Download or read book Tensor Network Contractions written by Shi-Ju Ran and published by Springer Nature. This book was released on 2020-01-27 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.

Download or read book Quantum Computing Physics Blockchains And Deep Learning Smart Networks written by Melanie Swan and published by World Scientific. This book was released on 2020-03-20 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum information and contemporary smart network domains are so large and complex as to be beyond the reach of current research approaches. Hence, new theories are needed for their understanding and control. Physics is implicated as smart networks are physical systems comprised of particle-many items interacting and reaching criticality and emergence across volumes of macroscopic and microscopic states. Methods are integrated from statistical physics, information theory, and computer science. Statistical neural field theory and the AdS/CFT correspondence are employed to derive a smart network field theory (SNFT) and a smart network quantum field theory (SNQFT) for the orchestration of smart network systems. Specifically, a smart network field theory (conventional or quantum) is a field theory for the organization of particle-many systems from a characterization, control, criticality, and novelty emergence perspective.This book provides insight as to how quantum information science as a paradigm shift in computing may influence other high-impact digital transformation technologies, such as blockchain and machine learning. Smart networks refer to the idea that the internet is no longer simply a communications network, but rather a computing platform. The trajectory is that of communications networks becoming computing networks (with self-executing code), and perhaps ultimately quantum computing networks. Smart network technologies are conceived as autonomous self-operating computing networks. This includes blockchain economies, deep learning neural networks, autonomous supply chains, self-piloting driving fleets, unmanned aerial vehicles, industrial robotics cloudminds, real-time bidding for advertising, high-frequency trading networks, smart city IoT sensors, and the quantum internet.

Download or read book Quantum Computing For The Brain written by Melanie Swan and published by World Scientific. This book was released on 2022-05-30 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Computing for the Brain argues that the brain is the killer application for quantum computing. No other system is as complex, as multidimensional in time and space, as dynamic, as less well-understood, as of peak interest, and as in need of three-dimensional modeling as it functions in real-life, as the brain.Quantum computing has emerged as a platform suited to contemporary data processing needs, surpassing classical computing and supercomputing. This book shows how quantum computing's increased capacity to model classical data with quantum states and the ability to run more complex permutations of problems can be employed in neuroscience applications such as neural signaling and synaptic integration. State-of-the-art methods are discussed such as quantum machine learning, tensor networks, Born machines, quantum kernel learning, wavelet transforms, Rydberg atom arrays, ion traps, boson sampling, graph-theoretic models, quantum optical machine learning, neuromorphic architectures, spiking neural networks, quantum teleportation, and quantum walks.Quantum Computing for the Brain is a comprehensive one-stop resource for an improved understanding of the converging research frontiers of foundational physics, information theory, and neuroscience in the context of quantum computing.

Download or read book Holographic Entanglement Entropy written by Mukund Rangamani and published by Springer. This book was released on 2017-05-08 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive overview of developments in the field of holographic entanglement entropy. Within the context of the AdS/CFT correspondence, it is shown how quantum entanglement is computed by the area of certain extremal surfaces. The general lessons one can learn from this connection are drawn out for quantum field theories, many-body physics, and quantum gravity. An overview of the necessary background material is provided together with a flavor of the exciting open questions that are currently being discussed. The book is divided into four main parts. In the first part, the concept of entanglement, and methods for computing it, in quantum field theories is reviewed. In the second part, an overview of the AdS/CFT correspondence is given and the holographic entanglement entropy prescription is explained. In the third part, the time-dependence of entanglement entropy in out-of-equilibrium systems, and applications to many body physics are explored using holographic methods. The last part focuses on the connection between entanglement and geometry. Known constraints on the holographic map, as well as, elaboration of entanglement being a fundamental building block of geometry are explained. The book is a useful resource for researchers and graduate students interested in string theory and holography, condensed matter and quantum information, as it tries to connect these different subjects linked by the common theme of quantum entanglement.

