To address Quantum Artificial Neural Networks as quantum dynamical computing systems, a formalization of quantum artificial neural networks as dynamical systems is developed, expanding the concept of unitary map to the neural computation setting and introducing a quantum computing field theory on the network. The formalism is illustrated in a simulation of a quantum recurrent neural network and the resulting field dynamics is researched upon, showing emergent neural waves with excitation and relaxation cycles at the level of the quantum neural activity field, as well as edge of chaos signatures, with the local neurons operating as far-from-equilibrium open quantum systems, exhibiting entropy fluctuations with complex dynamics including complex quasiperiodic patterns and power law signatures. The implications for quantum computer science, quantum complexity research, quantum technologies and neuroscience are also addressed.
To address Quantum Artificial Neural Networks as quantum dynamical computing systems, a formalization of quantum artificial neural networks as dynamical systems is developed, expanding the concept of unitary map to the neural computation setting and introducing a quantum computing field theory on the network. The formalism is illustrated in a simulation of a quantum recurrent neural network and the resulting field dynamics is researched upon, showing emergent neural waves with excitation and relaxation cycles at the level of the quantum neural activity field, as well as edge of chaos signatures, with the local neurons operating as far-from-equilibrium open quantum systems, exhibiting entropy fluctuations with complex dynamics including complex quasiperiodic patterns and power law signatures. The implications for quantum computer science, quantum complexity research, quantum technologies and neuroscience are also addressed.
Unitary quantum maps provide a bridge between classical and quantum dynamical systems theories, having been applied within the context of quantum chaos research. When applied to quantum artificial neural networks, as models of networked quantum computation, unitary quantum maps allow one to address these networks as quantum networked dynamical systems. In this chapter, we address the application of these maps to quantum artificial neural networks, specifically studying the simulation and implementation of these maps for quantum recurrent neural networks, simulating these networks as dynamical computational systems and researching the topological properties of the series of neural firing operators’ quantum averages for nonstationary network states. We also research the results of a simulation of one of these networks on a quantum computer by cloud-based access to IBM Q Experience resources. The results show the emergence of complex dynamics, fitting into similar classes as those of classical cellular automata and coupled maps, including topological markers of chaos, edge of chaos and fractal attractors in the sequences of quantum averages. The implications for quantum complexity research, quantum chaos theory and quantum computing are addressed.
The current work addresses quantum machine learning in the context of Quantum Artificial Neural Networks such that the networks' processing is divided in two stages: the learning stage, where the network converges to a specific quantum circuit, and the backpropagation stage where the network effectively works as a self-programing quantum computing system that selects the quantum circuits to solve computing problems. The results are extended to general architectures including recurrent networks that interact with an environment, coupling with it in the neural links' activation order, and self-organizing in a dynamical regime that intermixes patterns of dynamical stochasticity and persistent quasiperiodic dynamics, making emerge a form of noise resilient dynamical record.
In recent years, quantum computing has emerged as a potentially gamechanging technology, with applications across various disciplines, including AI and machine learning.In recent years, the combination of quantum computing and neural networks has led to the development of quantum neural networks (QNNs).This paper explores the potential of QNNs and their applications in solving complex problems that are challenging for classical neural networks.This paper explores the fundamental principles of quantum computing, the architecture of QNNs, and their advantages over classical neural networks.Furthermore, this will highlight key research areas and challenges in the development and utilization of QNNs.Through an in-depth analysis, it demonstrates the QNNs hold significant promise for addressing complex computational problems and advancing the field of artificial intelligence.
Artificial intelligence (AI) has drawn significant inspiration from neuroscience to develop artificial neural network (ANN) models. However, these models remain constrained by the Von Neumann architecture and struggle to capture the complexity of the biological brain. Quantum computing, with its foundational principles of superposition, entanglement, and unitary evolution, offers a promising alternative approach to modeling neural dynamics. This paper explores the possibility of a neuro-quantum model of the brain by introducing a stochastic quantum approach that incorporates random fluctuations of neuronal processing within a quantum framework. We propose a mathematical formalization of stochastic quantum neural networks (QNNS), where qubits evolve according to stochastic differential equations inspired by biological neuronal processes. We also discuss challenges related to decoherence, qubit stability, and implications for AI and computational neuroscience.
Quantum neural networks (QNNs) represent a cutting-edge approach to machine learning and artificial intelligence, harnessing the principles of quantum mechanics to process and analyze data in fundamentally new ways. Unlike classical neural networks, which operate on classical bits and are limited by the laws of classical physics, QNNs use quantum bits (qubits) and exploit quantum phenomena such as superposition and entanglement to achieve unprecedented computational power and efficiency. This chapter explores the principles and applications of QNNs, including their potential for solving complex optimisation problems, pattern recognition tasks, and quantum simulation tasks. We discuss various QNN architectures, training algorithms, and applications, highlighting their advantages and challenges compared to classical neural networks. Additionally, we explore the potential impact of QNNs on fields such as quantum computing, quantum communication, and quantum sensing, as well as their implications for society and the economy. Overall, this chapter provides insights into the emerging field of quantum neural networks and sets the stage for further research and innovation in this exciting area.
Quantum cybernetics and its connections to complex quantum systems science is addressed from the perspective of complex quantum computing systems. In this way, the notion of an autonomous quantum computing system is introduced in regards to quantum artificial intelligence, and applied to quantum artificial neural networks, considered as autonomous quantum computing systems, which leads to a quantum connectionist framework within quantum cybernetics for complex quantum computing systems. Several examples of quantum feedforward neural networks are addressed in regards to Boolean functions' computation, multilayer quantum computation dynamics, entanglement and quantum complementarity. The examples provide a framework for a reflection on the role of quantum artificial neural networks as a general framework for addressing complex quantum systems that perform network-based quantum computation, possible consequences are drawn regarding quantum technologies, as well as fundamental research in complex quantum systems science and quantum biology.