Download or read book Modelling Non Markovian Quantum Systems Using Tensor Networks written by Aidan Strathearn and published by Springer Nature. This book was released on 2020-08-31 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Process Tensor Networks for Non Markovian Open Quantum Systems written by Gerald E. Fux and published by . This book was released on 2022 with total page 0 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 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 Quantum inspired Machine Learning with Hidden Quantum Markov Models and Tensor Networks written by Siddarth Srinivasan and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The prospect of blending ideas from quantum information and machine learning has garnered interest in recent years, driven by their shared mathematical foundations in linear algebra and probability. A common way to categorize the research directions in this space is in terms of the goals (whether they are tackling classical or quantum problems) and methods (whether they rely on quantum-inspired classical computation or quantum computation). This work focuses on the potential of quantum-inspired classical machine learning approaches for solving select classical and quantum problems. In particular, we present our work on three main topics: (1) our formulation and learning algorithm for hidden quantum Markov models (HQMMs), a quantum-inspired analogue of hidden Markov models (HMMs) with greater expressiveness and without the learning challenges associated with previous proposals extending HMMs, (2) the connection between HQMMs (and similar proposals) and tensor networks, a general and tractable classical method for approximating high-dimensional classical and quantum systems with unfavorable scaling, and (3) our scalable implementation of 'iterative Bayesian unfolding', an expectation-maximization algorithm for quantum measurement error mitigation, the problem of post-processing results from a quantum computer to account for measurement errors.

Download or read book Simulation with Entropy Thermodynamics written by Christophe Goupil and published by MDPI. This book was released on 2021-03-11 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Tensor Network Algorithms for Three dimensional Quantum Systems written by Patrick Vlaar and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Strongly correlated systems can give rise to many types of fascinating emergent behavior, such as superconductivity or exotic magnetic phases. Numerical approaches have become essential tools to further our understanding of these systems. An important family is formed by algorithms based on tensor networks. In recent decades, these methods have turned into vital tools to study one- and two-dimensional quantum systems. Extensions of these algorithms to three-dimensional systems, though, have been relatively unexplored. The goal of this thesis is to develop new algorithms to study three-dimensional quantum systems. We make use of a tensor network Ansatz called the infinite projected entangled-pair state (iPEPS), which allows us to directly probe the thermodynamic limit. The main technical challenge is to find ways to evaluate expectation values, which require a contraction of the tensor network. In this thesis, we develop several efficient contraction algorithms both for general three-dimensional quantum systems and for layered two-dimensional quantum systems with weak interlayer coupling. We apply these algorithms to study the Shastry-Sutherland model, which closely describes the layered compound SrCu2(BO3)2. A discrepancy exists, however, in the extent of the plaquette phase, which is significantly smaller in the compound compared to the model. Through our simulations, we find that a possible explanation could be the interlayer coupling, which strongly reduces the extent of the plaquette phase already at weak coupling. With this thesis, we hope to show the potential of tensor networks for the accurate study of three-dimensional strongly-correlated quantum systems."--

Download or read book Quantum Information and Computation for Chemistry Volume 154 written by Sabre Kais and published by John Wiley & Sons. This book was released on 2014-01-31 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Vibrationally Mediated Chemical Dynamics written by Jacob Dean and published by Frontiers Media SA. This book was released on 2021-06-11 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 The Theory of Non Markovian Open Quantum Systems written by Cesar Alberto Rodriguez and published by . This book was released on 2008 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the role of correlations with the environment as the source of non-Markovian quantum evolutions. We first focus on the impact that correlations with the environment can have on the dynamical map that evolve the system. We expand the set of initial states of a system and its environment that are known to guarantee completely positive reduced dynamics for the system when the combined state evolves unitarily. We characterize the correlations in the initial state in terms of its quantum discord. The induced maps can be not completely positive when quantum correlations including, but not limited to, entanglement are present. We discuss the implications and limitations of the Markov approximation necessary to derive the Kossakowski-Lindblad master equation. A generalized non-Markovian master equation is derived from the dynamical map of systems correlated with their environment. The physical meaning of not completely positive maps is studied to obtain a consistent theory of non-Markovian quantum dynamics. These are associated to inverse maps necessary to establish correlations and they give rise to a canonical embedding map that is local in time. This master equation goes beyond the Kossakowski-Lindblad master equation. Non-equilibrium quantum thermodynamics can be be studied within this theory. Through out this discussion, the general dynamics of two interacting qubits is used as an example for illustrations.

Download or read book Mathematics for Future Computing and Communications written by Liao Heng and published by Cambridge University Press. This book was released on 2021-12-16 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: A panorama of new ideas in mathematics that are driving innovation in computing and communications.

Download or read book Tensor Network Simulations of Open Quantum Systems written by Dainius Kilda and published by . This book was released on 2020 with total page 211 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 Rethinking Causality in Quantum Mechanics written by Christina Giarmatzi and published by Springer Nature. This book was released on 2019-10-21 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Non Markovian Dynamics of Open Quantum Systems written by Carole Addis and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Tensor Network Methods for Low dimensional Quantum Systems written by Jheng-Wei Li and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: