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.
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 the last few years, quantum computing and machine learning fostered rapid developments in their respective areas of application, introducing new perspectives on how information processing systems can be realized and programmed. The rapidly growing field of Quantum Machine Learning aims at bringing together these two ongoing revolutions. Here we first review a series of recent works describing the implementation of artificial neurons and feed-forward neural networks on quantum processors. We then present an original realization of efficient individual quantum nodes based on variational unsampling protocols. While keeping full compatibility with the overall memory-efficient feed-forward architecture, such a construction effectively reduces the quantum circuit depth required to determine the activation probability of single neurons upon input of the relevant data-encoding quantum states. This suggests a viable approach towards the use of quantum neural networks for pattern classification on near-term quantum hardware.
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.
Quantum Artificial Intelligence (QAI) represents the convergence of quantum computing and machine learning, aiming to harness the computational power of quantum mechanics to enhance the efficiency, scalability, and generalization capability of intelligent systems. This article provides a tutorial on the foundations, models, and emerging directions of QAI. We first review the core concepts of quantum information and hybrid quantum–classical computing, followed by a detailed discussion of variational quantum circuits (VQCs)—the fundamental building blocks of quantum neural networks (QNNs). Building upon these foundations, we introduce representative QAI architectures, including Quantum Convolutional Neural Networks (QCNNs) for pattern recognition, Quantum Long Short-Term Memory (QLSTM) for sequential modeling, and Quantum Reinforcement Learning (QRL) for decision making and control. Advanced topics such as Quantum Architecture Search (QAS), Quantum Fast Weight Programmers (QFWP), and the Quantum-Train (QT) framework are presented to illustrate how classical and quantum models can dynamically co-design and reprogram one another. Furthermore, we discuss federated and distributed quantum learning, encoding complexity, and training challenges such as barren plateaus and hardware constraints. The article concludes with a forward-looking outlook on scalable QAI systems, autonomous quantum agents, and the long-term vision of self-programming, distributed intelligence. By bridging quantum theory, learning algorithms, and system architectures, this work aims to offer both foundational understanding and strategic insights for the next generation of hybrid quantum-classical intelligence.
Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting weighted sum. Several attempts to generalize neurons to the quantum regime have been proposed, but all proposals collided with the difficulty of implementing non-linear activation functions, which is essential for classical neurons, due to the linear nature of quantum mechanics. Here we propose a solution to this roadblock in the form of a small quantum circuit that naturally simulates neurons with threshold activation. Our quantum circuit defines a building block, the "quantum neuron", that can reproduce a variety of classical neural network constructions while maintaining the ability to process superpositions of inputs and preserve quantum coherence and entanglement. In the construction of feedforward networks of quantum neurons, we provide numerical evidence that the network not only can learn a function when trained with superposition of inputs and the corresponding output, but that this training suffices to learn the function on all individual inputs separately. When arranged to mimic Hopfield networks, quantum neural networks exhibit properties of associative memory. Patterns are encoded using the simple Hebbian rule for the weights and we demonstrate attractor dynamics from corrupted inputs. Finally, the fact that our quantum model closely captures (traditional) neural network dynamics implies that the vast body of literature and results on neural networks becomes directly relevant in the context of quantum machine learning.
In the past few years, quantum computing and machine learning fostered rapid developments in their respective areas of application, introducing new perspectives on how information processing systems can be realized and programmed. The rapidly growing field of quantum machine learning aims at bringing together these two ongoing revolutions. Here, we first review a series of recent works describing the implementation of artificial neurons and feedforward neural networks on quantum processors. We then present an original realization of efficient individual quantum nodes based on variational unsampling protocols. We investigate different learning strategies involving global and local layerwise cost functions, and we assess their performances also in the presence of statistical measurement noise. While keeping full compatibility with the overall memory-efficient feedforward architecture, our constructions effectively reduce the quantum circuit depth required to determine the activation probability of single neurons upon input of the relevant data-encoding quantum states. This suggests a viable approach toward the use of quantum neural networks for pattern classification on near-term quantum hardware.
This paper provides an introduction to quantum machine learning, exploring the potential benefits of using quantum computing principles and algorithms that may improve upon classical machine learning approaches. Quantum computing utilizes particles governed by quantum mechanics for computational purposes, leveraging properties like superposition and entanglement for information representation and manipulation. Quantum machine learning applies these principles to enhance classical machine learning models, potentially reducing network size and training time on quantum hardware. The paper covers basic quantum mechanics principles, including superposition, phase space, and entanglement, and introduces the concept of quantum gates that exploit these properties. It also reviews classical deep learning concepts, such as artificial neural networks, gradient descent, and backpropagation, before delving into trainable quantum circuits as neural networks. An example problem demonstrates the potential advantages of quantum neural networks, and the appendices provide detailed derivations. The paper aims to help researchers new to quantum mechanics and machine learning develop their expertise more efficiently.