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Author: Pejman Jouzdani Publisher: ISBN: Category : Languages : en Pages : 166
Book Description
As another example of passive error correcting codes with intrinsic Hamiltonian, the toric code is introduced. We also analyze the dynamics of the errors in the toric code known as anyons. We show numerically how the addition of disorder to the physical system underlying the toric code slows down the dynamics of the anyons. We go further and numerically analyze the presence of time-dependent noise and the consequent delocalization of localized errors. The main portion of this dissertation is dedicated to the surface code. We study the surface code coupled to a non-interacting bosonic bath. We show how the interaction between the code and the bosonic bath can effectively induce correlated errors. These correlated errors may be corrected up to some extend. The extension beyond which quantum error correction seems impossible is the error threshold of the code. This threshold is analyzed by mapping the effective correlated error model onto a statistical model. We then study the phase transition in the statistical model. The analysis is in two parts. First, we carry out derivation of the effective correlated model, its mapping onto a statistical model, and perform an exact numerical analysis. Second, we employ a Monte Carlo method to extend the numerical analysis to large system size. We also tackle the problem of surface code with correlated and single-qubit errors by an exact mapping onto a two-dimensional Ising model with boundary fields. We show how the phase transition point in one model, the Ising model, coincides with the intrinsic error threshold of the other model, the surface code.
Author: Pejman Jouzdani Publisher: ISBN: Category : Languages : en Pages : 166
Book Description
As another example of passive error correcting codes with intrinsic Hamiltonian, the toric code is introduced. We also analyze the dynamics of the errors in the toric code known as anyons. We show numerically how the addition of disorder to the physical system underlying the toric code slows down the dynamics of the anyons. We go further and numerically analyze the presence of time-dependent noise and the consequent delocalization of localized errors. The main portion of this dissertation is dedicated to the surface code. We study the surface code coupled to a non-interacting bosonic bath. We show how the interaction between the code and the bosonic bath can effectively induce correlated errors. These correlated errors may be corrected up to some extend. The extension beyond which quantum error correction seems impossible is the error threshold of the code. This threshold is analyzed by mapping the effective correlated error model onto a statistical model. We then study the phase transition in the statistical model. The analysis is in two parts. First, we carry out derivation of the effective correlated model, its mapping onto a statistical model, and perform an exact numerical analysis. Second, we employ a Monte Carlo method to extend the numerical analysis to large system size. We also tackle the problem of surface code with correlated and single-qubit errors by an exact mapping onto a two-dimensional Ising model with boundary fields. We show how the phase transition point in one model, the Ising model, coincides with the intrinsic error threshold of the other model, the surface code.
Author: Subir Sachdev Publisher: Cambridge University Press ISBN: 9780521004541 Category : Mathematics Languages : en Pages : 374
Book Description
Quantum Phase Transitions is the first book to describe in detail the fundamental changes that can occur in the macroscopic nature of matter at zero temperature due to small variations in a given external parameter. The subject plays a central role in the study of the electrical and magnetic properties of numerous important solid state materials. The author begins by developing the theory of quantum phase transitions in the simplest possible class of non-disordered, interacting systems - the quantum Ising and rotor models. Particular attention is paid to their non-zero temperature dynamic and transport properties in the vicinity of the quantum critical point. Several other quantum phase transitions of increasing complexity are then discussed and clarified. Throughout, the author interweaves experimental results with presentation of theoretical models, and well over 500 references are included. The book will be of great interest to graduate students and researchers in condensed matter physics.
Author: Publisher: ISBN: 9780429075629 Category : Electronic book Languages : en Pages : 728
Book Description
"Exploring a steadily growing field, this book focuses on quantum phase transitions (QPT), frontier area of research. It takes a look back as well as a look forward to the future and the many open problems that remain. The book covers new concepts and directions in QPT and specific models and systems closely tied to particular experimental realization or theoretical methods. Although mainly theoretical, the book includes experimental chapters that make the discussion of QPTs meaningful. The book also presents recent advances in the numerical methods used to study QPTs"--
Author: Zhenghan Wang Publisher: American Mathematical Soc. ISBN: 0821849301 Category : Computers Languages : en Pages : 134
Book Description
Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. In this approach, information is stored in the lowest energy states of many-anyon systems and processed by braiding non-abelian anyons. The computational answer is accessed by bringing anyons together and observing the result. Besides its theoretical esthetic appeal, the practical merit of the topological approach lies in its error-minimizing hypothetical hardware: topological phases of matter are fault-avoiding or deaf to most local noises, and unitary gates are implemented with exponential accuracy. Experimental realizations are pursued in systems such as fractional quantum Hall liquids and topological insulators. This book expands on the author's CBMS lectures on knots and topological quantum computing and is intended as a primer for mathematically inclined graduate students. With an emphasis on introducing basic notions and current research, this book gives the first coherent account of the field, covering a wide range of topics: Temperley-Lieb-Jones theory, the quantum circuit model, ribbon fusion category theory, topological quantum field theory, anyon theory, additive approximation of the Jones polynomial, anyonic quantum computing models, and mathematical models of topological phases of matter.
Author: Jiannis K. Pachos Publisher: Cambridge University Press ISBN: 1139936689 Category : Science Languages : en Pages : 220
Book Description
Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to topological quantum computation. The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way. Relevant calculations are fully explained, and numerous worked examples and exercises support and aid understanding. Special emphasis is given to the motivation and physical intuition behind every mathematical concept. Demystifying difficult topics by using accessible language, this book has broad appeal and is ideal for graduate students and researchers from various disciplines who want to get into this new and exciting research field.
Author: H. T. Diep Publisher: World Scientific ISBN: 9814440744 Category : Science Languages : en Pages : 644
Book Description
This book covers all principal aspects of currently investigated frustrated systems, from exactly solved frustrated models to real experimental frustrated systems, going through renormalization group treatment, Monte Carlo investigation of frustrated classical Ising and vector spin models, low-dimensional systems, spin ice and quantum spin glass. The reader can OCo within a single book OCo obtain a global view of the current research development in the field of frustrated systems.This new edition is updated with recent theoretical, numerical and experimental developments in the field of frustrated spin systems. The first edition of the book appeared in 2005. In this edition, more recent works until 2012 are reviewed. It contains nine chapters written by researchers who have actively contributed to the field. Many results are from recent works of the authors.The book is intended for postgraduate students as well as researchers in statistical physics, magnetism, materials science and various domains where real systems can be described with the spin language. Explicit demonstrations of formulas and full arguments leading to important results are given where it is possible to do so."
Author: Annick LESNE Publisher: Springer Science & Business Media ISBN: 364215123X Category : Science Languages : en Pages : 406
Book Description
During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist. This book aims at a pedagogical overview, offering to the students and researchers a thorough conceptual background and a simple account of a wide range of applications. It presents a complete tour of both the formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology.
Author: Pejman Jouzdani
Author: Pejman Jouzdani
Author: Lars Brink
Author: Subir Sachdev
Author: 
Author: Zhenghan Wang
Author: Ying Wai Li
Author: Jiannis K. Pachos
Author: Yousef Saad
Author: H. T. Diep
Author: Annick LESNE