Quantum annealing is a new-generation tool of information technology, which helps in solving combinatorial optimization problems with high precision, based on the concepts of quantum statistical physics. Detailed discussion on quantum spin glasses and its application in solving combinatorial optimization problems is required for better understanding of quantum annealing concepts. Fulfilling this requirement, the book highlights recent development in quantum spin glasses including Nishimori line, replica method and quantum annealing methods along with the essential principles. Separate chapters on simulated annealing, quantum dynamics and classical spin models are provided for enhanced learning. Important topics including adiabatic quantum computers and quenching dynamics are discussed in detail. This text will be useful for students of quantum computation, quantum information, statistical physics and computer science.

The process of realizing the ground state of some typical (frustrated) quantum many-body systems, starting from the ‘disordered’ or excited states, can be formally mapped to the search of solutions for computationally hard problems. The dynamics through the critical point, in between, are therefore extremely crucial. In the context of such computational optimization problems, the dynamics (of rapid quenching or slow annealing), while tuning the appropriate elds or uctuations, in particular while crossing the quantum critical point, are extremely intriguing and are being investigated these days intensively. Several successful methods and tricks are now well established. This volume gives a collection of introductory reviews on such developments written by well-known experts. It concentrates on quantum phase transitions and their dynamics as the transition or critical points are crossed. Both the quenching and annealing dynamics are extensively covered. We hope these timely reviews will inspire the young researchers to join and c- tribute to this fast-growing, intellectually challenging, as well as technologically demanding eld. We are extremely thankful to the contributors for their intensive work and pleasant cooperations. We are also very much indebted to Kausik Das for his help in compiling this book. Finally, we express our gratitude to Johannes Zittartz, Series Editor, LNP, and Christian Caron of physics editorial department of Springer for their encouragement and support.

physics

The book introduces some useful and little known techniques in statistical mechanics and field theory including multiple Legendre transforms, supersymmetry, Fourier transforms on a tree, infinitesimal permutations and Ward Takahashi Identities."--Jacket.

This superb new book is one of the first publications in recent years to provide a broad overview of this interdisciplinary field. Most of the book is written in a self contained manner, assuming only a general knowledge of statistical mechanics and basic probabilty theory . It provides the reader with a sound introduction to the field and to the analytical techniques necessary to follow its most recent developments

The celebrated Parisi solution of the Sherrington-Kirkpatrick model for spin glasses is one of the most important achievements in the field of disordered systems. Over the last three decades, through the efforts of theoretical physicists and mathematicians, the essential aspects of the Parisi solution were clarified and proved mathematically. The core ideas of the theory that emerged are the subject of this book, including the recent solution of the Parisi ultrametricity conjecture and a conceptually simple proof of the Parisi formula for the free energy. The treatment is self-contained and should be accessible to graduate students with a background in probability theory, with no prior knowledge of spin glasses. The methods involved in the analysis of the Sherrington-Kirkpatrick model also serve as a good illustration of such classical topics in probability as the Gaussian interpolation and concentration of measure, Poisson processes, and representation results for exchangeable arrays.

A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.

This pedagogical and self-contained text describes the modern mean field theory of simple structural glasses. The book begins with a thorough explanation of infinite-dimensional models in statistical physics, before reviewing the key elements of the thermodynamic theory of liquids and the dynamical properties of liquids and glasses. The central feature of the mean field theory of disordered systems, the existence of a large multiplicity of metastable states, is then introduced. The replica method is then covered, before the final chapters describe important, advanced topics such as Gardner transitions, complexity, packing spheres in large dimensions, the jamming transition, and the rheology of glass. Presenting the theory in a clear and pedagogical style, this is an excellent resource for researchers and graduate students working in condensed matter physics and statistical mechanics.

This book constitutes the refereed proceedings of the First International Workshop on Quantum Technology and Optimization Problems, QTOP 2019, held in Munich, Germany, in March 2019.The 18 full papers presented together with 1 keynote paper in this volume were carefully reviewed and selected from 21 submissions. The papers are grouped in the following topical sections: analysis of optimization problems; quantum gate algorithms; applications of quantum annealing; and foundations and quantum technologies.

Adiabatic quantum computation (AQC) is an alternative to the better-known gate model of quantum computation. The two models are polynomially equivalent, but otherwise quite dissimilar: one property that distinguishes AQC from the gate model is its analog nature. Quantum annealing (QA) describes a type of heuristic search algorithm that can be implemented to run in the ``native instruction set'' of an AQC platform. D-Wave Systems Inc. manufactures {quantum annealing processor chips} that exploit quantum properties to realize QA computations in hardware. The chips form the centerpiece of a novel computing platform designed to solve NP-hard optimization problems. Starting with a 16-qubit prototype announced in 2007, the company has launched and sold increasingly larger models: the 128-qubit D-Wave One system was announced in 2010 and the 512-qubit D-Wave Two system arrived on the scene in 2013. A 1,000-qubit model is expected to be available in 2014. This monograph presents an introductory overview of this unusual and rapidly developing approach to computation. We start with a survey of basic principles of quantum computation and what is known about the AQC model and the QA algorithm paradigm. Next we review the D-Wave technology stack and discuss some challenges to building and using quantum computing systems at a commercial scale. The last chapter reviews some experimental efforts to understand the properties and capabilities of these unusual platforms. The discussion throughout is aimed at an audience of computer scientists with little background in quantum computation or in physics. Table of Contents: Acknowledgments / Introduction / Adiabatic Quantum Computation / Quantum Annealing / The D-Wave Platform / Computational Experience / Bibliography / Author's Biography