Modelling Non Markovian Quantum Systems Using Tensor Networks

Author : Aidan Strathearn
Publisher : Springer Nature
Page : 113 pages
File Size : 47,7 Mb
Release : 2020-08-31
Category : Science
ISBN : 9783030549756

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Modelling Non-Markovian Quantum Systems Using Tensor Networks by Aidan Strathearn Pdf

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.

Author : Gerald E. Fux
Publisher : Unknown
Page : 0 pages
File Size : 43,5 Mb
Release : 2022
Category : Many-body problem
ISBN : OCLC:1423297901

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Process Tensor Networks for Non-Markovian Open Quantum Systems by Gerald E. Fux Pdf

Author : Shi-Ju Ran,Emanuele Tirrito,Cheng Peng,Xi Chen,Luca Tagliacozzo,Gang Su,Maciej Lewenstein
Publisher : Springer Nature
Page : 160 pages
File Size : 52,7 Mb
Release : 2020-01-27
Category : Science
ISBN : 9783030344894

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Tensor Network Contractions by Shi-Ju Ran,Emanuele Tirrito,Cheng Peng,Xi Chen,Luca Tagliacozzo,Gang Su,Maciej Lewenstein Pdf

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.

Author : Simone Montangero
Publisher : Springer
Page : 172 pages
File Size : 50,9 Mb
Release : 2018-11-28
Category : Science
ISBN : 9783030014094

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Introduction to Tensor Network Methods by Simone Montangero Pdf

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.

Author : Christophe Goupil
Publisher : MDPI
Page : 222 pages
File Size : 54,9 Mb
Release : 2021-03-11
Category : Science
ISBN : 9783036501147

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Simulation with Entropy Thermodynamics by Christophe Goupil Pdf

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.

Author : Jacob Dean,Doran Bennett,Margherita Maiuri,Michael Staniforth
Publisher : Frontiers Media SA
Page : 109 pages
File Size : 51,5 Mb
Release : 2021-06-11
Category : Science
ISBN : 9782889668748

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Vibrationally-Mediated Chemical Dynamics by Jacob Dean,Doran Bennett,Margherita Maiuri,Michael Staniforth Pdf

Author : Stefanie Czischek
Publisher : Springer Nature
Page : 205 pages
File Size : 47,5 Mb
Release : 2020-08-27
Category : Science
ISBN : 9783030527150

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Neural-Network Simulation of Strongly Correlated Quantum Systems by Stefanie Czischek Pdf

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.

Author : Maciej Lewenstein,Gang Su,Luca Tagliacozzo
Publisher : Unknown
Page : 158 pages
File Size : 51,7 Mb
Release : 2020-10-08
Category : Science
ISBN : 1013273621

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Tensor Network Contractions by Maciej Lewenstein,Gang Su,Luca Tagliacozzo Pdf

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.

Author : Liao Heng,Bill McColl
Publisher : Cambridge University Press
Page : 399 pages
File Size : 50,7 Mb
Release : 2021-12-16
Category : Computers
ISBN : 9781316513583

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Mathematics for Future Computing and Communications by Liao Heng,Bill McColl Pdf

A panorama of new ideas in mathematics that are driving innovation in computing and communications.

Author : Laurens Vanderstraeten
Publisher : Springer
Page : 219 pages
File Size : 48,8 Mb
Release : 2017-08-10
Category : Science
ISBN : 9783319641911

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Tensor Network States and Effective Particles for Low-Dimensional Quantum Spin Systems by Laurens Vanderstraeten Pdf

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.

