very little to be gain from such coarse information. This does not conflict with what we wrote above, about how knowledge of the noise bias has led to improved tailored protocols. In those examples, the hidden assumption was that the noise is biased but otherwise featureless. There exist other biased noise models exhibiting other types of correlations for which the tailored protocols fail. In other words, fixing some noise hypersurface while letting the other parameters fluctuate will result in vastly different noise models that react wildly differently to fault-tolerant protocols. To support these claims, we will present in numerical simulation results showing how the response of a given error correcting scheme can wildly fluctuate for noise models of equal strength.

These results lead us to ask what are the critical parameters which most strongly affect the response of a fault-tolerant scheme. To investigate this question, we have used machine learning techniques to attempt to correlate the response of a fault-tolerance scheme to the parameters of the noise model. Our results will be presented in . We have tried a few different machine learning algorithms and the critical parameters we found were more informative than generic noise strength measures, such as 