Research in the field of quantum algorithms and quantum error correction is progressing at an astounding rate. There are many good papers on both subjects, but reading even a few of these may seem a daunting task to the newcomer. The aim of this paper is to give a leisurely introduction to the basic theory of quantum error correcting codes without appealing to even the most basic notions in physics. Thus the article is not a substitute for important papers such as [12] or [7] but rather an advertisement for them. I would be pleased if, in addition, some readers view this as a useful companion article if and when they go on to read more substantial literature on the subject of quantum error correction. I present nothing new here. Rather, I give an elementary account of the important theorems and proofs which appear in these fundamental works using only undergraduate algebra and a bit of classical coding theory. In particular, I give a full proof of the Knill/Laflamme theorem as well as an elementary treatment of stabilizer codes. The goal is to make the literature dealing with this exciting new area more accessible to discrete mathematicians.
展开▼
