On Quantum Natural Policy Gradients

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 L\"owner 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.

Variational Quantum Policy Gradients with an Application to Quantum Control

Quantum Machine Learning models are composed by Variational Quantum Circuits (VQCs) in a very natural way. There are already some empirical results proving that such models provide an advantage in supervised/unsupervised learning tasks. However, when applied to Reinforcement Learning (RL), less is known. In this work, we consider Policy Gradients using a hardware-efficient ansatz. We prove that the complexity of obtaining an {\epsilon}-approximation of the gradient using quantum hardware scales only logarithmically with the number of parameters, considering the number of quantum circuits executions. We test the performance of such models in benchmarking environments and verify empirically that such quantum models outperform typical classical neural networks used in those environments, using a fraction of the number of parameters. Moreover, we propose the utilization of the Fisher Information spectrum to show that the quantum model is less prone to barren plateaus than its classical counterpart. As a different use case, we consider the application of such variational quantum models to the problem of quantum control and show its feasibility in the quantum-quantum domain.