  Threshold theorems for fault-tolerant quantum computing assume that errors
are of certain types. But how would one detect whether errors of the "wrong"
type occur in one's experiment, especially if one does not even know what type
of error to look for? The problem is that for many qubits a full state
description is impossible to analyze, and a full process description is even
more impossible to analyze. As a result, one simply cannot detect all types of
errors. Here we show through a quantum state estimation example (on up to 25
qubits) how to attack this problem using model selection. We use, in
particular, the Akaike Information Criterion. The example indicates that the
number of measurements that one has to perform before noticing errors of the
wrong type scales polynomially both with the number of qubits and with the
error size.
