  Error models for quantum computing processors describe their deviation from
ideal behavior and predict the consequences in applications. But those
processors' experimental behavior -- the observed outcome statistics of quantum
circuits -- are rarely consistent with error models, even in characterization
experiments like randomized benchmarking (RB) or gate set tomography (GST),
where the error model was specifically extracted from the data in question. We
show how to resolve these inconsistencies, and quantify the rate of unmodeled
errors, by augmenting error models with a parameterized wildcard error model.
Adding wildcard error to an error model relaxes and weakens its predictions in
a controlled way. The amount of wildcard error required to restore consistency
with data quantifies how much unmodeled error was observed, in a way that
facilitates direct comparison to standard gate error rates. Using both
simulated and experimental data, we show how to use wildcard error to reconcile
error models derived from RB and GST experiments with inconsistent data, to
capture non-Markovianity, and to quantify all of a processor's observed error.
