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Developments of Neural Networks in Quantum Physics

Yue Ban, Javier Echanobe, E. Torrontegui, Jorge Casanova

Published May 27, 2021• 0 citations
OpenAlex

Abstract

Quantum machine learning emerges from the symbiosis of quantum mechanics and machine learning. In particular, the latter gets displayed in quantum sciences as: (i) the use of classical machine learning as a tool applied to quantum physics problems, (ii) or the use of quantum resources such as superposition, entanglement, or quantum optimization protocols to enhance the performance of classification and regression tasks compare to their classical counterparts. This paper reviews examples in these two scenarios. On the one hand, the application of classical neural network to design a new quantum sensing protocol. On the other hand, the design of a quantum neural network based on the dynamics of a quantum perceptron optimized with the aid of shortcuts to adiabaticity gives rise to a short operation time and robust performance. These examples demonstrate the mutual reinforcement of both neural networks and quantum physics.

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Quantum machine learning emerges from the symbiosis of quantum mechanics and machine learning. In particular, the latter gets displayed in quantum sciences as: (i) the use of classical machine learning as a tool applied to quantum physics problems, (ii) or the use of quantum resources such as superposition, entanglement, or quantum optimization protocols to enhance the performance of classification and regression tasks compare to their classical counterparts. This paper reviews examples in these two scenarios. On the one hand, the application of classical neural network to design a new quantum sensing protocol. On the other hand, the design of a quantum neural network based on the dynamics of a quantum perceptron optimized with the aid of shortcuts to adiabaticity gives rise to a short operation time and robust performance. These examples demonstrate the mutual reinforcement of both neural networks and quantum physics.
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.
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.
Quantum Machine Learning is gaining prominence with the advent of real quantum processors. The quantum analogue of one of the most important and popular model of machine learning, namely Artificial Neural Network is studied and reviewed here in this paper. Various approaches to design and implement a quantum neural network has been studied. Most of the works done in this field involved a translation of classical neural network components into the language of quantum physics. But direct translation cannot be a solution as not every classical component has a quantum analogue. Non-linear activation functions are good examples of it. Quantum operators need to be linear and therefore finding alternate solutions to activation functions is an active area of research. Nevertheless, its advantages over the classical models are profound. Quantum superposition gives exponential storage capacity to a quantum network. Quantum parallelism can be put to use and to train the network with multiple inputs in one go. Despite being a new field, many real world applications of a quantum neural network has also been theorised. These models, their advantages, applications and limitations has been discussed in this paper.
Machine learning holds fundamental computational significance due to the increasing demand for efficient solutions to complex tasks in data analysis, pattern recognition, and optimization, which are essential for addressing the multifaceted challenges of modern society. As the volume of data proliferates at an unprecedented rate, the need for more powerful machine learning strategies becomes increasingly evident. Quantum neural networks (QNNs) represent an emerging and transformative research field that seeks to harness the unique principles of quantum mechanics to enhance the capabilities of machine learning algorithms. This survey examines various QNN approaches, including fully connected QNNs, quantum convolutional neural networks, equivariant QNNs, quantum Hopfield networks, quantum Boltzmann machines, quantum reservoir computing, and composite networks for quantum reinforcement learning, quantum generative learning, and quantum transfer learning. We summarize the relevant investigations on their performance, including learning accuracy, training time, and resource requirements, etc. Each QNN type has unique strengths and weaknesses, offering diverse solutions for different applications.
Machine Learning (ML) has changed the way computers work by letting them learn from data and make smart choices. However, traditional ML techniques encounter scalability and efficiency constraints as datasets get larger and computational problems become more complicated[1]. These restrictions could be circumvented by the new paradigms that quantum computing offers by using entanglement and superposition [2], [3]. The combination of the Quantum computing with the Machine Learning is called the Quantum Machine Learning(QML), offers efficiency improvements, new algorithmic opportunities, and speedups in certain linear algebraic operations. So, this review dives deeply into quantum-classical algorithms, with a particular emphasis on the approaches like quantum neural network and quantum support vector machines. We examine computational complexity, architectural design, benchmarking findings, and real-world applications (such as optimization, cryptography, and classification). We also discuss important issues including scalability, data encoding, and noise, and we suggest future paths for error prevention and scalable structures.
Despite rapid theoretical and practical progress, machine learning algorithms require large computational resources. However, new opportunities are opening up due to the advent of quantum computing devices that directly use the laws of quantum mechanics to bypass the technological and thermodynamic limitations of classical computing. Taking into account that artificial neural networks are actively used in solving a number of practical problems, with the advent of quantum computing technologies, the development of quantum neural networks for the implementation of quantum machine learning is very relevant. The article considers a quantum analogue of classical neurons that form quantum neural networks capable of performing universal quantum computations.