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.
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.
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.
A system of quantum computing structures is introduced and proven capable of making emerge, on average, the orbits of classical bounded nonlinear maps on \mathbb{C} through the iterative action of path-dependent quantum gates. The effects of emerging nonlinear dynamics and chaos upon the quantum averages of relevant observables and quantum probabilities are exemplified for a version of Chirikov's standard map on \mathbb{C} . Both the individual orbits and ensemble properties are addressed so that the Poincaré map for Chirikov's standard map, in the current quantum setting, is reinterpreted in terms of a quantum ensemble which is then formally introduced within the formalized system of quantum computing structures, in terms of quantum register machines, revealing three phases of quantum ensemble dynamics: the regular, the chaotic and an intermediate phase called complex quantum stochastic phase which shares similarities to the edge of chaos notion from classical cellular automata and classical random boolean networks' evolutionary computation.
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 computing and deep learning are increasingly becoming an emerging paradigm that can transform the way complex computational problems are approached. This chapter offers an overview of Quantum Neural Networks and Deep Learning, presenting material on how quantum mechanics can be merged with traditional neural networks. Quantum computing principles, including those of superposition, entanglement, and quantum parallelism, offer a very promising toolkit to overcome some of the big issues being faced today--such as high-dimensional data processing, faster optimization, and reduced computation complexity. The chapter describes the architecture and operation of QNNs, compares them with classical deep learning models, and points out their applications in drug-discovery-based research, image recognition, and cryptography. This chapter also considers existing barriers, such as hardware limitations and noise in quantum systems, and sheds some light on the ongoing research efforts and future avenues in hybrid quantum-classical models. Additionally, the chapter gave a detailed insight into bridge quantum theory and artificial intelligence and provided a simple yet in-depth foundation for anyone interested in the quantum augmentation of deep learning's transformative possibilities.
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.
Quantum artificial neural network (QANN) is one of the new paradigms built upon the combination of classical neural and quantum computations. It has great values for theoretic study and potentials to applications. In this paper, an intrinsic similarity of quantum theory and artificial neural network (ANN) theory has been highlighted and analyzed. The dynamic features of QANN are also discussed in details. As an application using dynamic features, a novel model of quantum neuron (QN) is described hereby with a focus on an operation function. Numerical results are illustrated to show that this the proposed QN model can perform a XOR function unrealizable with a classical neuron (CN). The model allows obtain a nonlinear mapping performed by two layers of classical ANN (CANN)