This chapter focuses on protecting quantum information against noise: the codes that store a logical qubit redundantly, the stabilizer formalism that makes them tractable, and the fault-tolerance results that turn imperfect hardware into reliable computation.
It is the hinge of the notebook. It depends on the noise and quantum-operations formalism developed in Chapter II, applies the circuit model of Chapter III, and sets the target that the physical platforms of Chapter VI are racing toward. The theory of error correction and fault tolerance lives here; the question of where real hardware currently stands relative to the fault-tolerance threshold is kept in Chapter VI, where it can be date-stamped and refreshed without disturbing the results below.