Tensor Network Contractions
Tensor Network Contractions

Author: Shi-Ju Ran

Publisher: Springer Nature

Published: 2020-01-27

Total Pages: 160

ISBN-13: 3030344894

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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.

Introduction to Tensor Network Methods
Introduction to Tensor Network Methods

Author: Simone Montangero

Publisher: Springer

Published: 2018-11-28

Total Pages: 172

ISBN-13: 3030014096

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This volume of lecture notes briefly introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra, and differential calculus. It then presents more advanced numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter. The book can be used for a graduate computational physics course. After successfully completing such a course, a student should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field.

Density Matrix and Tensor Network Renormalization
Density Matrix and Tensor Network Renormalization

Author: Tao Xiang

Publisher: Cambridge University Press

Published: 2023-08-31

Total Pages: 456

ISBN-13: 1009398717

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Renormalization group theory of tensor network states provides a powerful tool for studying quantum many-body problems and a new paradigm for understanding entangled structures of complex systems. In recent decades the theory has rapidly evolved into a universal framework and language employed by researchers in fields ranging from condensed matter theory to machine learning. This book presents a pedagogical and comprehensive introduction to this field for the first time. After an introductory survey on the major advances in tensor network algorithms and their applications, it introduces step-by-step the tensor network representations of quantum states and the tensor-network renormalization group methods developed over the past three decades. Basic statistical and condensed matter physics models are used to demonstrate how the tensor network renormalization works. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area.

Quantum Machine Learning
Quantum Machine Learning

Author: Peter Wittek

Publisher: Academic Press

Published: 2014-09-10

Total Pages: 176

ISBN-13: 0128010991

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Quantum Machine Learning bridges the gap between abstract developments in quantum computing and the applied research on machine learning. Paring down the complexity of the disciplines involved, it focuses on providing a synthesis that explains the most important machine learning algorithms in a quantum framework. Theoretical advances in quantum computing are hard to follow for computer scientists, and sometimes even for researchers involved in the field. The lack of a step-by-step guide hampers the broader understanding of this emergent interdisciplinary body of research. Quantum Machine Learning sets the scene for a deeper understanding of the subject for readers of different backgrounds. The author has carefully constructed a clear comparison of classical learning algorithms and their quantum counterparts, thus making differences in computational complexity and learning performance apparent. This book synthesizes of a broad array of research into a manageable and concise presentation, with practical examples and applications. - Bridges the gap between abstract developments in quantum computing with the applied research on machine learning - Provides the theoretical minimum of machine learning, quantum mechanics, and quantum computing - Gives step-by-step guidance to a broader understanding of this emergent interdisciplinary body of research

Quantum Chemistry and Dynamics of Excited States
Quantum Chemistry and Dynamics of Excited States

Author: Leticia González

Publisher: John Wiley & Sons

Published: 2021-02-01

Total Pages: 52

ISBN-13: 1119417759

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An introduction to the rapidly evolving methodology of electronic excited states For academic researchers, postdocs, graduate and undergraduate students, Quantum Chemistry and Dynamics of Excited States: Methods and Applications reports the most updated and accurate theoretical techniques to treat electronic excited states. From methods to deal with stationary calculations through time-dependent simulations of molecular systems, this book serves as a guide for beginners in the field and knowledge seekers alike. Taking into account the most recent theory developments and representative applications, it also covers the often-overlooked gap between theoretical and computational chemistry. An excellent reference for both researchers and students, Excited States provides essential knowledge on quantum chemistry, an in-depth overview of the latest developments, and theoretical techniques around the properties and nonadiabatic dynamics of chemical systems. Readers will learn: ● Essential theoretical techniques to describe the properties and dynamics of chemical systems ● Electronic Structure methods for stationary calculations ● Methods for electronic excited states from both a quantum chemical and time-dependent point of view ● A breakdown of the most recent developments in the past 30 years For those searching for a better understanding of excited states as they relate to chemistry, biochemistry, industrial chemistry, and beyond, Quantum Chemistry and Dynamics of Excited States provides a solid education in the necessary foundations and important theories of excited states in photochemistry and ultrafast phenomena.

Holographic Entanglement Entropy
Holographic Entanglement Entropy

Author: Mukund Rangamani

Publisher: Springer

Published: 2017-05-08

Total Pages: 245

ISBN-13: 3319525735

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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.

