TOC.md

TABLE OF CONTENTS

Phase 1 Basic Quantum Concepts

• Introduction

• 1.1 States

  • Vector notation
  • Classical bits
  • Quantum bits – qubits
  • Superposition
  • 2-Norm approach
    • Q# exercise: setup a Q# environment

• 1.2 Gates

  • Unitary matrix
  • The Control-NOT Gate (CNOT)
    • Q# exercise: CNOT gate
  • Circuit Representation
  • Hadamard Gate
    • Q# exercise: H gate
  • Bloch Sphere
  • Pauli Gates
    • Q# exercise: Pauli gates
  • Measurement
    • Q# exercise: Measurement using M operation
  • Interference

• 1.3 Entanglement

  • Bell states
  • Entanglement
  • Creating a Bell state
  • Q# exercise: Bell States
  • Greenberger – Horne – Zeilinger
    • Q# exercise: GHZ
  • Superdense coding
    • Q# exercise: Superdense Coding
    • Quirk

• 1.4 Teleportation

  • Q# exercise: Teleportation
  • Q# exercise: Another Teleportation Exercise

• 1.5 The No-Cloning Theorem

• 1.6 The CHSH Game

  • Q# exercise: CHSH Game

Phase 2 Quantum Algorithms

• 2.1 Quantum Oracles * Q# exercise: Oracles

• 2.2 Deutsch's Algorithm * Q# exercise: Deutsch's algorithm

• 2.3 Deutsch-Jozsa Algorithm * Q# exercise: Deutsch-Josza algorithm

• 2.4 Grover's Algorithm * Q# exercise: Grover's algorithm

• 2.5 Simon's Algorithm * Q# exercise: Simon's algorithm

• 2.6 Shor's Algorithm

Phase 3 Quantum Hardware Systems

• 3.1 Natural qubits
• 3.2 Silicon quantum dots
• 3.3 Crystal defects
• 3.4 Trapped ions
• 3.5 Superconducting circuits
• 3.6 Topological qubits

Phase 4 Looking Ahead

• Cryptography and Quantum Computing
• Standard Algorithms for Cryptography
• The impact of Quantum Computing on Cryptography
• How Shor's algorithm can affect cryptography?
• How do the quantum circuits for Shor's algorithm work?
• How Grover's algorithm can affect cryptography?
• How do the quantum circuits for Grover's algorithm work?
• Encryption in the post-Quantum era
• Mosca's Inequality equation
• Microsoft and Quantum Cryptography
• Post-Quantum Cryptography VPN
• Conclusion