Quantum Quenching, Annealing and Computation

✍ Scribed by R.D. Somma, G. Ortiz (auth.), Anjan Kumar Chandra, Arnab Das, Bikas K. Chakrabarti (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2010
• Tongue: English
• Leaves: 314
• Series: Lecture Notes in Physics 802
• Edition: 1
• Category: Library

✦ Synopsis

The process of realizing the ground state of some typical (frustrated) quantum many-body systems, starting from the 'disordered' or excited states, can formally be mapped onto the search of solutions for computationally hard problems. The dynamics through quantum critical points are especially crucial in the context of such computational optimization problems and have been investigated intensively in recent times.

Several successful methods are now well-established, and this volume compiles a collection of introductory reviews on such developments and related aspects. Written by well known experts, these lectures concentrate on quantum phase transitions and their dynamics as the transition or critical points are crossed. Both the quenching and annealing dynamics are extensively covered. The style has been kept as tutorial as possible in order to make this volume a suitable reference for young researchers joining this exciting and burgeoning field of research.

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✦ Table of Contents

Front Matter....Pages i-xi
Quantum Approach to Classical Thermodynamics and Optimization....Pages 1-20
Non-equilibrium Dynamics of Quantum Systems: Order Parameter Evolution, Defect Generation, and Qubit Transfer....Pages 21-56
Defect Production Due to Quenching Through a Multicritical Point and Along a Gapless Line....Pages 57-73
Adiabatic Perturbation Theory: From Landau–Zener Problem to Quenching Through a Quantum Critical Point....Pages 75-114
Quench Dynamics of Quantum and Classical Ising Chains: From the Viewpoint of the Kibble–Zurek Mechanism....Pages 115-143
Quantum Phase Transition in the Spin Boson Model....Pages 145-162
Influence of Local Moment Fluctuations on the Mott Transition....Pages 163-175
Signatures of Quantum Phase Transitions via Quantum Information Theoretic Measures....Pages 177-200
How Entangled Is a Many-Electron State?....Pages 201-214
Roles of Quantum Fluctuation in Frustrated Systems – Order by Disorder and Reentrant Phase Transition....Pages 215-234
Exploring Ground States of Quantum Spin Glasses by Quantum Monte Carlo Method....Pages 235-249
Phase Transition in a Quantum Ising Model with Long-Range Interaction....Pages 251-266
Length Scale-Dependent Superconductor–Insulator Quantum Phase Transitions in One Dimension: Renormalization Group Theory of Mesoscopic SQUIDs Array....Pages 267-282
Quantum-Mechanical Variant of the Thouless–Anderson–Palmer Equation for Error-Correcting Codes....Pages 283-295
Probabilistic Model of Fault Detection in Quantum Circuits....Pages 297-304
Back Matter....Pages 305-307

✦ Subjects

Phase Transitions and Multiphase Systems;Quantum Physics;Quantum Information Technology, Spintronics;Statistical Physics, Dynamical Systems and Complexity