Constrained and Vanishing Expressivity of Quantum Fourier Models

Understand

In this work, we highlight an unforeseen behavior of the expressivity of Parameterized Quantum Circuits (PQCs) 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.