Table of Contents

• Preface
• 1 Complex Numbers, Vector Space, and Dirac Notation
  • 1.1 Complex Numbers
  • 1.2 Complex Conjugation
  • 1.3 Vector Space
  • 1.4 Basis Set
  • 1.5 Dirac Notation
    • 1.5.1 Ket
    • 1.5.2 Bra
  • 1.6 Inner Product
  • 1.7 Linearly Dependent and Independent Vectors
  • 1.8 Dual Vector Space
  • 1.9 Computational Basis
  • 1.10 Outer Product
  • References
• 2 Basics of Quantum Mechanics
  • 2.1 Limitations of Classical Physics
    • 2.1.1 Blackbody Radiation
    • 2.1.2 Planck’s Constant
  • 2.2 Photoelectric Effect
  • 2.3 Classical Electromagnetic Theory
  • 2.4 Rutherford’s Model of the Atom
  • 2.5 Bohr’s Model of Atoms
  • 2.6 Particle and Wave Nature of Light
  • 2.7 Wave Function
  • 2.8 Postulates of Quantum Mechanics
  • References
• 3 Matrices and Operators
  • 3.1 Matrices
  • 3.2 Square Matrices
  • 3.3 Diagonal (or Triangular) Matrix
  • 3.4 Operators
    • 3.4.1 Rules for Operators
  • 3.5 Linear Operator
  • 3.6 Commutator
  • 3.7 Matrix Representation of a Linear Operator
  • 3.8 Symmetric Matrix
  • 3.9 Transpose Operation
  • 3.10 Orthogonal Matrices
  • 3.11 Identity Operator
  • 3.12 Adjoint Operator
  • 3.13 Hermitian Operator
  • 3.14 Unitary Operators
    • 3.14.1 Properties of Unitary Operators
  • 3.15 Projection Operator
  • References
• 4 Boolean Algebra, Logic Gates, and Quantum Information Processing
  • 4.1 Boolean Algebra
  • 4.2 Classical Circuit Computation Model
  • 4.3 Universal Logic Gates
  • 4.4 Quantum Computation
  • 4.5 The Quantum Bit and Its Representations
  • 4.6 Superposition in Quantum Systems
  • 4.7 Quantum Register
  • References
• 5 Quantum Gates and Circuits
  • 5.1 X Gate
  • 5.2 Y Gate
  • 5.3 Z Gate
  • 5.4 (Square Root of NOT) Gate
  • 5.5 Hadamard Gate
  • 5.6 Phase Gate
  • 5.7 T Gate
  • 5.8 Reversible Logic
  • 5.9 CNOT Gate
  • 5.10 Controlled-U Gate
  • 5.11 Reversible Gates
    • 5.11.1 Fredkin Gate (Controlled Swap Gate)
    • 5.11.2 Toffoli Gate (Controlled-Controlled-NOT)
    • 5.11.3 Peres Gate
  • References
• 6 Tensor Products, Superposition, and Quantum Entanglement
  • 6.1 Tensor Products
  • 6.2 Multi-Qubit Systems
  • 6.3 Superposition
  • 6.4 Entanglement
  • 6.5 Decoherence
  • References
• 7 Teleportation and Superdense Coding
  • 7.1 Quantum Teleportation
  • 7.2 No-Cloning Theorem
  • 7.3 Superdense Coding
  • References
• 8 Quantum Error Correction
  • 8.1 Classical Error-Correcting Codes
  • 8.2 Quantum Error-Correcting Codes
  • 8.3 Shor’s 3-Qubit Bit-Flop Code
  • 8.4 Error Correction
    • 8.4.1 Bit-Flip Error Correction
    • 8.4.2 Phase Error Correction
  • 8.5 Shor’s 9 Qubit Code
  • References
• 9 Quantum Algorithms
  • 9.1 Deutsch’s Algorithm
  • 9.2 Deutsch–Jozsa Algorithm
  • 9.3 Grover’s Search Algorithm
    • 9.3.1 Details of Grover’s Algorithm
  • 9.4 Shor’s Factoring Algorithm
  • References
• 10 Quantum Cryptography
  • 10.1 Principles of Information Security
  • 10.2 One-Time Pad
  • 10.3 Public Key Cryptography
  • 10.4 RSA Coding Scheme
  • 10.5 Quantum Cryptography
  • 10.6 Quantum Key Distribution
  • 10.7 BB84
  • 10.8 Ekart 91
  • References
• Index

About the Author

Parag K. Lala, is an electrical engineering professor at Texas A&M University - Texarkana and is the author or co-author of seven books and more than 145 technical papers. His current research interests are in quantum computing and cryptography, hardware-based DNA sequence matching, and biologically-inspired design of programmable digital systems. He is a Life Fellow of the IEEE.