  Federated learning has emerged as a viable distributed solution to train
machine learning models without the actual need to share data with the central
aggregator. However, standard neural network-based federated learning models
have been shown to be susceptible to data leakage from the gradients shared
with the server. In this work, we introduce federated learning with variational
quantum circuit model built using expressive encoding maps coupled with
overparameterized ans\"atze. We show that expressive maps lead to inherent
privacy against gradient inversion attacks, while overparameterization ensures
model trainability. Our privacy framework centers on the complexity of solving
the system of high-degree multivariate Chebyshev polynomials generated by the
gradients of quantum circuit. We present compelling arguments highlighting the
inherent difficulty in solving these equations, both in exact and approximate
scenarios. Additionally, we delve into machine learning-based attack strategies
and establish a direct connection between overparameterization in the original
federated learning model and underparameterization in the attack model.
Furthermore, we provide numerical scaling arguments showcasing that
underparameterization of the expressive map in the attack model leads to the
loss landscape being swamped with exponentially many spurious local minima
points, thus making it extremely hard to realize a successful attack. This
provides a strong claim, for the first time, that the nature of quantum machine
learning models inherently helps prevent data leakage in federated learning.
