Lectures On Quantum Computing Thermodynamics And Statistical Physics

This book is a collection of lecture notes from the Symposium on Quantum Computing, Thermodynamics, and Statistical Physics, held at Kinki University in March 2012. Quantum information theory has a deep connection with statistical physics and thermodynamics. This volume introduces some of the topics on interface among the mentioned fields. Subjects included in the lecture notes include quantum annealing method, nonequilibrium thermodynamics and spin glass theory, among others. These subjects were presented with much emphasis put in its relevance in quantum information theory. These lecture notes are prepared in a self-contained manner so that a reader with modest background may understand the subjects.

In order to equip hopeful graduate students with the knowledge necessary to pass the qualifying examination, the authors have assembled and solved standard and original problems from major American universities – Boston University, University of Chicago, University of Colorado at Boulder, Columbia, University of Maryland, University of Michigan, Michigan State, Michigan Tech, MIT, Princeton, Rutgers, Stanford, Stony Brook, University of Tennessee at Knoxville, and the University of Wisconsin at Madison – and Moscow Institute of Physics and Technology. A wide range of material is covered and comparisons are made between similar problems of different schools to provide the student with enough information to feel comfortable and confident at the exam. Guide to Physics Problems is published in two volumes: this book, Part 2, covers Thermodynamics, Statistical Mechanics and Quantum Mechanics; Part 1, covers Mechanics, Relativity and Electrodynamics. Praise for A Guide to Physics Problems: Part 2: Thermodynamics, Statistical Physics, and Quantum Mechanics: "... A Guide to Physics Problems, Part 2 not only serves an important function, but is a pleasure to read. By selecting problems from different universities and even different scientific cultures, the authors have effectively avoided a one-sided approach to physics. All the problems are good, some are very interesting, some positively intriguing, a few are crazy; but all of them stimulate the reader to think about physics, not merely to train you to pass an exam. I personally received considerable pleasure in working the problems, and I would guess that anyone who wants to be a professional physicist would experience similar enjoyment. ... This book will be a great help to students and professors, as well as a source of pleasure and enjoyment." (From Foreword by Max Dresden) "An excellent resource for graduate students in physics and, one expects, also for their teachers." (Daniel Kleppner, Lester Wolfe Professor of Physics Emeritus, MIT) "A nice selection of problems ... Thought-provoking, entertaining, and just plain fun to solve." (Giovanni Vignale, Department of Physics and Astronomy, University of Missouri at Columbia) "Interesting indeed and enjoyable. The problems are ingenious and their solutions very informative. I would certainly recommend it to all graduate students and physicists in general ... Particularly useful for teachers who would like to think about problems to present in their course." (Joel Lebowitz, Rutgers University) "A very thoroughly assembled, interesting set of problems that covers the key areas of physics addressed by Ph.D. qualifying exams. ... Will prove most useful to both faculty and students. Indeed, I plan to use this material as a source of examples and illustrations that will be worked into my lectures." (Douglas Mills, University of California at Irvine)

Recent years have shown important and spectacular convergences between techniques traditionally used in theoretical physics and methods emerging from modern mathematics (combinatorics, probability theory, topology, algebraic geometry, etc). These techniques, and in particular those of low-dimensional statistical models, are instrumental in improving our understanding of emerging fields, such as quantum computing and cryptography, complex systems, and quantum fluids. This book sets these issues into a larger and more coherent theoretical context than is currently available. For instance, understanding the key concepts of quantum entanglement (a measure of information density) necessitates a thorough knowledge of quantum and topological field theory, and integrable models. To achieve this goal, the lectures were given by international leaders in the fields of exactly solvable models in low dimensional condensed matter and statistical physics.

This textbook presents a concise yet detailed introduction to quantum physics. Concise, because it condenses the essentials to a few principles. Detailed, because these few principles – necessarily rather abstract – are illustrated by several telling examples. A fairly complete overview of the conventional quantum mechanics curriculum is the primary focus, but the huge field of statistical thermodynamics is covered as well. The text explains why a few key discoveries shattered the prevailing broadly accepted classical view of physics. First, matter appears to consist of particles which, when propagating, resemble waves. Consequently, some observable properties cannot be measured simultaneously with arbitrary precision. Second, events with single particles are not determined, but are more or less probable. The essence of this is that the observable properties of a physical system are to be represented by non-commuting mathematical objects instead of real numbers. Chapters on exceptionally simple, but highly instructive examples illustrate this abstract formulation of quantum physics. The simplest atoms, ions, and molecules are explained, describing their interaction with electromagnetic radiation as well as the scattering of particles. A short introduction to many particle physics with an outlook on quantum fields follows. There is a chapter on maximally mixed states of very large systems, that is statistical thermodynamics. The following chapter on the linear response to perturbations provides a link to the material equations of continuum physics. Mathematical details which would hinder the flow of the main text have been deferred to an appendix. The book addresses university students of physics and related fields. It will attract graduate students and professionals in particular who wish to systematize or refresh their knowledge of quantum physics when studying specialized texts on solid state and materials physics, advanced optics, and other modern fields.