Sustainable Interdependent Networks II
Sustainable Interdependent Networks II

Author: M. Hadi Amini

Publisher: Springer

Published: 2018-12-11

Total Pages: 316

ISBN-13: 3319989235

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This book paves the way for researchers working on the sustainable interdependent networks spread over the fields of computer science, electrical engineering, and smart infrastructures. It provides the readers with a comprehensive insight to understand an in-depth big picture of smart cities as a thorough example of interdependent large-scale networks in both theory and application aspects. The contributors specify the importance and position of the interdependent networks in the context of developing the sustainable smart cities and provide a comprehensive investigation of recently developed optimization methods for large-scale networks. There has been an emerging concern regarding the optimal operation of power and transportation networks. In the second volume of Sustainable Interdependent Networks book, we focus on the interdependencies of these two networks, optimization methods to deal with the computational complexity of them, and their role in future smart cities. We further investigate other networks, such as communication networks, that indirectly affect the operation of power and transportation networks. Our reliance on these networks as global platforms for sustainable development has led to the need for developing novel means to deal with arising issues. The considerable scale of such networks, due to the large number of buses in smart power grids and the increasing number of electric vehicles in transportation networks, brings a large variety of computational complexity and optimization challenges. Although the independent optimization of these networks lead to locally optimum operation points, there is an exigent need to move towards obtaining the globally-optimum operation point of such networks while satisfying the constraints of each network properly. The book is suitable for senior undergraduate students, graduate students interested in research in multidisciplinary areas related to future sustainable networks, and the researchers working in the related areas. It also covers the application of interdependent networks which makes it a perfect source of study for audience out of academia to obtain a general insight of interdependent networks.

Density Matrix Renormalization Group (DMRG)-based Approaches in Computational Chemistry
Density Matrix Renormalization Group (DMRG)-based Approaches in Computational Chemistry

Author: Haibo Ma

Publisher: Elsevier

Published: 2022-08-21

Total Pages: 337

ISBN-13: 0323856950

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Density Matrix Renormalization Group (DMRG)-based Approaches in Computational Chemistry outlines important theories and algorithms of DMRG-based approaches and explores their use in computational chemistry. Beginning with an introduction to DMRG and DMRG-based approaches, the book goes on to discuss the key theories and applications of DMRG, from DMRG for semi-empirical and ab-initio quantum chemistry, to DMRG in embedded environments, frequency spaces and quantum dynamics. Drawing on the experience of its expert authors, sections detail recent ideas and key developments, providing an up-to-date view of current developments in the field for students and researchers in quantum chemistry. - Provides an expertly-curated, consolidated overview of research in the field - Includes exercises that support learning and link theory to practice - Outlines key theories and algorithms for computational chemistry applications

Quantum Chemistry and Dynamics of Excited States
Quantum Chemistry and Dynamics of Excited States

Author: Leticia González

Publisher: John Wiley & Sons

Published: 2020-11-10

Total Pages: 688

ISBN-13: 1119417724

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An introduction to the rapidly evolving methodology of electronic excited states For academic researchers, postdocs, graduate and undergraduate students, Quantum Chemistry and Dynamics of Excited States: Methods and Applications reports the most updated and accurate theoretical techniques to treat electronic excited states. From methods to deal with stationary calculations through time-dependent simulations of molecular systems, this book serves as a guide for beginners in the field and knowledge seekers alike. Taking into account the most recent theory developments and representative applications, it also covers the often-overlooked gap between theoretical and computational chemistry. An excellent reference for both researchers and students, Excited States provides essential knowledge on quantum chemistry, an in-depth overview of the latest developments, and theoretical techniques around the properties and nonadiabatic dynamics of chemical systems. Readers will learn: ● Essential theoretical techniques to describe the properties and dynamics of chemical systems ● Electronic Structure methods for stationary calculations ● Methods for electronic excited states from both a quantum chemical and time-dependent point of view ● A breakdown of the most recent developments in the past 30 years For those searching for a better understanding of excited states as they relate to chemistry, biochemistry, industrial chemistry, and beyond, Quantum Chemistry and Dynamics of Excited States provides a solid education in the necessary foundations and important theories of excited states in photochemistry and ultrafast phenomena.