Modelling Non Markovian Quantum Systems Using Tensor Networks
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Modelling Non Markovian Quantum Systems Using Tensor Networks
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Author : Aidan Strathearn
language : en
Publisher: Springer Nature
Release Date : 2020-08-31
Modelling Non Markovian Quantum Systems Using Tensor Networks written by Aidan Strathearn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-31 with Science categories.
This thesis presents a revolutionary technique for modelling the dynamics of a quantum system that is strongly coupled to its immediate environment. This is a challenging but timely problem. In particular it is relevant for modelling decoherence in devices such as quantum information processors, and how quantum information moves between spatially separated parts of a quantum system. The key feature of this work is a novel way to represent the dynamics of general open quantum systems as tensor networks, a result which has connections with the Feynman operator calculus and process tensor approaches to quantum mechanics. The tensor network methodology developed here has proven to be extremely powerful: For many situations it may be the most efficient way of calculating open quantum dynamics. This work is abounds with new ideas and invention, and is likely to have a very significant impact on future generations of physicists.
Tensor Network Contractions
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Author : Shi-Ju Ran
language : en
Publisher: Springer Nature
Release Date : 2020-01-27
Tensor Network Contractions written by Shi-Ju Ran and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-27 with Science categories.
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
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Author : Simone Montangero
language : en
Publisher: Springer
Release Date : 2018-11-28
Introduction To Tensor Network Methods written by Simone Montangero and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-28 with Science categories.
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.
Simulation With Entropy Thermodynamics
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Author : Christophe Goupil
language : en
Publisher: MDPI
Release Date : 2021-03-11
Simulation With Entropy Thermodynamics written by Christophe Goupil and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-11 with Science categories.
Beyond its identification with the second law of thermodynamics, entropy is a formidable tool for describing systems in their relationship with their environment. This book proposes to go through some of these situations where the formulation of entropy, and more precisely, the production of entropy in out-of-equilibrium processes, makes it possible to forge an approach to the behavior of very different systems. Whether for dimensioning structures; influencing parameter variability; or optimizing power, efficiency, or waste heat reduction, simulations based on entropy production offer a tool that is both compact and reliable. In the case of systems marked by complexity, it appears to be the only way. In that sense, realistic optimization can be carried out, integrating within the same framework both the system and all the constraints and boundary conditions that define it. Simulations based on entropy give the researcher a powerful analytical framework that crosses the disciplines of physics and links them together.
Tensor Network Contractions
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Author : Maciej Lewenstein
language : en
Publisher:
Release Date : 2020-10-08
Tensor Network Contractions written by Maciej Lewenstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-08 with Science categories.
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.
Neural Network Simulation Of Strongly Correlated Quantum Systems
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Author : Stefanie Czischek
language : en
Publisher: Springer Nature
Release Date : 2020-08-27
Neural Network Simulation Of Strongly Correlated Quantum Systems written by Stefanie Czischek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-27 with Science categories.
Quantum systems with many degrees of freedom are inherently difficult to describe and simulate quantitatively. The space of possible states is, in general, exponentially large in the number of degrees of freedom such as the number of particles it contains. Standard digital high-performance computing is generally too weak to capture all the necessary details, such that alternative quantum simulation devices have been proposed as a solution. Artificial neural networks, with their high non-local connectivity between the neuron degrees of freedom, may soon gain importance in simulating static and dynamical behavior of quantum systems. Particularly promising candidates are neuromorphic realizations based on analog electronic circuits which are being developed to capture, e.g., the functioning of biologically relevant networks. In turn, such neuromorphic systems may be used to measure and control real quantum many-body systems online. This thesis lays an important foundation for the realization of quantum simulations by means of neuromorphic hardware, for using quantum physics as an input to classical neural nets and, in turn, for using network results to be fed back to quantum systems. The necessary foundations on both sides, quantum physics and artificial neural networks, are described, providing a valuable reference for researchers from these different communities who need to understand the foundations of both.
Quantum Information And Computation For Chemistry Volume 154
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Author : Sabre Kais
language : en
Publisher: John Wiley & Sons
Release Date : 2014-01-31
Quantum Information And Computation For Chemistry Volume 154 written by Sabre Kais and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-31 with Science categories.
Examines the intersection of quantum information and chemical physics The Advances in Chemical Physics series is dedicated to reviewing new and emerging topics as well as the latest developments in traditional areas of study in the field of chemical physics. Each volume features detailed comprehensive analyses coupled with individual points of view that integrate the many disciplines of science that are needed for a full understanding of chemical physics. This volume of the series explores the latest research findings, applications, and new research paths from the quantum information science community. It examines topics in quantum computation and quantum information that are related to or intersect with key topics in chemical physics. The reviews address both what chemistry can contribute to quantum information and what quantum information can contribute to the study of chemical systems, surveying both theoretical and experimental quantum information research within the field of chemical physics. With contributions from an international team of leading experts, Volume 154 offers seventeen detailed reviews, including: Introduction to quantum information and computation for chemistry Quantum computing approach to non-relativistic and relativistic molecular energy calculations Quantum algorithms for continuous problems and their applications Photonic toolbox for quantum simulation Vibrational energy and information transfer through molecular chains Tensor networks for entanglement evolution Reviews published in Advances in Chemical Physics are typically longer than those published in journals, providing the space needed for readers to fully grasp the topic: the fundamentals as well as the latest discoveries, applications, and emerging avenues of research. Extensive cross-referencing enables readers to explore the primary research studies underlying each topic.
Vibrationally Mediated Chemical Dynamics
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Author : Jacob Dean
language : en
Publisher: Frontiers Media SA
Release Date : 2021-06-11
Vibrationally Mediated Chemical Dynamics written by Jacob Dean and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-11 with Science categories.
Mathematics For Future Computing And Communications
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Author : Liao Heng
language : en
Publisher: Cambridge University Press
Release Date : 2021-12-16
Mathematics For Future Computing And Communications written by Liao Heng and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-16 with Computers categories.
A panorama of new ideas in mathematics that are driving innovation in computing and communications.
Tensor Network States And Effective Particles For Low Dimensional Quantum Spin Systems
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Author : Laurens Vanderstraeten
language : en
Publisher: Springer
Release Date : 2017-08-10
Tensor Network States And Effective Particles For Low Dimensional Quantum Spin Systems written by Laurens Vanderstraeten and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-10 with Science categories.
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.