Download or read book Emerging Technologies in Data Mining and Information Security written by João Manuel R. S. Tavares and published by Springer Nature. This book was released on 2021-05-04 with total page 994 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features research papers presented at the International Conference on Emerging Technologies in Data Mining and Information Security (IEMIS 2020) held at the University of Engineering & Management, Kolkata, India, during July 2020. The book is organized in three volumes and includes high-quality research work by academicians and industrial experts in the field of computing and communication, including full-length papers, research-in-progress papers, and case studies related to all the areas of data mining, machine learning, Internet of things (IoT), and information security.

Download or read book Emergent Phenomena in Correlated Matter written by Eva Pavarini and published by Forschungszentrum Jülich. This book was released on 2013 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Deep Learning and Physics written by Akinori Tanaka and published by Springer Nature. This book was released on 2021-03-24 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is deep learning for those who study physics? Is it completely different from physics? Or is it similar? In recent years, machine learning, including deep learning, has begun to be used in various physics studies. Why is that? Is knowing physics useful in machine learning? Conversely, is knowing machine learning useful in physics? This book is devoted to answers of these questions. Starting with basic ideas of physics, neural networks are derived naturally. And you can learn the concepts of deep learning through the words of physics. In fact, the foundation of machine learning can be attributed to physical concepts. Hamiltonians that determine physical systems characterize various machine learning structures. Statistical physics given by Hamiltonians defines machine learning by neural networks. Furthermore, solving inverse problems in physics through machine learning and generalization essentially provides progress and even revolutions in physics. For these reasons, in recent years interdisciplinary research in machine learning and physics has been expanding dramatically. This book is written for anyone who wants to learn, understand, and apply the relationship between deep learning/machine learning and physics. All that is needed to read this book are the basic concepts in physics: energy and Hamiltonians. The concepts of statistical mechanics and the bracket notation of quantum mechanics, which are explained in columns, are used to explain deep learning frameworks. We encourage you to explore this new active field of machine learning and physics, with this book as a map of the continent to be explored.

Download or read book Machine Learning In Pure Mathematics And Theoretical Physics written by Yang-hui He and published by World Scientific. This book was released on 2023-06-21 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The juxtaposition of 'machine learning' and 'pure mathematics and theoretical physics' may first appear as contradictory in terms. The rigours of proofs and derivations in the latter seem to reside in a different world from the randomness of data and statistics in the former. Yet, an often under-appreciated component of mathematical discovery, typically not presented in a final draft, is experimentation: both with ideas and with mathematical data. Think of the teenage Gauss, who conjectured the Prime Number Theorem by plotting the prime-counting function, many decades before complex analysis was formalized to offer a proof.Can modern technology in part mimic Gauss's intuition? The past five years saw an explosion of activity in using AI to assist the human mind in uncovering new mathematics: finding patterns, accelerating computations, and raising conjectures via the machine learning of pure, noiseless data. The aim of this book, a first of its kind, is to collect research and survey articles from experts in this emerging dialogue between theoretical mathematics and machine learning. It does not dwell on the well-known multitude of mathematical techniques in deep learning, but focuses on the reverse relationship: how machine learning helps with mathematics. Taking a panoramic approach, the topics range from combinatorics to number theory, and from geometry to quantum field theory and string theory. Aimed at PhD students as well as seasoned researchers, each self-contained chapter offers a glimpse of an exciting future of this symbiosis.

Download or read book Quantum Computing An Applied Approach written by Jack D. Hidary and published by Springer Nature. This book was released on 2021-09-29 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book integrates the foundations of quantum computing with a hands-on coding approach to this emerging field; it is the first to bring these elements together in an updated manner. This work is suitable for both academic coursework and corporate technical training. The second edition includes extensive updates and revisions, both to textual content and to the code. Sections have been added on quantum machine learning, quantum error correction, Dirac notation and more. This new edition benefits from the input of the many faculty, students, corporate engineering teams, and independent readers who have used the first edition. This volume comprises three books under one cover: Part I outlines the necessary foundations of quantum computing and quantum circuits. Part II walks through the canon of quantum computing algorithms and provides code on a range of quantum computing methods in current use. Part III covers the mathematical toolkit required to master quantum computing. Additional resources include a table of operators and circuit elements and a companion GitHub site providing code and updates. Jack D. Hidary is a research scientist in quantum computing and in AI at Alphabet X, formerly Google X.

