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Reinforcement Learning (RL) consists of designing agents that makeintelligent decisions without human supervision. When used alongside functionapproximators such as Neural Networks (NNs), RL is capable of solving extremelycomplex problems. Deep Q-Learning, a RL algorithm that uses Deep NNs, achievedsuper-human performance in some specific tasks. Nonetheless, it is alsopossible to use Variational Quantum Circuits (VQCs) as function approximatorsin RL algorithms. This work empirically studies the performance andtrainability of such VQC-based Deep Q-Learning models in classic controlbenchmark environments. More specifically, we research how data re-uploadingaffects both these metrics. We show that the magnitude and the variance of thegradients of these models remain substantial throughout training due to themoving targets of Deep Q-Learning. Moreover, we empirically show thatincreasing the number of qubits does not lead to an exponential vanishingbehavior of the magnitude and variance of the gradients for a PQC approximatinga 2-design, unlike what was expected due to the Barren Plateau Phenomenon. Thishints at the possibility of VQCs being specially adequate for being used asfunction approximators in such a context.

VQC-Based Reinforcement Learning with Data Re-uploading: Performance and Trainability