  In this work, we highlight an unforeseen behavior of the expressivity of
Parameterized Quantum Circuits (PQC) for machine learning. A large class of
these models, seen as Fourier Series which frequencies are derived from the
encoding gates, were thought to have their Fourier coefficients mostly
determined by the trainable gates. Here, we demonstrate a new correlation
between the Fourier coefficients of the quantum model and its encoding gates.
In addition, we display a phenomenon of vanishing expressivity in certain
settings, where some Fourier coefficients vanish exponentially when the number
of qubits grows. These two behaviors imply novel forms of constraints which
limit the expressivity of PQCs, and therefore imply a new inductive bias for
Quantum models. The key concept in this work is the notion of a frequency
redundancy in the Fourier series spectrum, which determines its importance.
Those theoretical behaviours are observed in numerical simulations.
