We develop a theory for finding quantum error correction (QEC) procedures
which are optimized for given noise channels. Our theory accounts for
uncertainties in the noise channel, against which our QEC procedures are
robust. We demonstrate via numerical examples that our optimized QEC procedures
always achieve a higher channel fidelity than the standard error correction
method, which is agnostic about the specifics of the channel. This demonstrates
the importance of channel characterization before QEC procedures are applied.
Our main novel finding is that in the setting of a known noise channel the
recovery ancillas are redundant for optimized quantum error correction. We show
this using a general rank minimization heuristic and supporting numerical
calculations. Therefore, one can further improve the fidelity by utilizing all
the available ancillas in the encoding block.Comment: 12 pages, 9 figure