implementation in ternary QCA and (b) simulation results.

Figure 12.7

(a) Diagram and operating principle of switches in the QCA-based Akers basic cell, (b) operating principle of switches in the Akers cell, (c) operating principle of switches in the binary cell, and (d) operating principle of switches in the ternary cell.

Figure 12.8

Numbering of cells in TPIM1.

Figure 12.9

Numbering of cells in TPIM2.

Figure 12.10

Numbering of cells in TPIM3.

Figure 13.1

Two-input AND gate using PIM structure in ternary QCA: (a) TAND1 model and (b) TAND2 model.

Figure 13.2

AND gate simulation results using ternary QCA-based PIM structure for (a) TAND1 and (b) TAND2.

Figure 13.3

Two-input OR gate using PIM structure in ternary QCA: (a) TOR1 model and (b) TOR2 model.

Figure 13.4

OR gate simulation results using ternary QCA-based PIM structure for (a) TOR1 and (b) TOR2.

Figure 13.5

XOR gate using ternary QCA-based PIM: (a) TXOR model and (b) truth table and simulation results.

Figure 13.6

Comparison of fault tolerance against extra-cell deposition and cell omission defects for PIM structures in binary and ternary QCA.

List of Tables

Table 3.1

Binary NOT gate response for different polarizations.

Table 3.2

Binary AND gate truth table in QCA technology.

Table 3.3

Binary gate truth table in QCA technology.

Table 4.1

Spin state of two electrons.

Table 4.2

Spin states of a three-particle system (with electrons).

Table 4.3

Vectors of quaternary input states.

Table 4.4

Polarization of a three-particle system in QQCA.

Table 4.5

Spin states of a four-electron system.

Table 4.6

Input states of the quinary system.

Table 4.7

Polarizations of the quinary system.

Table 5.1

QQCA cell polarizations.

Table 5.2

Truth table for the quaternary input drive.

Table 5.3

Truth table of the first structure of the quaternary output drive.

Table 5.4

The truth table of the second structure of the quaternary input drive.

Table 5.5

The truth table for determination of quaternary output using bQCA adder.

Table 5.6

Polarizations in QuQCA.

Table 5.7

Truth table of five-value input drive.

Table 5.8

Input states for the simplified output model in the quinary system.

Table 5.9

Truth table of the second input drive in QuQCA.

Table 5.10

QuQCA output truth table.

Table 5.11

Specifications of

n

-valued cell structures.

Table 5.12

Truth table of the proposed fuzzy pressure control system.

Table 7.1

Output of ternary NOT gate.

Table 7.2

Outputs of the ternary inverter gate for all polarization states.

Table 7.3

Interactions of two adjacent ternary cells (TQCA quantum wire).

Table 7.4

Outputs of the interactions of two adjacent ternary cells for all output states.

Table 7.5

Majority ternary gate output.

Table 7.6

Results of AND and OR gates with three values.

Table 7.7

Output of the QQCA-based NOT gate.

Table 7.8

Results of the QQCA-based NOT gate in different states and corresponding final values.

Table 7.9

Effect of two adjacent four-valued cells (QQCA-based wire).

Table 7.10

Output states of the interactions of two quaternary cells and the final results.

Table 7.11

QQCA majority gate output.

Table 7.12

Validity of QQCA-based AND and OR gates.

Table 7.13

Quaternary AND and OR gate truth table.

Table 7.14

NOT gate states in QuQCA.

Table 7.15

QuQCA NOT gate for all states and determining the final value (×1e-20).

Table 7.16

QuQCA-based wire truth table.

Table 7.17

Output states of the interactions of two QuQCA cells and final results (× 1e-20).

Table 7.18

Majority gate truth table in QuQCA.

Table 7.19

Truth tables of the quinary AND and OR gates.

Table 10.1

Parameters used in QCADesigner.

Table 10.2

Outputs of different inputs applied to BPIM3188.

Table 10.3

Cell omission fault evaluation in BPIM1.

Table 10.4

Extra-cell deposition fault evaluation in BPIM1187.

Table 10.5

Cell omission fault evaluation in BPIM2.

Table 10.6

Extra-cell deposition fault evaluation in BPIM2.

Table 10.7

Cell omission fault evaluation in BPIM3.

Table 10.8

Extra-cell deposition fault evaluation in BPIM3.

Table 10.9

Cell omission fault evaluation in BPIM4.

