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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Quantum Computing Fundamentals is the first systematic guidebook for the growing number of students who want to master the field's core concepts and practical techniques.

Leading security expert, researcher, instructor, and author Chuck Easttom II brings together all the knowledge you need—including essentials that other books assume you already know, such as basic linear algebra, logic gates, and elementary quantum physics. Easttom's quizzes, hands-on exercises, and review sections help you build true mastery right now. He walks you through building real applications with Q#, Microsoft's powerful new quantum computing programming language, and using Microsoft's simulator so you don't need your own quantum computer.
    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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