Iterative Optimization of Quantum Error Correcting Codes

We introduce an iterative algorithm for finding the optimal coding and decoding operations for an arbitrary channel. This algorithm does not require any error syndrome to be corrected completely, and hence might also find codes outside the usual Knill-Laflamme definition of error correcting codes. The iteration is shown to improve the figure of merit channel fidelity in every step. Our numerical studies so far suggest that Knill-Laflamme type codes and their basic properties, such as isometric encoding and homomorphic decoding, are often optimal even for channels with large errors, for which this theory was not originally designed