Download or read book Tensor Network States for the Description of Quantum Many body Systems written by and published by . This book was released on 2015 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Tensor Network States and Effective Particles for Low Dimensional Quantum Spin Systems written by Laurens Vanderstraeten and published by Springer. This book was released on 2017-08-10 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis develops new techniques for simulating the low-energy behaviour of quantum spin systems in one and two dimensions. Combining these developments, it subsequently uses the formalism of tensor network states to derive an effective particle description for one- and two-dimensional spin systems that exhibit strong quantum correlations. These techniques arise from the combination of two themes in many-particle physics: (i) the concept of quasiparticles as the effective low-energy degrees of freedom in a condensed-matter system, and (ii) entanglement as the characteristic feature for describing quantum phases of matter. Whereas the former gave rise to the use of effective field theories for understanding many-particle systems, the latter led to the development of tensor network states as a description of the entanglement distribution in quantum low-energy states.
Download or read book Introduction to Tensor Network Methods written by Simone Montangero and published by Springer. This book was released on 2018-11-28 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tensor Network States written by Justin Reyes and published by . This book was released on 2020 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor network states are ubiquitous in the investigation of quantum many-body (QMB) physics. Their advantage over other state representations is evident from their reduction in the computational complexity required to obtain various quantities of interest, namely observables. Additionally, they provide a natural platform for investigating entanglement properties within a system. In this dissertation, we develop various novel algorithms and optimizations to tensor networks for the investigation of QMB systems, including classical and quantum circuits. Specifically, we study optimizations for the two-dimensional Ising model in a transverse field, we create an algorithm for the k-SAT problem, and we study the entanglement properties of random unitary circuits. In addition to these applications, we reinterpret renormalization group principles from QMB physics in the context of machine learning to develop a novel algorithm for the tasks of classification and regression, and then utilize machine learning architectures for the time evolution of operators in QMB systems.
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 Tensor Network Contractions written by Maciej Lewenstein and published by . This book was released on 2020-10-08 with total page 158 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. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Download or read book Quantum Information Meets Quantum Matter written by Bei Zeng and published by Springer. This book was released on 2019-03-28 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book approaches condensed matter physics from the perspective of quantum information science, focusing on systems with strong interaction and unconventional order for which the usual condensed matter methods like the Landau paradigm or the free fermion framework break down. Concepts and tools in quantum information science such as entanglement, quantum circuits, and the tensor network representation prove to be highly useful in studying such systems. The goal of this book is to introduce these techniques and show how they lead to a new systematic way of characterizing and classifying quantum phases in condensed matter systems. The first part of the book introduces some basic concepts in quantum information theory which are then used to study the central topic explained in Part II: local Hamiltonians and their ground states. Part III focuses on one of the major new phenomena in strongly interacting systems, the topological order, and shows how it can essentially be defined and characterized in terms of entanglement. Part IV shows that the key entanglement structure of topological states can be captured using the tensor network representation, which provides a powerful tool in the classification of quantum phases. Finally, Part V discusses the exciting prospect at the intersection of quantum information and condensed matter physics – the unification of information and matter. Intended for graduate students and researchers in condensed matter physics, quantum information science and related fields, the book is self-contained and no prior knowledge of these topics is assumed.
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 Quantum Many body Systems and Tensor Network Algorithms written by Augustine Kshetrimayum and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry of Quantum States written by Ingemar Bengtsson and published by Cambridge University Press. This book was released on 2017-08-18 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and Kochen–Specker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.
Download or read book Quantum Many body Systems Far Out of Equilibrium Simulations with Tensor Networks written by Johannes Michael Hauschild and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Machine Learning Meets Quantum Physics written by Kristof T. Schütt and published by Springer Nature. This book was released on 2020-06-03 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designing molecules and materials with desired properties is an important prerequisite for advancing technology in our modern societies. This requires both the ability to calculate accurate microscopic properties, such as energies, forces and electrostatic multipoles of specific configurations, as well as efficient sampling of potential energy surfaces to obtain corresponding macroscopic properties. Tools that can provide this are accurate first-principles calculations rooted in quantum mechanics, and statistical mechanics, respectively. Unfortunately, they come at a high computational cost that prohibits calculations for large systems and long time-scales, thus presenting a severe bottleneck both for searching the vast chemical compound space and the stupendously many dynamical configurations that a molecule can assume. To overcome this challenge, recently there have been increased efforts to accelerate quantum simulations with machine learning (ML). This emerging interdisciplinary community encompasses chemists, material scientists, physicists, mathematicians and computer scientists, joining forces to contribute to the exciting hot topic of progressing machine learning and AI for molecules and materials. The book that has emerged from a series of workshops provides a snapshot of this rapidly developing field. It contains tutorial material explaining the relevant foundations needed in chemistry, physics as well as machine learning to give an easy starting point for interested readers. In addition, a number of research papers defining the current state-of-the-art are included. The book has five parts (Fundamentals, Incorporating Prior Knowledge, Deep Learning of Atomistic Representations, Atomistic Simulations and Discovery and Design), each prefaced by editorial commentary that puts the respective parts into a broader scientific context.
