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… 
View PDF on arXiv
415 Citations
Highly Influential Citations
7
Background Citations
76
Methods Citations
35

Figures from this paper

415 Citations

The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective

Quantum annealing – foundations and frontiers

We briefly review various computational methods for the solution of optimization problems. First, several classical methods such as Metropolis algorithm and simulated annealing are discussed. We…

Nonequilibrium work performed in quantum annealing

Quantum annealing is a generic solver of classical optimization problems that makes full use of quantum fluctuations. We consider work statistics given by a repetition of quantum annealing processes…

Classical Simulated Annealing Using Quantum Analogues

In this paper we consider the use of certain classical analogues to quantum tunneling behavior to improve the performance of simulated annealing on a discrete spin system of the general Ising form.…

Quantum Annealing and Thermalization: Insights from Integrability.

It is proved that quantum correlations can accelerate computations and, at the end of the annealing protocol, lead to the perfect Gibbs distribution of all microstates.

Performance of quantum annealing in solving optimization problems: A review

Quantum annealing is one of the optimization method for generic optimization problems. It uses quantum mechanics and is implemented by a quantum computer ideally. At the earlier stage, several…

Mathematical foundation of quantum annealing

Quantum annealing is a generic name of quantum algorithms that use quantum-mechanical fluctuations to search for the solution of an optimization problem. It shares the basic idea with quantum…

Thermal, quantum and simulated quantum annealing: analytical comparisons for simple models

We study various annealing dynamics, both classical and quantum, for simple mean-field models and explain how to describe their behavior in the thermodynamic limit in terms of differential equations.…

Multivariable optimization: Quantum annealing and computation

Recent developments in quantum annealing techniques have been indicating potential advantage of quantum annealing for solving NP-hard optimization problems. In this article we briefly indicate and…

Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing

Quantum Tunneling is ubiquitous across different fields, from quantum chemical reactions, and magnetic materials to quantum simulators and quantum computers. While simulating the real-time quantum…
...

References

SHOWING 1-10 OF 105 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

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

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.

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

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.

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

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.
...