  Parameterized quantum circuits (PQCs) have been widely used as a machine
learning model to explore the potential of achieving quantum advantages for
various tasks. However, the training of PQCs is notoriously challenging owing
to the phenomenon of plateaus and/or the existence of (exponentially) many
spurious local minima. In this work, we propose an efficient parameter
initialization strategy with theoretical guarantees. We prove that if the
initial domain of each parameter is reduced inversely proportional to the
square root of circuit depth, then the magnitude of the cost gradient decays at
most polynomially as a function of the depth. Our theoretical results are
verified by numerical simulations of variational quantum eigensolver tasks.
Moreover, we demonstrate that the reduced-domain initialization strategy can
protect specific quantum neural networks from exponentially many spurious local
minima. Our results highlight the significance of an appropriate parameter
initialization strategy and can be used to enhance the trainability of PQCs in
variational quantum algorithms.
