Introduction

Quantum error-correcting codes (QECCs) have turned out to have many applications; but their primary purpose, of course, is to protect quantum information from noise. This need manifests itself in two rather different situations. The first is in quantum computing. The qubits in a quantum computer are subject to noise due both to imprecision in the operations (or gates) and to interactions with the external environment. They undergo errors when they are acted upon, and when they are just being stored (though hopefully not at the same rate). All the qubits in the computer must be kept error-free long enough for the computation to be completed. This is the principle of fault tolerance.

A rather different situation occurs in quantum communication. Here, the sender and receiver (Alice and Bob) are assumed to be physically separated, and the qubits travel from the sender to the receiver over a (presumably noisy) channel. This channel is assumed to be the dominant source of errors. While the qubits may undergo processing before and after transmission, errors during this processing are considered negligible compared to the channel errors. This picture of transmission through a channel is similar in spirit to the paradigm underlying much of classical information theory.