An in-depth introduction to quantum error correction, fault-tolerant quantum computing, and related topics. Covers stabilizer codes, CSS codes, higher-dimensional codes, specific code constructions, entanglement purification protocols, and quantum channel capacity. Also bounds on quantum error correction: quantum Hamming bound, quantum Singleton bound, linear programming bounds and the quantum MacWilliams identity; and principles of fault-tolerant quantum computation: fault-tolerant error measurement, fault-tolerant gate design, the threshold for fault-tolerant quantum computation, and topological fault-tolerance.
Examples of qudit stabilizer codes, polynomial codes, Clifford group for qudits, introduction to fault-tolerance, definition of transversal gates, definition of fault-tolerant gates
Clifford group as symplectic group, generators of the Clifford group & encoding circuits for stabilizer codes, efficient simulation of Clifford group circuits, efficient simulation of Pauli measurements