Introduction to Quantum Information

Lecturer

Patrick Hayden, Stanford

Lecture Schedule:

• 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

Supplementary and Background Reading

• 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.