Quantum Computing

by Parag Lala

Overview

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A self-contained, reader-friendly introduction to the principles and applications of quantum computing 


Especially valuable to those without a prior knowledge of quantum mechanics, this electrical engineering text presents the concepts and workings of quantum information processing systems in a clear, straightforward, and practical manner. The book is written in a style that helps readers who are not familiar with non-classical information processing more easily grasp the essential concepts; only prior exposure to classical physics, basic digital design, and introductory linear algebra is assumed.


Quantum Computing: A Beginner’s Introduction presents each topic in a tutorial style with examples, illustrations, and diagrams to clarify the material. Written by an experienced electrical engineering educator and author, this is a self-contained resource, with all the necessary pre-requisite material included within the text.


Coverage includes: 


• Complex Numbers, Vector Space, and Dirac Notation 
• Basics of Quantum Mechanics 
• Matrices and Operators 
• Boolean Algebra, Logic Gates and Quantum Information Processing 
• Quantum Gates and Circuit 
• Tensor Products, Superposition and Quantum Entanglement 
• Teleportation and Superdense Coding 
• Quantum Error Correction 
• Quantum Algorithms 
• Quantum Cryptography

Product Details

ISBN-13:	9781260123111
Publisher:	McGraw Hill LLC
Publication date:	01/28/2019
Edition description:	New Edition
Pages:	176
Product dimensions:	5.90(w) x 8.90(h) x 0.50(d)

About the Author

Parag K. Lala, is an electrical engineering professor at Texas A&M University - Texarkana and is the author or co-author of seven books and more than 145 technical papers. His current research interests are in quantum computing and cryptography, hardware-based DNA sequence matching, and biologically-inspired design of programmable digital systems. He is a Life Fellow of the IEEE.

Table of Contents

Dedication vi

Preface vii

1 Complex Numbers, Vector Space, and Dirac Notation 1

1.1 Complex Numbers 1

1.2 Complex Conjugation 3

1.3 Vector Space 4

1.4 Basis Set 5

1.5 Dirac Notation 8

1.5.1 Ket 8

1.5.2 Bra 10

1.6 Inner Product 12

1.7 Linearly Dependent and Independent Vectors 13

1.8 Dual Vector Space 13

1.9 Computational Basis 15

1.10 Outer Product 16

References 16

2 Basics of Quantum Mechanics 17

2.1 Limitations of Classical Physics 17

2.1.1 Blackbody Radiation 18

2.1.2 Planck's Constant 19

2.2 Photoelectric Effect 19

2.3 Classical Electromagnetic Theory 21

2.4 Rutherford's Model of the Atom 23

2.5 Bohr's Model of Atoms 24

2.6 Particle and Wave Nature of Light 25

2.7 Wave Function 27

2.8 Postulates of Quantum Mechanics 29

References 30

3 Matrices and Operators 31

3.1 Matrices 32

3.2 Square Matrices 33

3.3 Diagonal (or Triangular) Matrix 34

3.4 Operators 35

3.4.1 Rules for Operators 35

3.5 Linear Operator 36

3.6 Commutator 37

3.7 Matrix Representation of a Linear Operator 38

3.8 Symmetric Matrix 39

3.9 Transpose Operation 39

3.10 Orthogonal Matrices 40

3.11 Identity Operator 40

3.12 Adjoint Operator 41

3.13 Hermitian Operator 43

3.14 Unitary Operators 44

3.14.1 Properties of Unitary Operators 45

3.15 Projection Operator 45

References 46

4 Boolean Algebra, Logic Gates, and Quantum Information Processing 47

4.1 Boolean Algebra 47

4.2 Classical Circuit Computation Model 50

4.3 Universal Logic Gates 52

4.4 Quantum Computation 53

4.5 The Quantum Bit and Its Representations 53

4.6 Superposition in Quantum Systems 57

4.7 Quantum Register 58

References 59

5 Quantum Gates and Circuits 61

5.1 X Gate 61

5.2 Y Gate 62

5.3 Z Gate 63

5.4 √NOT (Square Root of NOT) Gate 63

5.5 Hadamard Gate 65

5.6 Phase Gate 67

5.7 T Gate 68

5.8 Reversible Logic 68

5.9 CNOT Gate 69

5.10 Controlled-U Gate 71

5.11 Reversible Gates 74

5.11.1 Fredkin Gate (Controlled Swap Gate) 74

5.11.2 Toffoli Gate (Controlled-Controlled-NOT) 76

5.11.3 Peres Gate 77

References 78

6 Tensor Products, Superposition, and Quantum Entanglement 79

6.1 Tensor Products 79

6.2 Multi-Qubit Systems 82

6.3 Superposition 84

6.4 Entanglement 86

6.5 Decoherence 91

References 92

7 Teleportation and Superdense Coding 93

7.1 Quantum Teleportation 93

7.2 No-Cloning Theorem 98

7.3 Superdense Coding 100

References 106

8 Quantum Error Correction 107

8.1 Classical Error-Correcting Codes 108

8.2 Quantum Error-Correcting Codes 110

8.3 Shor's 3-Qubit Bit-Flop Code 112

8.4 Error Correction 114

8.4.1 Bit-Flip Error Correction 115

8.4.2 Phase Error Correction 118

8.5 Shor's 9 Qubit Code 122

References 126

9 Quantum Algorithms 127

9.1 Deutsch's Algorithm 127

9.2 Deutsch-Jozsa Algorithm 130

9.3 Grover's Search Algorithm 133

9.3.1 Details of Grover's Algorithm 134

9.4 Shor's Factoring Algorithm 139

References 144

10 Quantum Cryptography 145

10.1 Principles of Information Security 146

10.2 One-Time Pad 148

10.3 Public Key Cryptography 149

10.4 RSA Coding Scheme 150

10.5 Quantum Cryptography 151

10.6 Quantum Key Distribution 152

10.7 BB84 153

10.8 Ekart 91 158

References 160

Index 161