Foundations of quantum error correction 
Created by John Watrous
This is a course on quantum error correction, with a focus on foundational concepts. It begins with an explanation of what quantum error correcting codes are and how they work. It then moves on to the discretization of errors phenomenon, the stabilizer formalism for describing quantum error correcting codes, Calderbank–Shor–Steane (CSS) codes, and several key examples of quantum error correcting codes, including the toric code and surface codes. The course also discusses fault-tolerant quantum computation, in which quantum computations are performed on error-corrected quantum information.
Lessons
- Introduction
- Classical repetition codes
- Repetition code for qubits
- The 9-qubit Shor code
- Discretization of errors
- Introduction
- Pauli operations and observables
- Repetition code revisited
- Stabilizer codes
Helpful materials
Additional references
Alongside this course, you may find these resources to be helpful or interesting:
Michael Nielsen and Isaac Chuang. Quantum Computation and Quantum Information.
Phillip Kaye, Raymond Laflamme, and Michele Mosca. An Introduction to Quantum Computing.