  This research explores the trainability of Parameterized Quantum
circuit-based policies in Reinforcement Learning, an area that has recently
seen a surge in empirical exploration. While some studies suggest improved
sample complexity using quantum gradient estimation, the efficient trainability
of these policies remains an open question. Our findings reveal significant
challenges, including standard Barren Plateaus with exponentially small
gradients and gradient explosion. These phenomena depend on the type of
basis-state partitioning and mapping these partitions onto actions. For a
polynomial number of actions, a trainable window can be ensured with a
polynomial number of measurements if a contiguous-like partitioning of
basis-states is employed. These results are empirically validated in a
multi-armed bandit environment.
