Topics

  • Fundamentals of quantum theory
    • addition of probability amplitudes
    • quantum interference
    • mathematical description of states and evolution of closed quantum systems (Hilbert space, unitary evolution)
    • measurements (projectors, Born rule)
    • Pauli matrices
  • Distinguishability of quantum states
  • The Bloch sphere
    • parametrisation
    • action of quantum gates on the Bloch vector
  • The definition of quantum entanglement (the tensor product structure)
  • The no-cloning theorem, and quantum teleportation
  • Quantum gates
    • phase gate
    • Hadamard
    • controlled-\texttt{NOT}
    • SWAP
    • the Hadamard-phase-Hadamard network
    • phase “kick-back” induced by controlled-U
    • phase “kick-back” induced by quantum Boolean function evaluation
  • Quantum algorithms
    • Deutsch
    • Bernstein-Vazirani
    • Simon
  • Bell’s theorem
    • Quantum correlations
    • CHSH inequality
  • Density matrices
    • partial trace
    • statistical mixture of pure states
    • Born rule for density matrices
    • quantum entanglement in terms of density matrices
  • Completely positive maps
    • Kraus operators
    • the Choi matrix
    • positive versus completely positive maps
    • partial-transpose
  • The simple model of decoherence
  • Quantum error correction of bit-flip and phase-flip errors