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
Author(s): William (Chuck) Easttom II
Edition: 1
Publisher: Addison-Wesley Professional
Year: 2021
Language: English
Pages: 384
Tags: Quantum Computing; Quantum Algorithms; Linear Algebra; Information Theory; Quantum Theory; Quantum Entanglement; QKD; Quantum Architecture; Quantum Hardware; Cryptography; Asymmetric Algorithms; Lattice-Based Cryptography; Multivariate Cryptography; Quantum Resistant Cryptography; Quantum Programming; Q#; QASM
Preface
Part I Preparatory Material
Chapter 1: Introduction to Essential Linear Algebra
1.1 What Is Linear Algebra?
1.2 Some Basic Algebra
1.2.1 Groups, Rings, and Fields
1.3 Matrix Math
1.3.1 Matrix Addition and Multiplication
1.3.2 Matrix Transposition
1.3.3 Submatrix
1.3.4 Identity Matrix
1.3.5 Deeper Into the Matrix
1.4 Vectors and Vector Spaces
1.5 Set Theory
1.6 Summary
Test Your Skills
Chapter 2: Complex Numbers
2.1 What Are Complex Numbers?
2.2 Algebra of Complex Numbers
2.3 Complex Numbers Graphically
2.4 Vector Representations of Complex Numbers
2.5 Pauli Matrices
2.5.1 Algebraic Properties of Pauli Matrices
2.6 Transcendental Numbers
2.7 Summary
Test Your Skills
Chapter 3: Basic Physics for Quantum Computing
3.1 The Journey to Quantum
3.2 Quantum Physics Essentials
3.2.1 Basic Atomic Structure
3.2.2 Hilbert Spaces
3.2.3 Uncertainty
3.2.4 Quantum States
3.2.5 Entanglement
3.3 Summary
Test Your Skills
Chapter 4: Fundamental Computer Science for Quantum Computing
4.1 Data Structures
4.1.1 List
4.1.2 Binary Tree
4.2 Algorithms
4.2.1 Sorting Algorithms
4.3 Computational Complexity
4.3.1 Cyclomatic Complexity
4.3.2 Halstead Metrics
4.4 Coding Theory
4.5 Logic Gates
4.5.1 AND
4.5.2 OR
4.5.3 XOR
4.5.4 Application of Logic Gates
4.6 Computer Architecture
4.7 Summary
Test Your Skills
Chapter 5: Basic Information Theory
5.1 Basic Probability
5.1.1 Basic Probability Rules
5.2 Set Theory
5.3 Information Theory
5.3.1 Theorem 1: Shannon’s Source Coding Theorem
5.3.2 Theorem 2: Noisy Channel Theorem
5.3.3 Information Entropy
5.3.4 Information Diversity
5.4 Quantum Information
5.5 Summary
Test Your Skills
Part II Basic Quantum Computing
Chapter 6: Basic Quantum Theory
6.1 Further with Quantum Mechanics
6.1.1 Bra-Ket Notation
6.1.2 Hamiltonian
6.1.3 Wave Function Collapse
6.1.4 Schrödinger’s Equation
6.2 Quantum Decoherence
6.3 Quantum Electrodynamics
6.4 Quantum Chromodynamics
6.5 Feynman Diagram
6.6 Summary
Test Your Skills
Chapter 7: Quantum Entanglement and QKD
7.1 Quantum Entanglement
7.2 Interpretation
7.2.1 The Copenhagen Interpretation
7.2.2 The Many-Worlds Interpretation
7.2.3 Decoherent Histories
7.2.4 Objective Collapse Theory
7.3 QKE
7.3.1 BB84 Protocol
7.3.2 B92 Protocol
7.3.3 SARG04
7.3.4 Six-State Protocol
7.3.5 E91
7.3.6 Implementations
7.4 Summary
Test Your Skills
Chapter 8: Quantum Architecture
8.1 Further with Qubits
8.2 Quantum Gates
8.2.1 Hadamard Gate
8.2.2 Phase Shift Gates
8.2.3 Pauli Gates
8.2.4 Swap Gates
8.2.5 Fredkin Gate
8.2.6 Toffoli Gates
8.2.7 Controlled Gates
8.2.8 Ising Gates
8.2.9 Gottesman–Knill Theorem
8.3 More with Gates
8.4 Quantum Circuits
8.5 The D-Wave Quantum Architecture
8.5.1 SQUID
8.6 Summary
Test Your Skills
Chapter 9: Quantum Hardware
9.1 Qubits
9.1.1 Photons
9.1.2 Electron
9.1.3 Ions
9.1.4 NMRQC
9.1.5 Bose-Einstein Condensate Quantum Computing
