In the last few years, deep reinforcement learning has been proposed as a method to perform online learning in energy-efficiency scenarios such as HVAC control, electric car energy management, or building energy management, just to mention a few. On the other hand, quantum machine learning was born during the last decade to extend classic machine learning to a quantum level. In this work, we propose to study the benefits and limitations of quantum reinforcement learning to solve energy-efficiency scenarios. As a testbed, we use existing energy-efficiency-based reinforcement learning simulators and compare classic algorithms with the quantum proposal. Results in HVAC control, electric vehicle fuel consumption, and profit optimization of electrical charging stations applications suggest that quantum neural networks are able to solve problems in reinforcement learning scenarios with better accuracy than their classical counterpart, obtaining a better cumulative reward with fewer parameters to be learned.

Quantum neural networks constitute one of the most promising applications of Quantum Machine Learning, as they leverage both the capabilities of classical neural networks and the unique advantages of quantum mechanics. Moreover, quantum mechanics has demonstrated its ability to detect atypical patterns in data that are challenging for classical approaches to recognize. However, despite their potential, there are still open questions such as barren plateau phenomenon and the challenges of scalability and the curse of dimensionality, which become particularly relevant in Reinforcement Learning (RL) when working in environments with high-dimensional state and action spaces. This study delves into the critical realm of representing classical data as quantum states, a topic of keen interest across the scientific community. The aim is to construct streamlined circuits for efficient execution on quantum computers and simulators using minimal qubits and entanglement gates to evade barren plateau phenomena and reducing computational times. Our investigation examines and validates the efficacy of three strategies for data management and dimensionality reduction in real-world, large-scale environments for Quantum Reinforcement Learning, particularly in energy efficiency scenarios. The techniques encompass amplitude encoding, linear layer preprocessing, and data reuploading, supplemented by trainable parameters. This research sheds light on the potential of quantum machine learning in enhancing real-world environments, including energy efficiency scenarios and showcases the capabilities of quantum neural networks in the reinforcement learning landscape.

We propose a decoding algorithm for a class of convolutional codes called skew Reed-Solomon convolutional codes. These are convolutional codes of designed Hamming distance endowed with a cyclic structure yielding a left ideal of a non-commutative ring (a quotient of a skew polynomial ring). In this setting, right and left division algorithms exist, so our algorithm follows the guidelines of the Sugiyama's procedure for finding the error locator and error evaluator polynomials for Goppa block codes.

We study localizing and colocalizing subcategories of a comodule category of a coalgebra C over a field, using the correspondence between localizing subcategories and equivalence classes of idempotent elements in the dual algebra C∗. In this framework, we give a useful description of the localization functor by means of the Morita–Takeuchi context defined by the quasi-finite injective cogenerator of the localizing subcategory. Applying this description; first we characterize that a localizing subcategory , with associated idempotent element e ∊ C∗, is colocalizing if and only if eC is a quasi-finite eCe-comodule and, in addition,  is perfect whenever eC is injective. And second, we prove that a localizing subcategory  is stable if and only if e is a semicentral idempotent element of C∗. We apply the theory to path coalgebras and obtain, in particular, that the “localized” coalgebra of a path coalgebra is again a path coalgebra.

We design a non-commutative version of the Peterson–Gorenstein–Zierler decoding algorithm for a class of codes that we call skew RS codes. These codes are left ideals of a quotient of a skew polynomial ring, which endow them of a sort of non-commutative cyclic structure. Since we work over an arbitrary field, our techniques may be applied both to linear block codes and convolutional codes. In particular, our decoding algorithm applies for block codes beyond the classical cyclic case.