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Quantum Metropolis sampling

(2011) NATURE. 471(7336). p.87-90
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Abstract
The original motivation to build a quantum computer came from Feynman(1), who imagined a machine capable of simulating generic quantum mechanical systems-a task that is believed to be intractable for classical computers. Such a machine could have far-reaching applications in the simulation of many-body quantum physics in condensed-matter, chemical and high-energy systems. Part of Feynman's challenge was met by Lloyd(2), who showed how to approximately decompose the time evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm(3), a method that has basically acquired a monopoly on the simulation of interacting particles. Here we demonstrate how to implement a quantum version of the Metropolis algorithm. This algorithm permits sampling directly from the eigenstates of the Hamiltonian, and thus evades the sign problem present in classical simulations. A small-scale implementation of this algorithm should be achievable with today's technology.
Keywords
ALGORITHMS, SIMULATIONS, COMPUTATION, COMPLEXITY, SYSTEMS

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Please use this url to cite or link to this publication:

Chicago
Temme, K, TJ Osborne, KG Vollbrecht, D Poulin, and Frank Verstraete. 2011. “Quantum Metropolis Sampling.” Nature 471 (7336): 87–90.
APA
Temme, K, Osborne, T., Vollbrecht, K., Poulin, D., & Verstraete, F. (2011). Quantum Metropolis sampling. NATURE, 471(7336), 87–90.
Vancouver
1.
Temme K, Osborne T, Vollbrecht K, Poulin D, Verstraete F. Quantum Metropolis sampling. NATURE. 2011;471(7336):87–90.
MLA
Temme, K, TJ Osborne, KG Vollbrecht, et al. “Quantum Metropolis Sampling.” NATURE 471.7336 (2011): 87–90. Print.
@article{8589225,
  abstract     = {The original motivation to build a quantum computer came from Feynman(1), who imagined a machine capable of simulating generic quantum mechanical systems-a task that is believed to be intractable for classical computers. Such a machine could have far-reaching applications in the simulation of many-body quantum physics in condensed-matter, chemical and high-energy systems. Part of Feynman's challenge was met by Lloyd(2), who showed how to approximately decompose the time evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm(3), a method that has basically acquired a monopoly on the simulation of interacting particles. Here we demonstrate how to implement a quantum version of the Metropolis algorithm. This algorithm permits sampling directly from the eigenstates of the Hamiltonian, and thus evades the sign problem present in classical simulations. A small-scale implementation of this algorithm should be achievable with today's technology.},
  author       = {Temme, K and Osborne, TJ and Vollbrecht, KG and Poulin, D and Verstraete, Frank},
  issn         = {0028-0836},
  journal      = {NATURE},
  keywords     = {ALGORITHMS,SIMULATIONS,COMPUTATION,COMPLEXITY,SYSTEMS},
  language     = {eng},
  number       = {7336},
  pages        = {87--90},
  title        = {Quantum Metropolis sampling},
  url          = {http://dx.doi.org/10.1038/nature09770},
  volume       = {471},
  year         = {2011},
}

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