Quantum Computing Fundamentals

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

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

About the Author :
Dr. Chuck Easttom is the author of 31 books, including several on computer security, forensics, and cryptography. His books are used at more than 60 universities. He has also authored scientific papers (more than 70 so far) on digital forensics, cyber warfare, cryptography, and applied mathematics. He is an inventor with 22 computer science patents. He holds a Doctor of Science in cyber security (dissertation topic: a study of lattice-based cryptographic algorithms for post-quantum computing). He also has a Ph.D. in Technology, focusing on nanotechnology (dissertation title: “The Effects of Complexity on Carbon Nanotube Failures”) and a Ph.D. in Computer Science (dissertation title: “On the Application of Graph Theory to Digital Forensics”). He also has three master’s degrees (one in applied computer science, one in education, and one in systems engineering). He is a senior member of the IEEE and a senior member of the ACM (Association of Computing Machinery) as well as a member of IACR (International Association of Cryptological Research) and INCOSE (International Council on Systems Engineering). He is also a distinguished speaker of the ACM and a distinguished visitor of the IEEE Computer Society. He currently is an adjunct lecturer for Georgetown University.