  Noise in quantum systems is a major obstacle to implementing many quantum
algorithms on large quantum circuits. In this work, we study the effects of
noise on the Rademacher complexity of quantum circuits, which is a measure of
statistical complexity that quantifies the richness of classes of functions
generated by these circuits. We consider noise models that are represented by
convex combinations of unitary channels and provide both upper and lower bounds
for the Rademacher complexities of quantum circuits characterized by these
noise models. In particular, we find a lower bound for the Rademacher
complexity of noisy quantum circuits that depends on the Rademacher complexity
of the corresponding noiseless quantum circuit as well as the free robustness
of the circuit. Our results show that the Rademacher complexity of quantum
circuits decreases with the increase in noise.
