Quantum Computing and Quantum Information

Lecturer: Aram Harrow
Coordinates: IFT. 8,9,10,13,15,16 April. 11:00-13:00.

This course is for graduate students who have some familiarity with quantum mechanics and/or quantum information. The goals are to introduce some of the key developments that have occurred since Nielsen and Chuang in algorithms, information theory, error correction and complexity theory. For background, I will assume that students are comfortable with Chapter 2 of Nielsen and Chuang, or Sections 1-4 and 9 of these notes from Watrous (see also videos.)

Lectures

8 April, 2026: introduction, states, channels, distance measures, purifications, bit commitment
Lecture notes 1. Exercise sheet 1.
Further reading: Watrous sections 9-12 (more mathematical). N&C chapters 8 and 9 (more physics).

9 April, 2026: quantum error correction
Lecture notes 2. Exercise sheet 2.
Further reading: Watrous sections 13-16. N&C chapter 10.

10 April, 2026: QECC continued. stabilizer codes, CSS codes, topological codes. FTQC
Lecture notes 3. Exercise sheet 3.
Further reading: N&C chapters 11 and 12.

13 April, 2026: algorithms. quantum walks, quantum singular value transform, Hamiltonian simulation.
Lecture notes 4. Exercise sheet 4.
Further reading: Watrous Part II or N&C Chapters 5 and 6.

15 April, 2026: quantum complexity. QMA and PostBQP.
Lecture notes 5.
Further reading: MIT OCW class on quantum complexity theory

16 April, 2026: information theory and many-body physics.
Lecture notes 6. Exercise sheet 6.
Further reading: Quantum Information Theory (aka "From Classical to Quantum Shannon Theory.") by Mark Wilde. book and arxiv. M. B. Hastings. Locality in Quantum Systems. lecture notes from Les Houches summer school. 1008.5137. Jeongwan Haah, Matthew B. Hastings, Robin Kothari, Guang Hao Low. Quantum algorithm for simulating real time evolution of lattice Hamiltonians 1801.03922, FOCS 2018.