• 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