# Quantum Lectures

A selection of my lectures at the Perimeter Institute for Theoretical Physics

### Quantum Theory (2019)

- Lecture 1: Course overview, motivation, concept map, visualization tools (Bloch sphere, circuit diagrams, optical circuits)
- Lecture 2: Ideal postulates of QT (pure preparations, unitary transformations, and projective measurements), Quantum state tomography
- Lecture 3: Realistic postulates of QT (density operators, CPTP maps)
- Lecture 4: Course overview, motivation, concept map, visualization tools (Bloch sphere, circuit diagrams, optical circuits)
- Lecture 5: Composite systems, Entanglement
- Lecture 6: Purifications/Dilations
- Lecture 7: Review of concept map; putting it all together with an example (quantum control of a single qubit)

### Special Topics in Quantum Theory (2018)

- Lecture 3: Path integrals in non-relativistic QM

### Explorations in Quantum Information (2016)

- Lecture 10: Nonlinear optics
- Lecture 11: Wigner Functions
- Lecture 13: Sources of non-classical light (single photons, higher Fock states, squeezed states, Schrödinger cat states)
- Lecture 14: Measurement based quantum computing (cluster states) & Fusion gates

### Quantum Mechanics (2015)

- Lecture 1: The wavefunction; solving the Schrödinger Equation in 1D (particle-in-a-box, harmonic oscillator, free particle), Schrödinger Equation in 3D (Hydrogen atom)
- Lecture 2: Dirac notation; operators, eigenvalues and eigenstates; matrix representations of operators and state vectors; measurement; time-evolution; time-independent perturbation theory; time-dependent potentials
- Lecture 3: The Gaussian integral; path integrals in quantum mechanics; examples for free particle and harmonic oscillator
- Lecture 4: Tensor product structure, entanglement and the postulates of quantum mechanics for open systems