Inside field of Machine Learning or ML one finds the formulation of artificial neural networks or ANN as a robust method to predict data under minimal bias. It constitutes a key procedure inside field of Artificial Intelligence that has demonstrated to be fast, efficient and autonomous in some cases. A deep understanding at the usage of ANN would lead to construct advanced as well as robust tools to predict behavior of systems. Mathematically speaking, once data has been trained, ML emerges as a powerful algorithm to predict unseen data but with a certain probability. Inspired in Quantum Mechanics being a theory fundamental in physic based at probabilities one can wonder if ANN based at the concept of perceptron might be improved through a mathematical methodology by using the formalism of Quantum Mechanics. The aim of paper is to explore novel mathematical mechanisms that would allow to fine the probabilities of prediction inside ML.
Inside field of Machine Learning or ML one finds the formulation of artificial neural networks or ANN as a robust method to predict data under minimal bias. It constitutes a key procedure inside field of Artificial Intelligence that has demonstrated to be fast, efficient and autonomous in some cases. A deep understanding at the usage of ANN would lead to construct advanced as well as robust tools to predict behavior of systems. Mathematically speaking, once data has been trained, ML emerges as a powerful algorithm to predict unseen data but with a certain probability. Inspired in Quantum Mechanics being a theory fundamental in physic based at probabilities one can wonder if ANN based at the concept of perceptron might be improved through a mathematical methodology by using the formalism of Quantum Mechanics. The aim of paper is to explore novel mathematical mechanisms that would allow to fine the probabilities of prediction inside ML.
This chapter offers a clear and accessible introduction to the field of quantum-inspired neural computing. This area combines ideas from quantum mechanics with traditional neural network models to create new possibilities in machine learning and optimization metaheuristic algorithms. Unlike actual quantum computing, quantum-inspired approaches work on classical computers but borrow key concepts like superposition, entanglement, and probabilistic behaviour to improve how neural networks learn and process information. The study begins by explaining why researchers are interested in using quantum principles in neural networks. It then introduces the basic mathematical ideas behind these concepts, such as quantum states and transformations, and shows how they can be used to design more powerful and flexible learning systems. It focuses on discussing current models, outlining the distinctions between quantum-inspired and true quantum systems, and evaluating the potential benefits and challenges of this approach. In addition, Quantum-inspired neural computing introduces a novel framework that bridges classical artificial intelligence with principles derived from quantum mechanics. By simulating quantum behaviours on classical hardware, it opens new avenues for developing more adaptive and efficient learning models. This emerging approach offers promising advantages in areas such as optimization, parallel processing, and high-dimensional data representation. Finally, despite its potential, the field faces notable limitations and challenges. These include the lack of limited theoretical formalization, and difficulties in scaling models for complex real-world applications. Moreover, distinguishing genuine quantum-inspired advantages from conservative algorithmic improvements remains an current research apprehension.
The teaching of physics is currently linked to the developments that occur in the field of computing; therefore, it cannot be ignored that new technologies are being developed from neural networks and evolving in terms of artificial intelligence. Physics has adopted these systems in order to be able to perform data processing, system analysis, image processing and signal classification in a more optimal way, which are applied in areas such as optics, astronomy, quantum mechanics, among others. In parallel, a relationship has been created between neural networks and quantum computing, for which this document seeks to investigate and delve into these structures and identify the links with quantum formalism. The established roadmap is developed from the construction and analysis of neural network algorithms, which are based on two main components, the activation functions and the self-regulation of statistical weights that structure the bases of machine learning, which allows multidisciplinary research between computational physics and quantum mechanics for the optimization and evolution of the concept of "classical" neural network, affirming to date the inexistence of a quantum system of the neural network, but the conceptual and mathematical association bases for the future development of the concept of the quantum neural network, in this way, based on the use of fundamental concepts of quantum mechanics, it is possible to blur the abstract nature of said physical theory and reflect the applicability in machine learning, a potential field for the development of artificial intelligence.
Artificial neural networks (ANNs) have gained significant attention in various fields due to their ability to learn from data and extract meaningful patterns. Quantum machine learning (QML) has opened new opportunities for ANNs, with the advent of quantum computing. This chapter provides an introduction to the use of ANNs in QML, discussing fundamentals of QML and quantum mechanics, adaptability of ANN components, quantum-inspired classical ANNs, quantum perceptrons, activation functions, quantum hidden layers, backpropagation, quantum convolutional neural networks (CNNs), and quantum feed-forward neural networks (FNNs). The chapter also discusses the potential impact of quantum ANNs on industries and research disciplines, including quantum chemistry, quantum error correction, and quantum machine learning for quantum computers. The chapter also discusses limitations of quantum ANNs, such as noise and the need for large-scale quantum processors, and future directions for quantum ANNs, such as hybrid models and quantum neural networks with machine learning acceleration.