9.1.6 GaAs Quantum Dots
9.2 How Many Qubits Are Needed?
9.3 Addressing Decoherence
9.3.1 Supercooling
9.3.2 Dealing with Noise
9.3.3 Filtering Noise
9.4 Topological Quantum Computing
9.4.1 Basic Braid Theory
9.4.2 More on Braid Theory
9.4.3 More on Topological Computing
9.5 Quantum Essentials
9.5.1 Quantum Data Plane
9.5.2 Measurement Plane
9.5.3 Control Processor Plane
9.6 Quantum Networking
9.6.1 Tokyo QKD
9.6.2 Beijing-Shanghai Quantum Link
9.6.3 Micius Satellite
9.6.4 Distributed Quantum Computing
9.7 Summary
Test Your Skills
Chapter 10: Quantum Algorithms
10.1 What Is an Algorithm?
10.2 Deutsch’s Algorithm
10.3 Deutsch-Jozsa Algorithm
10.4 Bernstein-Vazirani Algorithm
10.5 Simon’s Algorithm
10.6 Shor’s Algorithm
10.6.1 The Quantum Period-Finding Function
10.7 Grover’s Algorithm
10.8 Summary
Test Your Skills
Part III Quantum Computing and Cryptography
Chapter 11: Current Asymmetric Algorithms
11.1 RSA
11.1.1 RSA Example 1
11.1.2 RSA Example 2
11.1.3 Factoring RSA Keys
11.2 Diffie-Hellman
11.2.1 Elgamal
11.2.2 MQV
11.3 Elliptic Curve
11.3.1 ECC Diffie-Hellman
11.3.2 ECDSA
11.4 Summary
Test Your Skills
Chapter 12: The Impact of Quantum Computing on Cryptography
12.1 Asymmetric Cryptography
12.1.1 How Many Qubits Are Needed?
12.2 Specific Algorithms
12.2.1 RSA
12.2.2 Diffie-Hellman
12.2.3 ECC
12.2.4 Symmetric Ciphers
12.2.5 Cryptographic Hashes
12.3 Specific Applications
12.3.1 Digital Certificates
12.3.2 SSL/TLS
12.3.4 Public Key Infrastructure (PKI)
12.3.5 VPN
12.3.6 SSH
12.4 Summary
Test Your Skills
Chapter 13: Lattice-based Cryptography
13.1 Lattice-Based Mathematical Problems
13.1.1 Shortest Integer Problem
13.1.2 Shortest Vector Problem
13.1.3 Closest Vector Problem
13.2 Cryptographic Algorithms
13.2.1 NTRU
13.2.2 GGH
13.2.3 Peikert’s Ring
13.3 Solving Lattice Problems
13.3.1 Lenstra-Lenstra-Lovász (LLL)
13.4 Summary
Test Your Skills
Chapter 14: Multivariate Cryptography
14.1 Mathematics
14.2 Matsumoto-Imai
14.3 Hidden Field Equations
14.4 Multivariate Quadratic Digital Signature Scheme (MQDSS)
14.5 SFLASH
14.6 Summary
Test Your Skills
Chapter 15: Other Approaches to Quantum Resistant Cryptography
15.1 Hash Functions
15.1.1 Merkle-Damgaard
15.1.2 SWIFFT
15.1.3 Lamport Signature
15.2 Code-Based Cryptography
15.2.1 McEliece
15.2.2 Niederreiter Cryptosystem
15.3 Supersingular Isogeny Key Exchange
15.3.1 Elliptic Curves
15.3.2 SIDH
15.4 Summary
Test Your Skills
Part IV Quantum Programming
Chapter 16: Working with Q#
16.1 Basic Programming Concepts
16.1.1 Variables and Statements
16.1.2 Control Structures
16.1.3 Object-Oriented Programming
16.2 Getting Started with Q#
16.3 Grover’s Algorithm
16.3.1 Grover’s Algorithm Reviewed
16.3.2 The Code for Grover’s Algorithm
16.4 Deutsch-Jozsa Algorithm
16.4.1 Deutsch-Jozsa Algorithm Reviewed
16.4.2 The Code for Deutsch-Jozsa Algorithm
16.5 Bit Flipping
16.6 Summary
Test Your Skills
Chapter 17: Working with QASM
17.1 Basic Programming Concepts
17.1.1 Instructions
17.1.2 Commands
17.2 Getting Started with QASM
17.3 Quantum Error Correction
17.4 Grover’s Algorithm
17.4.1 Grover’s Algorithm Reviewed
17.4.2 The Code for Grover’s Algorithm
17.5 Deutsch-Jozsa Algorithm
17.5.1 Deutsch-Jozsa Algorithm Reviewed
17.5.2 The Code for the Deutsch-Jozsa Algorithm
17.6 Summary
Test Your Skills
Appendix: Answers to Test Your Skills Questions
Index
