Colloquium : Quantum annealing and analog quantum computation

@article{Das2008ColloquiumQ,
  title={Colloquium : Quantum annealing and analog quantum computation},
  author={Arnab Das and Bikas K. Chakrabarti},
  journal={Reviews of Modern Physics},
  year={2008},
  volume={80},
  pages={1061-1081}
}
The recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations is reviewed here. The concept is introduced in successive steps through studying the mapping of such computationally hard problems to classical spin-glass problems, quantum spin-glass problems arising with the introduction of quantum fluctuations, and the annealing behavior of the systems as these fluctuations are reduced slowly to zero. This provides a… 
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References

SHOWING 1-10 OF 166 REFERENCES
CORRIGENDUM: Optimization using quantum mechanics: quantum annealing through adiabatic evolution
We review here some recent work in the field of quantum annealing, alias adiabatic quantum computation. The idea of quantum annealing is to perform optimization by a quantum adiabatic evolution which…
Theory of Quantum Annealing of an Ising Spin Glass
TLDR
By comparing classical and quantum Monte Carlo annealing protocols on the two-dimensional random Ising model (a prototype spin glass), this work confirms the superiority of quantumAnnealing relative to classical annealed and proposes a theory of quantum annealer based on a cascade of Landau-Zener tunneling events.
Adiabatic quantum computation is equivalent to standard quantum computation
TLDR
The model of adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its exact computational power has been unknown, so this result implies that the adiABatic computation model and the standard quantum circuit model are polynomially equivalent.
Convergence theorems for quantum annealing
We prove several theorems to give sufficient conditions for convergence of quantum annealing, which is a protocol to solve generic optimization problems by quantum dynamics. In particular, the…
Residual Energies after Slow Quantum Annealing
The features of residual energy after quantum annealing are investigated. The quantum annealing method exploits quantum fluctuations to find out the ground state of the classical disordered…
Experimental implementation of an adiabatic quantum optimization algorithm.
TLDR
A nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm that agrees well with the prediction of a simple decoherence model is reported.
Quantum computation and quantum information
  • T. Paul
  • Physics
    Mathematical Structures in Computer Science
  • 2007
This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal…
Information and computation: Classical and quantum aspects
TLDR
How quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers is reviewed.
Quantum annealing in a kinetically constrained system.
TLDR
It has been shown that for certain barrier characteristics, quantum annealing might by far surpass its thermal counter part in reaching the ground state faster.
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
TLDR
For the small examples that the authors could simulate, the quantum adiabatic algorithm worked well, providing evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.
...
...