Patrick Hayden, Stanford
Lecture 1: Open systems formalism - Monday, June 7 - 2:00 - 3:15 p.m.
Density operators and ensemble ambiguity
Quantum channels and measurements
Distance measures (trace distance and fidelity)
Lecture 2: Entropy - Tuesday, June 8 - 2:00 - 3:15 p.m.
Von Neumann entropy, relative entropy and mutual information
Holevo and Pinsker's theorems
Renyi entropy and one-shot entropies
Compression
Lecture 3: Entanglement - Wednesday, June 9 - 2:00 - 3:15 p.m.
Schmidt decomposition
Mixed state entanglement
Cost and distillation
Other measures
Entanglement of purification and reflected entropy
Lecture 4: Error correction - Thursday, June 10 - 2:00 - 3:15 p.m.
Decoupling (exact and approximate)
Conditions for quantum error correction
Stabilizer codes
Toric code & GKP oscillator code
Lecture 5: Circuits and complexity - Friday, June 11 - 10:45 a.m. to 12:00 p.m.
Quantum gates and universality
Circuit complexity of random unitaries
Example: k-designs
Simulating quantum computation
Nearly all the lecture material is covered in detail in John Preskill's lecture notes. They are available on his quantum information course page.
The course will assume comfort with quantum mechanics: the Hilbert space formalism, bras and kets, the harmonic oscillator, coherent states, X & P as generators of displacements, the no-cloning theorem, density operators and partial trace.