Appears in collection : CEMRACS 2025: Quantum Computing / CEMRACS 2025: Calcul quantique

It is widely assumed that we will not have large-scale quantum computers without a fair amount of built-in quantum error correction. Quantum error-correcting codes address precisely this issue. They generalise the theory of classical error-correcting codes, drawing upon many of its concepts, and introduce significant differences as well. We will recall the most relevant concepts of classical error correction and introduce quantum stabiliser codes, as well as the somewhat more manageable subclass of CSS codes. We will then steer the lectures towards the modern topic of quantum Low Density Parity Check (LDPC) codes that have recently seen striking new developments.