We consider error correction procedures designed specifically for the amplitude damping channel. We analyze amplitude damping errors in the stabilizer formalism. This analysis allows a generalization of the [4,1] `approximate amplitude damping code o
f quant-ph/9704002. We present this generalization as a class of [2(M+1),M] codes and present quantum circuits for encoding and recovery operations. We also present a [7,3] amplitude damping code based on the classical Hamming code. All of these are stabilizer codes whose encoding and recovery operations can be completely described with Clifford group operations. Finally, we describe optimization options in which recovery operations may be further adapted according to the damping probability gamma.
