Abstract
This chapter describes a well-studied class of quantum codes, namely stabilizer codes and related quantum codes. The basic concept of stabilizer codes was introduced in Chapter 7. Here stabilizer codes are described more rigorously. After introducing stabilizer codes, their properties and encoded operations are introduced. Further, stabilizer codes are described using finite geometry interpretation. The standard form of stabilizer codes is introduced and used to provide efficient encoder and decoder implementations in a subsequent section. Nonbinary stabilizer codes are then described. Next, subsystem codes are introduced and described, followed by the topological codes. The section after that relates to surface codes. Entanglement-assisted codes are described in the final section.
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