Author : Dominic Gribben
Publisher : Unknown
Page : 0 pages
File Size : 54,5 Mb
Release : 2022
Category : Quantum systems
ISBN : OCLC:1423298733

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Simulating and Understanding Quantum Processes Using Tensor Networks by Dominic Gribben Pdf

Author : Christina Giarmatzi
Publisher : Springer Nature
Page : 157 pages
File Size : 44,6 Mb
Release : 2019-10-21
Category : Science
ISBN : 9783030319304

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Rethinking Causality in Quantum Mechanics by Christina Giarmatzi Pdf

Causality is central to understanding the mechanisms of nature: some event "A" is the cause of another event “B”. Surprisingly, causality does not follow this simple rule in quantum physics: due to to quantum superposition we might be led to believe that "A causes B” and that "B causes A”. This idea is not only important to the foundations of physics but also leads to practical advantages: a quantum circuit with such indefinite causality performs computationally better than one with definite causality. This thesis provides one of the first comprehensive introductions to quantum causality, and presents a number of advances. It provides an extension and generalization of a framework that enables us to study causality within quantum mechanics, thereby setting the stage for the rest of the work. This comprises: mathematical tools to define causality in terms of probabilities; computational tools to prove indefinite causality in an experiment; means to experimentally test particular causal structures; and finally an algorithm that detects the exact causal structure in an quantum experiment.

Author : Ángel Rivas,Susana F. Huelga
Publisher : Springer Science & Business Media
Page : 97 pages
File Size : 46,7 Mb
Release : 2011-10-01
Category : Science
ISBN : 3642233546

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Open Quantum Systems by Ángel Rivas,Susana F. Huelga Pdf

In this volume the fundamental theory of open quantum systems is revised in the light of modern developments in the field. A unified approach to the quantum evolution of open systems is presented by merging concepts and methods traditionally employed by different communities, such as quantum optics, condensed matter, chemical physics and mathematical physics. The mathematical structure and the general properties of the dynamical maps underlying open system dynamics are explained in detail. The microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions, is also discussed. Because of the step-by-step explanations, this work is a useful reference to novices in this field. However, experienced researches can also benefit from the presentation of recent results.

Author : John B. Parkinson,Damian J. J. Farnell
Publisher : Springer Science & Business Media
Page : 159 pages
File Size : 43,8 Mb
Release : 2010-09-20
Category : Science
ISBN : 9783642132896

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An Introduction to Quantum Spin Systems by John B. Parkinson,Damian J. J. Farnell Pdf

The topic of lattice quantum spin systems is a fascinating and by now well established branch of theoretical physics. Based on a set of lectures, this book has a level of detail missing from others, and guides the reader through the fundamentals of the field.

Author : Antonios M. Alvertis
Publisher : Springer Nature
Page : 213 pages
File Size : 42,9 Mb
Release : 2021-10-25
Category : Science
ISBN : 9783030854546

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On Exciton–Vibration and Exciton–Photon Interactions in Organic Semiconductors by Antonios M. Alvertis Pdf

What are the physical mechanisms that underlie the efficient generation and transfer of energy at the nanoscale? Nature seems to know the answer to this question, having optimised the process of photosynthesis in plants over millions of years of evolution. It is conceivable that humans could mimic this process using synthetic materials, and organic semiconductors have attracted a lot of attention in this respect. Once an organic semiconductor absorbs light, bound pairs of electrons with positively charged holes, termed `excitons’, are formed. Excitons behave as fundamental energy carriers, hence understanding the physics behind their efficient generation and transfer is critical to realising the potential of organic semiconductors for light-harvesting and other applications, such as LEDs and transistors. However, this problem is extremely challenging since excitons can interact very strongly with photons. Moreover, simultaneously with the exciton motion, organic molecules can vibrate in hundreds of possible ways, having a very strong effect on energy transfer. The description of these complex phenomena is often beyond the reach of standard quantum mechanical methods which rely on the assumption of weak interactions between excitons, photons and vibrations. In this thesis, Antonios Alvertis addresses this problem through the development and application of a variety of different theoretical methods to the description of these strong interactions, providing pedagogical explanations of the underlying physics. A comprehensive introduction to organic semiconductors is followed by a review of the background theory that is employed to approach the relevant research questions, and the theoretical results are presented in close connection with experiment, yielding valuable insights for experimentalists and theoreticians alike.