Quantum information is extremely fragile: interaction with the environment (decoherence) and imperfect gates and measurements introduce errors all the time. Building a large, reliable quantum computer depends on handling that noise, and the main tool for doing so is quantum error correction.
It starts with correcting quantum errors: repetition codes, the 9-qubit Shor code, and the idea that arbitrary errors reduce to bit flips and phase flips. Next it covers the stabilizer formalism, a mathematical tool for describing a broad class of codes, and then more advanced code constructions: CSS codes, the toric code, and surface and color codes. It closes with fault-tolerant quantum computation: how to compute on encoded qubits when the gates themselves are noisy, and the threshold theorem.
Watch the lessons in order, then continue on to Quantum Cryptography & Applications.
Why quantum computers need error correction, how classical repetition codes work, and how the idea extends to qubits with the 9-qubit Shor code and the discretization of errors.
A mathematical tool for specifying and analyzing a broad class of quantum error correcting codes, known as stabilizer codes.
More sophisticated codes that can tolerate higher error rates: CSS codes, the toric code, and a brief look at surface codes and color codes.
How to perform computations on encoded qubits when gates and measurements are noisy: noise models, controlling error propagation, and the threshold theorem.