Codeword stabilized quantum codes for asymmetric channels

In this study we present a method that adapts the codeword stabilized (CWS) quantum code framework to the problem of finding asymmetric quantum codes. Making use of the the corresponding Pauli error models for amplitude and phase-damping models, we focus on codes that correct one or two amplitude-damping errors. As a result, we are able to exhaustively search for all possible codes up to length 9 by applying local Clifford operations on graph states. With a similar method, we also look at codes for the Pauli error models that detect a single amplitude error and detect multiple phase damping errors. Many new codes with good parameters are found, including non-additive codes and degenerate codes.