Quantum Computing Fundamentals, 1st edition

Published by Addison Wesley (January 14, 2022) © 2021

  • William Chuck Easttom

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ISBN-13: 9780137460328
Quantum Computing Fundamentals
Published 2022

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ISBN-13: 9780136793816
Quantum Computing Fundamentals
Published 2021

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    Preface xvii

Part I Preparatory Material

Chapter 1: Introduction to Essential Linear Algebra 2

    1.1 What Is Linear Algebra?.. . . . . . . . . . . . . . . . . . . . 3

    1.2 Some Basic Algebra.. . . . . . . . . . . . . . . . . . . . . 4

    1.3 Matrix Math.. . . . . . . . . . . . . . . . . . . . . . . . 10

    1.4 Vectors and Vector Spaces.. . . . . . . . . . . . . . . . . . 23

    1.5 Set Theory.. . . . . . . . . . . . . . . . . . . . . . . . . 25

    1.6 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 29

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 29

Chapter 2: Complex Numbers 32

    2.1 What Are Complex Numbers?.. . . . . . . . . . . . . . . . . 32

    2.2 Algebra of Complex Numbers.. . . . . . . . . . . . . . . . . 34

    2.3 Complex Numbers Graphically.. . . . . . . . . . . . . . . . 38

    2.4 Vector Representations of Complex Numbers.. . . . . . . . . . 45

    2.5 Pauli Matrices.. . . . . . . . . . . . . . . . . . . . . . . 48

    2.6 Transcendental Numbers.. . . . . . . . . . . . . . . . . . . 56

    2.7 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 58

Chapter 3: Basic Physics for Quantum Computing 60

    3.1 The Journey to Quantum.. . . . . . . . . . . . . . . . . . . 61

    3.2 Quantum Physics Essentials.. . . . . . . . . . . . . . . . . 65

    3.3 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 77

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 77

Chapter 4: Fundamental Computer Science for Quantum Computing 80

    4.1 Data Structures.. . . . . . . . . . . . . . . . . . . . . . . 81

    4.2 Algorithms.. . . . . . . . . . . . . . . . . . . . . . . . . 88

    4.3 Computational Complexity.. . . . . . . . . . . . . . . . . . 93

    4.4 Coding Theory.. . . . . . . . . . . . . . . . . . . . . . . 95

    4.5 Logic Gates.. . . . . . . . . . . . . . . . . . . . . . . . 96

    4.6 Computer Architecture.. . . . . . . . . . . . . . . . . . . 100

    4.7 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 103

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 103

Chapter 5: Basic Information Theory 106

    5.1 Basic Probability.. . . . . . . . . . . . . . . . . . . . . . 107

    5.2 Set Theory.. . . . . . . . . . . . . . . . . . . . . . . . 108

    5.3 Information Theory.. . . . . . . . . . . . . . . . . . . . . 112

    5.4 Quantum Information.. . . . . . . . . . . . . . . . . . . . 118

    5.5 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 120

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 120

Part II Basic Quantum Computing

Chapter 6: Basic Quantum Theory 122

    6.1 Further with Quantum Mechanics.. . . . . . . . . . . . . . . 123

    6.2 Quantum Decoherence.. . . . . . . . . . . . . . . . . . . 129

    6.3 Quantum Electrodynamics.. . . . . . . . . . . . . . . . . . 131

    6.4 Quantum Chromodynamics.. . . . . . . . . . . . . . . . . 133

    6.5 Feynman Diagram.. . . . . . . . . . . . . . . . . . . . . 134

    6.6 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 136

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 136

Chapter 7: Quantum Entanglement and QKD 138

    7.1 Quantum Entanglement.. . . . . . . . . . . . . . . . . . . 138

    7.2 Interpretation.. . . . . . . . . . . . . . . . . . . . . . . 143

    7.3 QKE.. . . . . . . . . . . . . . . . . . . . . . . . . . . 146

    7.4 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 151

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 152

Chapter 8: Quantum Architecture 154

    8.1 Further with Qubits.. . . . . . . . . . . . . . . . . . . . . 154

    8.2 Quantum Gates.. . . . . . . . . . . . . . . . . . . . . . 158

    8.3 More with Gates.. . . . . . . . . . . . . . . . . . . . . . 166

    8.4 Quantum Circuits. . . . . . . . . . . . . . . . . . . . . . 167

    8.5 The D-Wave Quantum Architecture.. . . . . . . . . . . . . . 169

    8.6 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 172

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 172

Chapter 9: Quantum Hardware 174

    9.1 Qubits.. . . . . . . . . . . . . . . . . . . . . . . . . . 174

    9.2 How Many Qubits Are Needed?. . . . . . . . . . . . . . . . 181

    9.3 Addressing Decoherence.. . . . . . . . . . . . . . . . . . 182