Download or read book Spherical NeurO n s for Geometric Deep Learning written by Pavlo Melnyk and published by Linköping University Electronic Press. This book was released on 2024-09-03 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: Felix Klein’s Erlangen Programme of 1872 introduced a methodology to unify non-Euclidean geometries. Similarly, geometric deep learning (GDL) constitutes a unifying framework for various neural network architectures. GDL is built from the first principles of geometry—symmetry and scale separation—and enables tractable learning in high dimensions. Symmetries play a vital role in preserving structural information of geometric data and allow models (i.e., neural networks) to adjust to different geometric transformations. In this context, spheres exhibit a maximal set of symmetries compared to other geometric entities in Euclidean space. The orthogonal group O(n) fully encapsulates the symmetry structure of an nD sphere, including both rotational and reflection symmetries. In this thesis, we focus on integrating these symmetries into a model as an inductive bias, which is a crucial requirement for addressing problems in 3D vision as well as in natural sciences and their related applications. In Paper A, we focus on 3D geometry and use the symmetries of spheres as geometric entities to construct neurons with spherical decision surfaces—spherical neurons—using a conformal embedding of Euclidean space. We also demonstrate that spherical neuron activations are non-linear due to the inherent non-linearity of the input embedding, and thus, do not necessarily require an activation function. In addition, we show graphically, theoretically, and experimentally that spherical neuron activations are isometries in Euclidean space, which is a prerequisite for the equivariance contributions of our subsequent work. In Paper B, we closely examine the isometry property of the spherical neurons in the context of equivariance under 3D rotations (i.e., SO(3)-equivariance). Focusing on 3D in this work and based on a minimal set of four spherical neurons (one learned spherical decision surface and three copies), the centers of which are rotated into the corresponding vertices of a regular tetrahedron, we construct a spherical filter bank. We call it a steerable 3D spherical neuron because, as we verify later, it constitutes a steerable filter. Finally, we derive a 3D steerability constraint for a spherical neuron (i.e., a single spherical decision surface). In Paper C, we present a learnable point-cloud descriptor invariant under 3D rotations and reflections, i.e., the O(3) actions, utilizing the steerable 3D spherical neurons we introduced previously, as well as vector neurons from related work. Specifically, we propose an embedding of the 3D steerable neurons into 4D vector neurons, which leverages end-to-end training of the model. The resulting model, termed TetraSphere, sets a new state-of-the-art performance classifying randomly rotated real-world object scans. Thus, our results reveal the practical value of steerable 3D spherical neurons for learning in 3D Euclidean space. In Paper D, we generalize to nD the concepts we previously established in 3D, and propose O(n)-equivariant neurons with spherical decision surfaces, which we call Deep Equivariant Hyper-spheres. We demonstrate how to combine them in a network that directly operates on the basis of the input points and propose an invariant operator based on the relation between two points and a sphere, which as we show, turns out to be a Gram matrix. In summary, this thesis introduces techniques based on spherical neurons that enhance the GDL framework, with a specific focus on equivariant and invariant learning on point sets.

Download or read book Journal of the Physical Society of Japan written by and published by . This book was released on 2017 with total page 846 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Smart Modelling for Engineering Systems written by Margarita N. Favorskaya and published by Springer Nature. This book was released on 2021-01-30 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of research papers selected for presentation at the International Conference on Smart Computational Methods in Continuum Mechanics 2021, organized by Moscow Institute of Physics and Technology and the Institute for Computer Aided Design of Russian Academy of Sciences. The work is presented in two volumes. The primary objective of the book is to report the state-of-the-art on smart computational paradigms in continuum mechanics and explore the use of artificial intelligence paradigms such as neural nets and machine learning for improving the performance of the designed engineering systems. The book includes up-to-date smart computational methods which are used to solve problems in continuum mechanics, engineering, seismic prospecting, non-destructive testing, and so on. The main features of the book are the research papers on the application of novel smart methods including neural nets and machine learning, computational algorithms, smart software systems, and high-performance computer systems for solving complex engineering problems. The case studies pertaining to the real-world applications in the above fields are included. The book presents a collection of best research papers in English language from some of the world leaders in the field of smart system modelling and design of engineering systems.