This book is a collection of contributions from a Summer Workshop on “Physics, Mathematics, and All That Quantum Jazz”. Subjects of the symposium include quantum information theory, quantum annealing, Bose gases, and thermodynamics from a viewpoint of quantum physics. Contributions to this book are prepared in a self-contained manner so that readers with a modest background may understand the subjects. Contents:My Life as a Quantum Physicist (M Nakahara)A Review on Operator Quantum Error Correction — Dedicated to Professor Mikio Nakahara on the Occasion of His 60th Birthday (C-K Li, Y-T Poon and N-S Sze)Implementing Measurement Operators in Linear Optical and Solid-State Qubits (Y Ota, S Ashhab and F Nori)Fast and Accurate Simulation of Quantum Computing by Multi-Precision MPS: Recent Development (A Saitoh)Entanglement Properties of a Quantum Lattice-Gas Model on Square and Triangular Ladders (S Tanaka, R Tamura and H Katsura)On Signal Amplification from Weak-Value Amplification (Y Shikano)Topological Protection of Quantum Information (K Fujii)Quantum Annealing with Antiferromagnetic Fluctuations for Mean-Field Models (Y Seki and H Nishimori)A Method to Change Phase Transition Nature — Toward Annealing Methods (R Tamura and S Tanaka)Computational Analysis of the First Stage of the Photosynthetic System, the Light-Dependent Reaction, by Quantum Chemical Simulation Method (M Tada-Umezaki)Two-Qubit Gate Operation on Selected Nearest Neighboring Qubits in a Neutral Atom Quantum Computer (E Hosseini Lapasar, K Kasamatsu, S Nic Chormaic, T Takui, Y Kondo, M Nakahara and T Ohmi)A Simple Operator Quantum Error Correction Scheme Avoiding Fully Correlated Errors (C Bagnasco, Y Kondo and M Nakahara)Black Hole Predictability, Classical and Quantum (A Ishibashi)Classical Field Simulation of Finite-Temperature Bose Gases (T Sato)Atomic Quantum Simulations of Lattice Gauge Theory: Effect of Gauge Symmetry Breaking (K Kasamatsu, I Ichinose and T Matsui)Recursive Construction of Noiseless Subsystem for Qudits (U Güngördü, C-K Li, M Nakahara, Y-T Poon and N-S Sze)Composite Quantum Gates for Precise Quantum Control (M Bando, T Ichikawa, Y Kondo and M Nakahara)New Formulation of Statistical Mechanics Using Thermal Pure Quantum States (S Sugiura and A Shimizu)Thermodynamics in Unitary Time Evolution (T N Ikeda)Second Law of Thermodynamics with QC-Mutual Information (T Sagawa) Readership: Graduate students and researchers in physics, mathematics, informatics and computer science. Accessible to advanced undergraduate students. Key Features:This book includes wide-ranging areas of quantum physics, e.g., quantum annealing, topological quantum computation, quantum error correction, and foundation of thermodynamicsSome of the authors are PhD students. This book includes very recent topics relating to quantum physicsProminent authors: Professor Mikio Nakahara and Professor Chi-Kwong Li, Professor Akihiro Ishibashi, and Professor Kenichi KasamatsuKeywords:Quantum Information Science;Statistical Physics;Strongly Correlated Systems;Thermodynamics;Mathematics

This volume deals with topics of contemporary interest covering both experimental results and theoretical considerations. Different aspects of the physics and chemistry of the vitreous state are discussed in a series of three lectures by internationally respected researchers on the statistical physics of glasses.A wide range of topics in statistical physics such as critical behaviour, computer simulations of colloid aggregation, kinetic theory of tunneling diffusion, normal mode analysis of liquids and neutron scattering in C60 are also covered. This book provides a useful survey and will be of interest to researchers.

This book is a collection of contributions to the Symposium on Interface between Quantum Information and Statistical Physics held at Kinki University in November 2011. Subjects of the symposium include quantum adiabatic computing, quantum simulator using bosons, classical statistical physics, among others. Contributions to this book are prepared in a self-contained manner so that a reader with a modest background may understand the subjects.