    9.4 Topological Quantum Computing.. . . . . . . . . . . . . . . 186

    9.5 Quantum Essentials.. . . . . . . . . . . . . . . . . . . . 187

    9.6 Quantum Networking.. . . . . . . . . . . . . . . . . . . . 188

    9.7 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 191

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 191

Chapter 10: Quantum Algorithms 194

    10.1 What Is an Algorithm?. . . . . . . . . . . . . . . . . . . . 194

    10.2 Deutsch's Algorithm.. . . . . . . . . . . . . . . . . . . . 197

    10.3 Deutsch-Jozsa Algorithm.. . . . . . . . . . . . . . . . . . 199

    10.4 Bernstein-Vazirani Algorithm.. . . . . . . . . . . . . . . . . 201

    10.5 Simon's Algorithm.. . . . . . . . . . . . . . . . . . . . . 202

    10.6 Shor's Algorithm.. . . . . . . . . . . . . . . . . . . . . . 203

    10.7 Grover's Algorithm. . . . . . . . . . . . . . . . . . . . . 209

    10.8 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 211

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 211

Part III Quantum Computing and Cryptography

Chapter 11: Current Asymmetric Algorithms 212

    11.1 RSA. . . . . . . . . . . . . . . . . . . . . . . . . . . 213

    11.2 Diffie-Hellman.. . . . . . . . . . . . . . . . . . . . . . . 216

    11.3 Elliptic Curve.. . . . . . . . . . . . . . . . . . . . . . . 219

    11.4 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 227

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 227

Chapter 12: The Impact of Quantum Computing on Cryptography 228

    12.1 Asymmetric Cryptography.. . . . . . . . . . . . . . . . . . 229

    12.2 Specific Algorithms.. . . . . . . . . . . . . . . . . . . . . 231

    12.3 Specific Applications. . . . . . . . . . . . . . . . . . . . 233

    12.3.1 Digital Certificates. . . . . . . . . . . . . . . . . . 233

    12.3.2 SSL/TLS. . . . . . . . . . . . . . . . . . . . . . 234

    12.4 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 241

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 241

Chapter 13: Lattice-based Cryptography 244

    13.1 Lattice-Based Mathematical Problems.. . . . . . . . . . . . . 245

    13.2 Cryptographic Algorithms. . . . . . . . . . . . . . . . . . 249

    13.3 Solving Lattice Problems.. . . . . . . . . . . . . . . . . . 256

    13.4 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 259

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 259

Chapter 14: Multivariate Cryptography 262

    14.1 Mathematics.. . . . . . . . . . . . . . . . . . . . . . . 262

    14.2 Matsumoto-Imai.. . . . . . . . . . . . . . . . . . . . . . 264

    14.3 Hidden Field Equations. . . . . . . . . . . . . . . . . . . 266

    14.4 Multivariate Quadratic Digital Signature Scheme (MQDSS).. . . . 268

    14.5 SFLASH.. . . . . . . . . . . . . . . . . . . . . . . . . 269

    14.6 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 271

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 271

Chapter 15: Other Approaches to Quantum Resistant Cryptography 274

    15.1 Hash Functions.. . . . . . . . . . . . . . . . . . . . . . 274

    15.2 Code-Based Cryptography.. . . . . . . . . . . . . . . . . 279

    15.3 Supersingular Isogeny Key Exchange.. . . . . . . . . . . . . 281

    15.4 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 289

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 289

Part IV Quantum Programming

Chapter 16: Working with Q# 292

    16.1 Basic Programming Concepts.. . . . . . . . . . . . . . . . 292

    16.2 Getting Started with Q#.. . . . . . . . . . . . . . . . . . . 298

    16.3 Grover's Algorithm. . . . . . . . . . . . . . . . . . . . . 303

    16.4 Deutsch-Jozsa Algorithm.. . . . . . . . . . . . . . . . . . 307

    16.5 Bit Flipping.. . . . . . . . . . . . . . . . . . . . . . . . 310

    16.6 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 311

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 311

Chapter 17: Working with QASM 314

    17.1 Basic Programming Concepts.. . . . . . . . . . . . . . . . 315

    17.2 Getting Started with QASM.. . . . . . . . . . . . . . . . . 319

    17.3 Quantum Error Correction. . . . . . . . . . . . . . . . . . 320

    17.4 Grover's Algorithm. . . . . . . . . . . . . . . . . . . . . 322

    17.5 Deutsch-Jozsa Algorithm.. . . . . . . . . . . . . . . . . . 326

    17.6 Summary.. . . . . . . . . . . . . . . . . . . . . . . . . 328

    Test Your Skills. . . . . . . . . . . . . . . . . . . . . . . 328

Appendix: Answers to Test Your Skills Questions 330



9780136793816, TOC, 5/7/2021


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