Erratum to “Tethered Monte Carlo: Computing the effective potential without critical slowing down” [Nucl. Phys. B 807 (2009) 424–454]

Fernández, L. A.; Martı́n-Mayor, V.; Yllanes, David

doi:10.1016/j.nuclphysb.2009.04.022

Cited by 11 publications

(31 citation statements)

References 35 publications

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“…43 The couplings and the initial configurations were chosen at random with a combination of congruential and Parisi-Rapuano random number generator. 38,39 . 44 The local field is defined as h x = y:|| x− y||=1 J x, y σ y .…”

Section: Discussionmentioning

confidence: 99%

Inherent structures inm-component spin glasses

Baity‐Jesi

Parisi

2015

Phys. Rev. B

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We observe numerically the properties of the infinite-temperature inherent structures of mcomponent vector spin glasses in three dimensions. An increase of m implies a decrease of the amount of minima of the free energy, down to the trivial presence of a unique minimum. For little m correlations are small and the dynamics are quickly arrested, while for larger m low-temperature correlations crop up and the convergence is slower, to a limit that appears to be related with the system size.

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Section: Discussionmentioning

confidence: 99%

Inherent structures inm-component spin glasses

Baity‐Jesi

Parisi

2015

Phys. Rev. B

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“…5 In our simulations, the minimal temperature value T min = 0.045 corresponds effectively to zero temperature. This follows from the minimal energy gap of our instances being ∆ = 2 together with our use of a 64-bit (pseudo) random-number generator [50].…”

Section: The Parallel Tempering Simulationsmentioning

confidence: 99%

Unraveling Quantum Annealers using Classical Hardness

Martı́n-Mayor

Hen

2015

Sci Rep

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Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as ‘D-Wave’ chips, promise to solve practical optimization problems potentially faster than conventional ‘classical’ computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spin-glass theory that recognize ‘temperature chaos’ as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the D-Wave Two chip on different temperature-chaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip.

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“…A recent alternative is Tethered Monte Carlo [36], which allows one to reconstruct the Helmholtz effective potential without random walks in the space of the effective coordinate. The method is a generalization of Lustig's microcanonical Monte Carlo [30].…”

Section: Introductionmentioning

confidence: 99%

“…We illustrate it with its application to two challenging problems: hard-spheres crystallization and the diluted antiferromagnet in an external field (the much easier problem of the ferromagnetic Ising model was considered in Refs. [36,37]). We make emphasis on the algorithmic aspects of the computation.…”

Section: Introductionmentioning

confidence: 99%

Tethered Monte Carlo: Managing Rugged Free-Energy Landscapes with a Helmholtz-Potential Formalism

2011

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Tethering methods allow us to perform Monte Carlo simulations in ensembles with conserved quantities. Specifically, one couples a reservoir to the physical magnitude of interest, and studies the statistical ensemble where the total magnitude (system+reservoir) is conserved. The reservoir is actually integrated out, which leaves us with a fluctuation-dissipation formalism that allows us to recover the appropriate Helmholtz effective potential with great accuracy. These methods are demonstrating a remarkable flexibility. In fact, we illustrate two very different applications: hard spheres crystallization and the phase transition of the diluted antiferromagnet in a field (the physical realization of the random field Ising model). The tethered approach holds the promise to transform cartoon drawings of corrugated free-energy landscapes into real computations. Besides, it reduces the algorithmic dynamic slowing-down, probably because the conservation law holds non-locally.

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Erratum to “Tethered Monte Carlo: Computing the effective potential without critical slowing down” [Nucl. Phys. B 807 (2009) 424–454]

Cited by 11 publications

References 35 publications

Inherent structures inm-component spin glasses

Inherent structures inm-component spin glasses

Unraveling Quantum Annealers using Classical Hardness

Tethered Monte Carlo: Managing Rugged Free-Energy Landscapes with a Helmholtz-Potential Formalism

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