  We investigate how the addition of quantum resources changes the statistical
complexity of quantum circuits by utilizing the framework of quantum resource
theories. Measures of statistical complexity that we consider include the
Rademacher complexity and the Gaussian complexity, which are well-known
measures in computational learning theory that quantify the richness of classes
of real-valued functions. We derive bounds for the statistical complexities of
quantum circuits that have limited access to certain resources and apply our
results to two special cases: (1) stabilizer circuits that are supplemented
with a limited number of T gates and (2) instantaneous quantum polynomial-time
Clifford circuits that are supplemented with a limited number of CCZ gates. We
show that the increase in the statistical complexity of a quantum circuit when
an additional quantum channel is added to it is upper bounded by the free
robustness of the added channel. Finally, we derive bounds for the
generalization error associated with learning from training data arising from
quantum circuits.
