Quantum Quenching, Annealing and Computation

1. Front Matter

   Pages i-xi

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2. Quantum Approach to Classical Thermodynamics and Optimization

   • R.D. Somma, G. Ortiz

   Pages 1-20

3. Non-equilibrium Dynamics of Quantum Systems: Order Parameter Evolution, Defect Generation, and Qubit Transfer

   • S. Mondal, D. Sen, K. Sengupta

   Pages 21-56

4. Defect Production Due to Quenching Through a Multicritical Point and Along a Gapless Line

   • U. Divakaran, V. Mukherjee, A. Dutta, D. Sen

   Pages 57-73

5. Adiabatic Perturbation Theory: From Landau–Zener Problem to Quenching Through a Quantum Critical Point

   • C. De Grandi, A. Polkovnikov

   Pages 75-114

6. Quench Dynamics of Quantum and Classical Ising Chains: From the Viewpoint of the Kibble–Zurek Mechanism

   • S. Suzuki

   Pages 115-143

7. Quantum Phase Transition in the Spin Boson Model

   • S. Florens, D. Venturelli, R. Narayanan

   Pages 145-162

8. Influence of Local Moment Fluctuations on the Mott Transition

   • C. Janani, S. Florens, T. Gupta, R. Narayanan

   Pages 163-175

9. Signatures of Quantum Phase Transitions via Quantum Information Theoretic Measures

   • I. Bose, A. Tribedi

   Pages 177-200

10. How Entangled Is a Many-Electron State?

    • V. Subrahmanyam

    Pages 201-214

11. Roles of Quantum Fluctuation in Frustrated Systems – Order by Disorder and Reentrant Phase Transition

    • S. Tanaka, M. Hirano, S. Miyashita

    Pages 215-234

12. Exploring Ground States of Quantum Spin Glasses by Quantum Monte Carlo Method

    • A.K. Chandra, A. Das, J. Inoue, B.K. Chakrabarti

    Pages 235-249

13. Phase Transition in a Quantum Ising Model with Long-Range Interaction

    • A. Ganguli, S. Dasgupta

    Pages 251-266

14. Length Scale-Dependent Superconductor–Insulator Quantum Phase Transitions in One Dimension: Renormalization Group Theory of Mesoscopic SQUIDs Array

    • S. Sarkar

    Pages 267-282

15. Quantum-Mechanical Variant of the Thouless–Anderson–Palmer Equation for Error-Correcting Codes

    • J. Inoue, Y. Saika, M. Okada

    Pages 283-295

16. Probabilistic Model of Fault Detection in Quantum Circuits

    • A. Banerjee, A. Pathak

    Pages 297-304

17. Back Matter

    Pages 305-307

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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.

• Monte Carlo method
• Renormalization group
• classical and quantum Ising model
• frustrated quantum many-body systems
• optimization
• quantum circuits
• quantum critical points
• quantum phase transitions
• quenching and anneiling
• spin glasses

• Centre for Applied Mathematics &, Computational Science, Saha Institute of Nuclear Physics, Kolkata, India

  Anjan Kumar Chandra, Bikas K. Chakrabarti

• Theoretical Physics (ICTP), Abdus Salam International Centre for, Trieste, Italy

  Arnab Das

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