Table 10.10

Extra-cell deposition fault evaluation in BPIM4.

Table 12.1

Cell omission defect analysis for TPIM1.

Table 12.2

Extra-cell deposition defect analysis for TPIM1.

Table 12.3

Cell omission defect analysis for TPIM2.

Table 12.4

Extra-cell deposition defect analysis for TPIM2.

Table 12.5

Cell omission defect analysis for TPIM3.

Table 12.6

Extra-cell deposition defect analysis for TPIM3.

Table 13.1

Parameters of proposed binary and ternary RAM and PIM cells.

Table 13.2

Design parameters of binary and ternary gates.

Table 13.3

Comparison of binary and ternary XOR structures.

Table B.1

Output results of the ternary AND gate in all cases.

Table B.2

Output of ternary OR gates in all cases.

Table B.3

Outputs of the quaternary AND gates in all cases.

Table B.4

Output results of quaternary OR gate.

Table B.5

Output results of Coulomb energy values in the quaternary AND gate for all states (× 1e-20 (J)).

Table B.6

Output results of Coulomb energy values for the quinary OR gate in all states (× 1e-20 (J)).

About the Authors

Reza Sabbaghi-Nadooshan received his BS and MS degrees in electrical engineering from the Iran University of Science and Technology, Tehran, Iran, in 1991 and 1994, respectively, and his PhD degree in electrical engineering from the Science and Research Branch, Islamic Azad University, Tehran, in 2010. He is a Professor with the Department of Electrical Engineering in the Central Tehran Branch, Islamic Azad University. Having published over 100 research papers in various international journals and conferences, his research interests include multiple-valued logic, quantum dot cellular automata (QCA), and nanocomputing. He is on the panel of reviewers for various international journals.

Reza Akbari-Hasanjani was born in Iran in 1987. He received his BSc, MSc, and PhD degrees in electrical engineering from Islamic Azad University, Central Tehran Branch, Tehran, Iran, in 2012, 2015, and 2022, respectively. His interests are in various research areas, including nanocomputing, reversible computation, multiple-value logic, and QCA. These fields have captivated his attention and driven him to explore innovative solutions within the realm of electrical engineering.

Leila Dehbozorgi was born in Iran in 1981. She received her PhD degree in electrical engineering from Islamic Azad University, Central Tehran Branch, Tehran, Iran, in 2023. Her interests are in various research areas, including nanocomputing, QCA, reversible computation, multiple-value logic, and neural networks.

Majid Haghparast is a researcher at the University of Jyväskylä, Finland, and a senior member of IEEE. He has authored over 90 papers in peer-reviewed journals and conferences. In addition, he serves as Editorial Board Member for Cluster Computing (Springer), Journal of Computational Electronics (Springer), and Optical and Quantum Electronics (Springer). Throughout his career, Majid has supervised or advised on over 10 PhD and 40 master’s theses. His primary focus is on quantum computing and quantum software engineering, where he has been involved in various projects.

Hamid Reza Akbari-Hasanjani was born in Iran in 1989. He received his PhD in analytical chemistry from Damghan University, Semnan, Iran, in 2019. He has been a member of the Iranian Chemical Society (ICS) since 2019. His interests are quantum dot synthesis, electrochemical biosensors, electroanalysis, and bioinformatics.

Preface

Examining new technologies for electrical and computer scientists is more interesting today. This appeal is likely to endure indefinitely as technologies are advancing rapidly and scientists are trying every day to enhance human comfort through technological advancements. Addressing the question of which technologies could replace complementary metal–oxide–semiconductor (CMOS) transistors has spurred researchers to explore alternatives such as quantum dot cellular automata (QCA). The evolution of technologies paves the way for scientists to develop new computing systems that seamlessly support multi-valued calculations. One such computational approach involves leveraging the spin states in QCA cells, leading us to compile and publish a book on multi-value QCA technology. This book provides a composite solution for multi-value logic in QCA circuits. It comprises 14 chapters in which multi-valued cells are investigated, from computation to the design of logical gates. Intended for senior undergraduate and graduate levels in nanoelectronics, computer arithmetic, memory, and processing in memory (PIM), the book is also valuable resource for researchers exploring emerging nanotechnologies and their architectural implications.

