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Quantum Annealing

  • Sei Suzuki
  • Jun-ichi Inoue
  • Bikas K. Chakrabarti
Part of the Lecture Notes in Physics book series (LNP, volume 862)

Abstract

Quantum annealing is an intriguing algorithm for a generic combinatorial optimisation problem. The basic model of quantum annealing is the application of a strong transverse field to an Ising model which encodes an optimisation problem, and weakening the transverse field with time. When the transverse field vanishes, one reads out the solution from the final state. Quantum annealing has attracted much attentions as one of the algorithms of quantum computation from not only quantum physics but also statistical physics, computer and information sciences, and mathematics. Chapter 8 focuses on this quantum annealing. It includes the non-crossing rule of energy levels and the quantum adiabatic theorem as the basic theories underlying quantum annealing, and a review of early numerical and experimental implementations of quantum annealing. The latter part of this chapter is devoted to theoretical investigation into the efficiency and convergence conditions of quantum annealing. In particular, size scaling of the runtime and decay rate of errors are discussed there. In addition, several theorems for the convergence condition are presented. Appendices of this chapter include mathematical details which are supplementary to the proofs of the theorems for the convergence condition.

Keywords

Simulated Annealing Ising Model Travel Salesman Problem Quantum Phase Transition Quantum Critical Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sei Suzuki
    • 1
  • Jun-ichi Inoue
    • 2
  • Bikas K. Chakrabarti
    • 3
  1. 1.Dept. of Physics and MathematicsAoyama Gakuin UniversitySagamiharaJapan
  2. 2.Graduate School of Information Science and TechnologyHokkaido UniversitySapporoJapan
  3. 3.Saha Institute of Nuclear PhysicsKolkataIndia

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