Introduction to quantum computing
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Contents

  • Introduction
  • Learning outcomes
  • 1 Why quantum computing?
    • 1.1 What can classical computers do?
    • 1.2 What can quantum computers do?
  • 2 Background mathematics and terminology
    • 2.1 Matrix multiplication
    • 2.2 Finding the eigenvalues and eigenvectors of a two multiplication two matrix
    • 2.3 Complex numbers
    • 2.4 Operators and superposition
  • 3 Setting the scene in quantum physics
    • 3.1 Spin-½ particles
    • 3.2 Representing a general spin state
    • 3.3 Spin observables
    • 3.4 Two-particle spin states
    • 3.5 Entanglement
  • 4 Classical computing
    • 4.1 Classical bits and logic gates
    • 4.2 Classical Boolean gates
  • 5 Qubits and quantum gates
    • 5.1 Defining a qubit
    • 5.2 Single qubit gates
      • 5.2.1 The NOT gate
      • 5.2.2 The Hadamard gate
      • 5.2.3 Sequences of gates
    • 5.3 Two-qubit gates
      • 5.3.1 Two-qubit states
      • 5.3.2 How the CNOT gate works
    • 5.4 Quantum circuits
      • 5.4.1 Circuits with multiple gates
      • 5.4.2 Measurements
      • 5.4.3 Activity
  • 6 Real-world quantum computing
    • 6.1 Schrödinger’s cat
    • 6.2 A few examples of quantum technologies
  • 7 Summary
  • 8 Quiz
  • Acknowledgements

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