Lu­ís Soares Barbosa

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.

Gilberto Cunha, Alexandra Ramôa, André Sequeira et al.

Reinforcement learning (RL) provides a principled framework for decision-making in partially observable environments, which can be modeled as Markov decision processes and compactly represented through dynamic decision Bayesian networks. Recent advances demonstrate that inference on sparse Bayesian networks can be accelerated using quantum rejection sampling combined with amplitude amplification, leading to a computational speedup in estimating acceptance probabilities.\\ Building on this result, we introduce Quantum Bayesian Reinforcement Learning (QBRL), a hybrid quantum-classical look-ahead algorithm for model-based RL in partially observable environments. We present a rigorous, oracle-free time complexity analysis under fault-tolerant assumptions for the quantum device. Unlike standard treatments that assume a black-box oracle, we explicitly specify the inference process, allowing our bounds to more accurately reflect the true computational cost. We show that, for environments whose dynamics form a sparse Bayesian network, horizon-based near-optimal planning can be achieved sub-quadratically faster through quantum-enhanced belief updates. Furthermore, we present numerical experiments benchmarking QBRL against its classical counterpart on simple yet illustrative decision-making tasks. Our results offer a detailed analysis of how the quantum computational advantage translates into decision-making performance, highlighting that the magnitude of the advantage can vary significantly across different deployment settings.

André Sequeira, Luis Paulo Santos, Luis Soares Barbosa

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.

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.

Nuno Oliveira, Luis Soares Barbosa

Applications developed over the cloud coordinate several, often anonymous, computational resources, distributed over different execution nodes, within flexible architectures. Coordination models able to represent quantitative data provide a powerful basis for their analysis and validation. This paper extends IMCreo, a semantic model for Stochastic reo based on interactive Markov chains, to enhance its scalability, by regarding each channel and node, as well as interface components, as independent stochastic processes that may (or may not) synchronise with the rest of the coordination circuit.

Alexandre Madeira, Manuel A. Martins, Luís S. Barbosa

Hierarchical transition systems provide a popular mathematical structure to represent state-based software applications in which different layers of abstraction are represented by inter-related state machines. The decomposition of high level states into inner sub-states, and of their transitions into inner sub-transitions is common refinement procedure adopted in a number of specification formalisms. This paper introduces a hybrid modal logic for k-layered transition systems, its first-order standard translation, a notion of bisimulation, and a modal invariance result. Layered and hierarchical notions of refinement are also discussed in this setting.