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

@article{Bapst2012TheQA,
  title={The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective},
  author={Victor Bapst and Laura Foini and Florent Krzakala and Guilhem Semerjian and Francesco Zamponi},
  journal={ArXiv},
  year={2012},
  volume={abs/1210.0811}
}
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References

SHOWING 1-10 OF 345 REFERENCES
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.
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.
Noise resistance of adiabatic quantum computation using random matrix theory
TLDR
A fully analytical study of the resistance to noise of quantum algorithms using perturbation theory combined with a theoretical noise model based on random matrices drawn from the Gaussian orthogonal ensemble, whose elements vary in time and form a stationary random process.
Colloquium : Quantum annealing and analog quantum computation
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
HOW TO MAKE THE QUANTUM ADIABATIC ALGORITHM FAIL
TLDR
It is shown that poor choices for the Hamiltonian can guarantee that the quantum adiabatic algorithm will not find the minimum if the run time grows more slowly than .
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
TLDR
It is suggested that the adiabatic computation model and the conventional quantum computation model are polynomially equivalent and this result can be extended to the physically realistic setting of particles arranged on a two-dimensional grid with nearest neighbor interactions.
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
Case studies in quantum adiabatic optimization
Quantum adiabatic optimization is a quantum algorithm for solving classical optimization problems (E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser. Quantum computation by adiabatic evolution, 2000.
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.
...
1
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4
5
...