Download or read book Quantum Computing for the Brain written by Melanie Swan and published by Wspc (Europe). This book was released on 2022 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Computing for the Brain argues that the brain is the killer application for quantum computing. No other system is as complex, as multidimensional in time and space, as dynamic, as less well-understood, as of peak interest, and as in need of three-dimensional modeling as it functions in real-life, as the brain. Quantum computing has emerged as a platform suited to contemporary data processing needs, surpassing classical computing and supercomputing. This book shows how quantum computing's increased capacity to model classical data with quantum states and the ability to run more complex permutations of problems can be employed in neuroscience applications such as neural signaling and synaptic integration. State-of-the-art methods are discussed such as quantum machine learning, tensor networks, Born machines, quantum kernel learning, wavelet transforms, Rydberg atom arrays, ion traps, boson sampling, graph-theoretic models, quantum optical machine learning, neuromorphic architectures, spiking neural networks, quantum teleportation, and quantum walks. Quantum Computing for the Brain is a comprehensive one-stop resource for an improved understanding of the converging research frontiers of foundational physics, information theory, and neuroscience in the context of quantum computing.

Download or read book Querying Artificial Intelligence on the Dark Universe in a Quintessential Encoding of Space time written by Ariel Fernández and published by Cambridge Scholars Publishing. This book was released on 2023-08-30 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the possibility of the use of artificial intelligence (AI) to solve one of the cosmos’ biggest mysteries: the nature of undetectable forms of matter, namely dark matter and dark energy, which make up 95% of the universe. The book describes the outcome of this quest in terms of an entangled ur-universe that admits no observer, and incorporates an extra dimension to encode space-time as a latent manifold. A cosmic engine fueled by dark energy that maintains the topology of the universe during its expansion, involving autocatalytic vacuum creation, is identified. The physical picture of the cosmos presented in the book paves the way for a solution to the cosmological constant problem and provides a cogent explanation for the huge gap between the predicted and measured values that has troubled physicists for decades.

Download or read book Understanding Quantum Phase Transitions written by Lincoln Carr and published by CRC Press. This book was released on 2010-11-02 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum phase transitions (QPTs) offer wonderful examples of the radical macroscopic effects inherent in quantum physics: phase changes between different forms of matter driven by quantum rather than thermal fluctuations, typically at very low temperatures. QPTs provide new insight into outstanding problems such as high-temperature superconductivit

Download or read book Gauge Gravity Duality written by Martin Ammon and published by Cambridge University Press. This book was released on 2015-04-09 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first textbook on this important topic, for graduate students and researchers in particle and condensed matter physics.

Download or read book Topological Dynamics in Metamodel Discovery with Artificial Intelligence written by Ariel Fernández and published by CRC Press. This book was released on 2022-12-21 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: The leveraging of artificial intelligence (AI) for model discovery in dynamical systems is cross-fertilizing and revolutionizing both disciplines, heralding a new era of data-driven science. This book is placed at the forefront of this endeavor, taking model discovery to the next level. Dealing with artificial intelligence, this book delineates AI’s role in model discovery for dynamical systems. With the implementation of topological methods to construct metamodels, it engages with levels of complexity and multiscale hierarchies hitherto considered off limits for data science. Key Features: Introduces new and advanced methods of model discovery for time series data using artificial intelligence Implements topological approaches to distill "machine-intuitive" models from complex dynamics data Introduces a new paradigm for a parsimonious model of a dynamical system without resorting to differential equations Heralds a new era in data-driven science and engineering based on the operational concept of "computational intuition" Intended for graduate students, researchers, and practitioners interested in dynamical systems empowered by AI or machine learning and in their biological, engineering, and biomedical applications, this book will represent a significant educational resource for people engaged in AI-related cross-disciplinary projects.