Out-of-Model Effects and Overdispersion in Gate Set Tomography

In real QCVV experiments, for example Gate Set Tomography (GST), it is normal to find that, even when fitting arbitrary models, there is significant evidence for out-of-model effects. In GST we use statistical testing to report our confidence in the presence of these effects. We propose a method for quantifying out-of-model effects which qualifies the predictions of the model by, instead of giving an output probability distribution for a quantum circuit, giving a distribution over probability distributions for that circuit. We refer to this as the Dirichlet-Multinomial ansatz. In its simplest form this ansatz introduces a single additional parameter in our model called the "overdispersion parameter," which characterizes the spread of this probability distribution centered upon the predicted value of the output probabilities coming from GST. We've applied this to the reanalysis of a set of single qubit GST data and found that, even with a single additional parameter, this substantially reduces the model violation. Sandia National Labs is a multimission laboratory managed and operated by NTESS, LLC, a wholly owned subsidiary of Honeywell International Inc., for DOE's NNSA under contract DE-NA0003525.