  We examine the transformation of noise under a quantum error correcting code
(QECC) concatenated repeatedly with itself, by analyzing the effects of a
quantum channel after each level of concatenation using recovery operators that
are optimally adapted to use error syndrome information from the previous
levels of the code. We use the Shannon entropy of these channels to estimate
the thresholds of correctable noise for QECCs and find considerable
improvements under this adaptive concatenation. Similar methods could be used
to increase quantum fault tolerant thresholds.