2024 IRAN-Tehran               

Reza Sabbaghi-Nadooshan

Reza Akbari-Hasanjani

Leila Dehbozorgi

Majid Haghparast

Hamid Reza Akbari-Hasanjani

Introduction

In recent years, the downscaling of complementary metal–oxide–semiconductor (CMOS) technology has presented challenges, prompting the introduction of alternative technologies to address them. Among these, quantum dot cellular automata (QCA) is a suitable candidate, which has received significant attention in the design of digital circuits. The advantages of QCA technology encompass its tiny dimensions, high speed, low delay, and low power consumption.

So far, binary quantum dot cellular automata (bQCA) has been thoroughly investigated, while multi-value QCA remains unexplored. This technology is one of the most current topics that has received attention, particularly due to its proximity to fuzzy logic. By studying the previous research on the strengths and weaknesses of QCA cells, we found that no comprehensive model considers the calculations of Hamiltonian matrix polarization and power consumption in a cell in multi-valued cells.

This book introduces computational methods for designing multi-valued cells and their basic gates. We calculate the polarization values by adjusting the number of particles within the desired systems to accomplish this objective. In designing a quaternary cell, the combination of bQCA and ternary quantum dot cellular automata (TQCA) cells is used to achieve stability in the design of basic gates.

The external electrostatic model is employed in designing basic gates using the proposed cells. This model is based on the interaction between the electrons of each cell and those of other cells. In the subsequent step, the value of the Hamiltonian matrix is calculated to determine the power consumption of each cell.

In the next step, the basic gates are simulated using MATLAB software to validate the proposed cells, and the amount of electrostatic energy is calculated in all cases. Then, to verify all the calculations for simulating the gates and ternary circuits, two simulators with appropriate dimensions are presented for ternary and quaternary circuits.

In the following chapters, the structures of processing in memory (PIM) and more extended bQCA and TQCA circuits will be designed and analyzed. Multi-value PIM structures represent a new subject in the digital realm and have not been implemented in TQCA thus far. In this book, two different designs are proposed for PIM cells. One design explores the impact of memory relocation, while the other examines the effects of reducing cell count and optimizing components of PIM in bQCA and TQCA. Moreover, the effect of faults/defects on the designed structures is investigated. The results show that compared to binary structures, many of the proposed ternary structures, especially the PIM structures, exhibit greater fault tolerance against cell omission and extra-cell deposition defects, and they are more optimal in terms of cost function and occupied area. Consequently, PIMs have the potential to serve as a suitable alternative to random-access memories (RAMs) in the future.

The simulation results obtained with the ternary and quaternary simulators are entirely consistent with the MATLAB simulation results and previous studies conducted on other technologies, such as CMOS. These results demonstrate significant progress in designing multi-valued cells, indicating the feasibility of designing multi-valued circuits with functionality closely resembling fuzzy logic.

1Quantum Dots

1.1 Introduction to Quantum Dots

Nanotechnology, specifically the field of nanostructured materials and quantum dots (QDs), has gained significant interest in recent years. It has applications in various fields, such as medicine, chemistry, physics, engineering, electronics, optoelectronics, and biology [1–3].

Nanostructured materials, which can be categorized as two-dimensional (e.g., thin films or quantum wells), one-dimensional (e.g., quantum wires), or zero-dimensional (dots), can bridge the gap between bulk materials and molecular structures. The optical and electronic properties of these materials vary with particle size, especially when the size is less than 100 nm. QDs, referred to as zero-dimensional structures, exhibit discrete quantized energy states due to the limited number of electrons they can accommodate [4].

The discovery of QDs dates back to 1981, when they were first observed in a glass matrix. Since then, significant advancements have been made in synthesizing and understanding their properties. QDs, composed of semiconductor nanocrystals, show distinct advantages over traditional organic dyes, such as tunable broad excitation and narrow emission spectra, high signal brightness, and photostability. They have found applications in fluorescence imaging, sensing, light-emitting diodes (LEDs), solar cells, and more [5].

Furthermore, QDs have been integrated into electrochemical biosensors to improve their analytical performance. These biosensors, which utilize nanomaterials, combine a biological recognition element with an electrochemical transduction element to provide specific quantitative analytical information. QDs enhance the electron-transfer speed, amplify electrochemical signals through increased surface area, and serve as signal labels, enabling the development of ultrasensitive electrochemical biosensors. These nanosensors have the potential to revolutionize personalized detection tools and “point-of-care” diagnostics [6, 7].