Error models in quantum computation: An application of model selection

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 almost impossible to analyze due to the exponentially large state space, and a full process description requires even more resources. 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.