ABSTRACT
In this chapter we begin to examine quantum stabilizer codes in detail. Sec tion 3.1 introduces the theoretical framework that underlies this class of quan tum error correcting codes, and some examples are given in Section 3.2. Sec tion 3.3 shows how these codes can be described in terms of a binary vector space with symplectic inner product, and finally, concatenated quantum er ror correcting codes are introduced in Section 3.4. The latter discussion will focus on concatenated codes that are put together using quantum stabilizer codes. We will see in Chapter 6 that concatenated codes play an important role in establishing the accuracy threshold theorem for fault-tolerant quantum computing.