The intersection of artificial intelligence (AI) and quantum mechanics represents a frontier of scientific exploration, offering the potential to revolutionize our understanding of quantum systems. Despite the promise, significant challenges remain in effectively integrating AI techniques within quantum mechanics frameworks. This study aims to investigate the applications of AI in quantum mechanics, identifying both the challenges and opportunities presented by this interdisciplinary approach. The focus is on understanding how AI can enhance quantum simulations, optimize computations, and improve experimental designs. A comprehensive literature review was conducted, analyzing recent advancements in AI algorithms applied to quantum mechanics. Case studies were examined to illustrate successful implementations and the limitations encountered. Key metrics for evaluation included computational efficiency, accuracy, and scalability. Findings indicate that AI techniques, particularly machine learning and neural networks, can significantly expedite quantum simulations and enhance predictive accuracy. However, challenges such as data sparsity, interpretability of AI models, and the integration of AI with quantum algorithms were identified as significant barriers to progress. This research highlights the transformative potential of AI in advancing quantum mechanics while acknowledging the inherent challenges. Addressing these challenges will require collaborative efforts across disciplines, paving the way for innovative solutions that leverage AI to deepen our understanding of quantum phenomena and improve technological applications.
One of the most promising new directions in quantum computing and artificial intelligence convergence is the Quantum Neural Networks (QNNs) that can potentially revolutionize the manner in which intelligent systems are designed, trained, and implemented. Although traditional deep learning models have proven to be incredibly successful in fields like computer vision, natural language processing and autonomous systems, they are becoming limited by computational bottlenecks, energy use, and scalability constraints when operating on large high-dimensional data. The distinctive principles of quantum mechanics (superposition, entanglement, and quantum parallelism) may be applied to the QNNs to provide a distinct computational paradigm with the ability to execute exponentially complicated computations more effectively than his classical counterparts. This article gives an in-depth analysis of QNNs as the new frontier of artificial intelligence. We start with the description of the theoretical foundations of quantum computation and their realization in the form of neural networks. We then examine state-of-the-art QNN architectures, such as hybrid quantum-classical models that help overcome present quantum hardware limitations in relation to the capabilities of classical machine learning. Some of the upcoming applications are showcased including molecular simulation and drug discovery and financial modeling, optimization, cryptography and intelligent automation. Such applications reveal the revolutionary power of QNNs to tackle the issues that cannot be tackled by traditional systems. Nonetheless, there are also major obstacles on the way to a practical implementation of QNN. Problems that still remain a barrier to widespread adoption include quantum decoherence, noise in near-term quantum devices, and the inability to scale qubit architectures or to train large-scale quantum models. In order to overcome these obstacles, we speak about the current research work on the topic of error correction, variational algorithms, and hybrid system designs. Also we examine the ethical and societal ramifications of quantum-accelerated AI, such as security, data sovereignty, and technological equity globally.
The simulation of quantum matter with classical hardware plays a central role in the discovery and development of quantum many-body systems, with far-reaching implications in condensed matter physics and quantum technologies. In general, efficient and sophisticated algorithms are required to overcome the severe challenge posed by the exponential scaling of the Hilbert space of quantum systems. In contrast, hardware built with quantum bits of information are inherently capable of efficiently finding solutions of quantum many-body problems. While a universal and scalable quantum computer is still beyond the horizon, recent advances in qubit manufacturing and coherent control of synthetic quantum matter are leading to a new generation of intermediate scale quantum hardware. \n \nThe complexity underlying quantum many-body systems closely resembles the one encountered in many problems in the world of information and technology. In both contexts, the complexity stems from a large number of interacting degrees of freedom. A powerful strategy in the latter scenario is machine learning, a subfield of artificial intelligence where large amounts of data are used to extract relevant features and patterns. In particular, artificial neural networks have been demonstrated to be capable of discovering low-dimensional representations of complex objects from high-dimensional dataset, leading to the profound technological revolution we all witness in our daily life. \n \nIn this Thesis, we envision a new paradigm for scientific discovery in quantum physics. On the one hand, we have the essentially unlimited data generated with the increasing amount of highly controllable quantum hardware. On the other hand, we have a set of powerful algorithms that efficiently capture non-trivial correlations from high-dimensional data. Therefore, we fully embrace this data-driven approach to quantum mechanics, and anticipate new exciting possibilities in the field of quantum many-body physics and quantum information science. We revive a powerful stochastic neural network called a restricted Boltzmann machine, which slowly moved out of fashion after playing a central role in the machine learning revolution of the early 2010s. We introduce a neural-network representation of quantum states based on this generative model. We propose a set of algorithms to reconstruct unknown quantum states from measurement data and numerically demonstrate their potential, with important implications for current experiments. These include the reconstruction of experimentally inaccessible properties, such as entanglement, and diagnostics to determine sources of noise. Furthermore, we introduce a machine learning framework for quantum error correction, where a neural network learns the best decoding strategy directly from data. We expect that the full integration between quantum hardware and artificial intelligence will become the gold standard, and will drive the world into the era of fault-tolerant quantum computing and large-scale quantum simulations.