Download or read book Density Matrix and Tensor Network Renormalization written by Tao Xiang and published by Cambridge University Press. This book was released on 2023-08-31 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tensor Network Descriptions of Quantum Entanglement in Path Integrals Thermalisation and Machine Learning written by Andrew Hallam and published by . This book was released on 2019 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the major ways in which quantum mechanics differs from classical mechanics is the existence of special quantum correlations - entanglement. Typical quantum states are highly entangled, making them complex and inefficient to represent. Physically interesting states are unusual, they are only weakly entangled. By restricting ourselves to weak entanglement, efficient representations of quantum states can be found. A tensor network is constructed by taking objects called tensors that encode spatially local information and gluing them together to create a large network that describes a complex quantum state. The manner in which the tensors are connected defines the entanglement structure of the quantum state. Tensors networks are therefore a natural framework for describing physical behaviour of complex quantum systems. In this thesis we utilize tensor networks to solve a number of interesting problems. Firstly, we study a Feynman path integral written over tensor network states. As a sum over classical trajectories, a Feynman path integral can struggle to capture entanglement. Combining the path integral with tensor networks overcomes this.We consider the effect of quadratic fluctuations on the tensor network path integral and calculate corrections to observables numerically and analytically. We also study the time evolution of complex quantum systems. By projecting quantum dynamics onto a classical phase space defined using tensor networks, we relate thermal behaviour of quantum systems to classical chaos. In doing so we demonstrate a relationship between entanglement growth and chaos. By studying the dynamics of coupled quantum chains we also gain insight into how quantum correlations spread over time. As noted, tensor networks are remarkably efficient. In the final section of this thesis we use tensor networks to create compressed machine learning algorithms. Their efficiency means that tensor networks can use $50$ times fewer parameters with no significant decrease in performance.
Download or read book Looking Inside Jets written by Simone Marzani and published by Springer. This book was released on 2019-05-11 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise primer reviews the latest developments in the field of jets. Jets are collinear sprays of hadrons produced in very high-energy collisions, e.g. at the LHC or at a future hadron collider. They are essential to and ubiquitous in experimental analyses, making their study crucial. At present LHC energies and beyond, massive particles around the electroweak scale are frequently produced with transverse momenta that are much larger than their mass, i.e., boosted. The decay products of such boosted massive objects tend to occupy only a relatively small and confined area of the detector and are observed as a single jet. Jets hence arise from many different sources and it is important to be able to distinguish the rare events with boosted resonances from the large backgrounds originating from Quantum Chromodynamics (QCD). This requires familiarity with the internal properties of jets, such as their different radiation patterns, a field broadly known as jet substructure. This set of notes begins by providing a phenomenological motivation, explaining why the study of jets and their substructure is of particular importance for the current and future program of the LHC, followed by a brief but insightful introduction to QCD and to hadron-collider phenomenology. The next section introduces jets as complex objects constructed from a sequential recombination algorithm. In this context some experimental aspects are also reviewed. Since jet substructure calculations are multi-scale problems that call for all-order treatments (resummations), the bases of such calculations are discussed for simple jet quantities. With these QCD and jet physics ingredients in hand, readers can then dig into jet substructure itself. Accordingly, these notes first highlight the main concepts behind substructure techniques and introduce a list of the main jet substructure tools that have been used over the past decade. Analytic calculations are then provided for several families of tools, the goal being to identify their key characteristics. In closing, the book provides an overview of LHC searches and measurements where jet substructure techniques are used, reviews the main take-home messages, and outlines future perspectives.
Download or read book Vibrational Dynamics Of Molecules written by Joel M Bowman and published by World Scientific. This book was released on 2022-06-14 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vibrational Dynamics of Molecules represents the definitive concise text on the cutting-edge field of vibrational molecular chemistry. The chapter contributors are a Who's Who of world leaders in the field. The editor, Joel Bowman, is widely considered as one of the founding fathers of theoretical reaction dynamics. The included topics span the field, from fundamental theory such as collocation methods and vibrational CI methods, to interesting applications such as astrochemistry, supramolecular systems and virtual computational spectroscopy. This is a useful reference for theoretical chemists, spectroscopists, physicists, undergraduate and graduate students, lecturers and software developers.
