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Quantum Computing Fundamentals

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Description

  • Copyright 2021
  • Pages: 384
  • Edition: 1st
  • eBook (Watermarked)
  • ISBN-10: 0-13-679392-4
  • ISBN-13: 978-0-13-679392-2

ONE-VOLUME INTRODUCTION TO QUANTUM COMPUTING

  • Clearly explains core concepts, terminology, and techniques
  • Covers the foundational physics, math, and information theory you need
  • Provides hands-on practice with quantum programming
  • The perfect beginner's guide for anyone interested in a quantum computing career


Dr. Chuck Easttom brings together complete coverage of basic quantum computing concepts, terminology, and issues, along with key skills to get you started.

Drawing on 30+ years as a computer science instructor, consultant, and researcher, Easttom demystifies the field's underlying technical concepts and math, shows how quantum computing systems are designed and built, explains their implications for cyber security, and previews advances in quantum-resistant cryptography. Writing clearly and simply, he introduces two of today's leading quantum programming languages, Microsoft Q# and QASM, and guides you through sample projects. Throughout, tests, projects, and review questions help you deepen and apply your knowledge.

Whether you're a student, professional, or manager, this guide will prepare you for the quantum computing revolution--and expand your career options, too.

  • Master the linear algebra and other mathematical skills you'll need
  • Explore key physics ideas such as quantum states and uncertainty
  • Review data structures, algorithms, and computing complexity
  • Work with probability and set theory in quantum computing
  • Familiarize yourself with basic quantum theory and formulae
  • Understand quantum entanglement and quantum key distribution
  • Discover how quantum computers are architected and built
  • Explore several leading quantum algorithms
  • Compare quantum and conventional asymmetric algorithms
  • See how quantum computing might break traditional cryptography
  • Discover several approaches to quantum-resistant cryptography
  • Start coding with Q#, Microsoft's quantum programming language
  • Simulate quantum gates and algorithms with QASM


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Table of Contents

    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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