André Sequeira, Luis Paulo Santos, Luís Soares Barbosa
Variational Quantum Circuits are being used as versatile Quantum Machine Learning models. Some empirical results exhibit an advantage in supervised and generative learning tasks. However, when applied to Reinforcement Learning, less is known. In this work, we considered a Variational Quantum Circuit composed of a low-depth hardware-efficient ansatz as the parameterized policy of a Reinforcement Learning agent. We show that an $ε$-approximation of the policy gradient can be obtained using a logarithmic number of samples concerning the total number of parameters. We empirically verify that such quantum models behave similarly or even outperform typical classical neural networks used in standard benchmarking environments and in quantum control, using only a fraction of the parameters. Moreover, we study the Barren Plateau phenomenon in quantum policy gradients using the Fisher Information Matrix spectrum.
Reinforcement Learning (RL) consists of designing agents that make intelligent decisions without human supervision. When used alongside function approximators such as Neural Networks (NNs), RL is capable of solving extremely complex problems. Deep Q-Learning, a RL algorithm that uses Deep NNs, achieved super-human performance in some specific tasks. Nonetheless, it is also possible to use Variational Quantum Circuits (VQCs) as function approximators in RL algorithms. This work empirically studies the performance and trainability of such VQC-based Deep Q-Learning models in classic control benchmark environments. More specifically, we research how data re-uploading affects both these metrics. We show that the magnitude and the variance of the gradients of these models remain substantial throughout training due to the moving targets of Deep Q-Learning. Moreover, we empirically show that increasing the number of qubits does not lead to an exponential vanishing behavior of the magnitude and variance of the gradients for a PQC approximating a 2-design, unlike what was expected due to the Barren Plateau Phenomenon. This hints at the possibility of VQCs being specially adequate for being used as function approximators in such a context.
André Sequeira, Luis Paulo Santos, Luis Soares Barbosa
This research delves into the role of the quantum Fisher Information Matrix (FIM) in enhancing the performance of Parameterized Quantum Circuit (PQC)-based reinforcement learning agents. While previous studies have highlighted the effectiveness of PQC-based policies preconditioned with the quantum FIM in contextual bandits, its impact in broader reinforcement learning contexts, such as Markov Decision Processes, is less clear. Through a detailed analysis of Löwner inequalities between quantum and classical FIMs, this study uncovers the nuanced distinctions and implications of using each type of FIM. Our results indicate that a PQC-based agent using the quantum FIM without additional insights typically incurs a larger approximation error and does not guarantee improved performance compared to the classical FIM. Empirical evaluations in classic control benchmarks suggest even though quantum FIM preconditioning outperforms standard gradient ascent, in general it is not superior to classical FIM preconditioning.