639 research outputs found
Chaos in spin glasses revealed through thermal boundary conditions
We study the fragility of spin glasses to small temperature perturbations
numerically using population annealing Monte Carlo. We apply thermal boundary
conditions to a three-dimensional Edwards-Anderson Ising spin glass. In thermal
boundary conditions all eight combinations of periodic versus antiperiodic
boundary conditions in the three spatial directions are present, each appearing
in the ensemble with its respective statistical weight determined by its free
energy. We show that temperature chaos is revealed in the statistics of
crossings in the free energy for different boundary conditions. By studying the
energy difference between boundary conditions at free-energy crossings, we
determine the domain-wall fractal dimension. Similarly, by studying the number
of crossings, we determine the chaos exponent. Our results also show that
computational hardness in spin glasses and the presence of chaos are closely
related.Comment: 4 pages, 4 figure
Multi-overlap simulations of spin glasses
We present results of recent high-statistics Monte Carlo simulations of the
Edwards-Anderson Ising spin-glass model in three and four dimensions. The study
is based on a non-Boltzmann sampling technique, the multi-overlap algorithm
which is specifically tailored for sampling rare-event states. We thus
concentrate on those properties which are difficult to obtain with standard
canonical Boltzmann sampling such as the free-energy barriers F^q_B in the
probability density P_J(q) of the Parisi overlap parameter q and the behaviour
of the tails of the disorder averaged density P(q) = [P_J(q)]_av.Comment: 14 pages, Latex, 18 Postscript figures, to be published in NIC Series
- Publication Series of the John von Neumann Institute for Computing (NIC
Dynamics of the Wang-Landau algorithm and complexity of rare events for the three-dimensional bimodal Ising spin glass
We investigate the performance of flat-histogram methods based on a
multicanonical ensemble and the Wang-Landau algorithm for the three-dimensional
+/- J spin glass by measuring round-trip times in the energy range between the
zero-temperature ground state and the state of highest energy. Strong
sample-to-sample variations are found for fixed system size and the
distribution of round-trip times follows a fat-tailed Frechet extremal value
distribution. Rare events in the fat tails of these distributions corresponding
to extremely slowly equilibrating spin glass realizations dominate the
calculations of statistical averages. While the typical round-trip time scales
exponential as expected for this NP-hard problem, we find that the average
round-trip time is no longer well-defined for systems with N >= 8^3 spins. We
relate the round-trip times for multicanonical sampling to intrinsic properties
of the energy landscape and compare with the numerical effort needed by the
genetic Cluster-Exact Approximation to calculate the exact ground state
energies. For systems with N >= 8^3 spins the simulation of these rare events
becomes increasingly hard. For N >= 14^3 there are samples where the
Wang-Landau algorithm fails to find the true ground state within reasonable
simulation times. We expect similar behavior for other algorithms based on
multicanonical sampling.Comment: 9 pages, 12 figure
Population annealing: Theory and application in spin glasses
Population annealing is an efficient sequential Monte Carlo algorithm for
simulating equilibrium states of systems with rough free energy landscapes. The
theory of population annealing is presented, and systematic and statistical
errors are discussed. The behavior of the algorithm is studied in the context
of large-scale simulations of the three-dimensional Ising spin glass and the
performance of the algorithm is compared to parallel tempering. It is found
that the two algorithms are similar in efficiency though with different
strengths and weaknesses.Comment: 16 pages, 10 figures, 4 table
Seeking Quantum Speedup Through Spin Glasses: The Good, the Bad, and the Ugly
There has been considerable progress in the design and construction of
quantum annealing devices. However, a conclusive detection of quantum speedup
over traditional silicon-based machines remains elusive, despite multiple
careful studies. In this work we outline strategies to design hard tunable
benchmark instances based on insights from the study of spin glasses - the
archetypal random benchmark problem for novel algorithms and optimization
devices. We propose to complement head-to-head scaling studies that compare
quantum annealing machines to state-of-the-art classical codes with an approach
that compares the performance of different algorithms and/or computing
architectures on different classes of computationally hard tunable spin-glass
instances. The advantage of such an approach lies in having to only compare the
performance hit felt by a given algorithm and/or architecture when the instance
complexity is increased. Furthermore, we propose a methodology that might not
directly translate into the detection of quantum speedup, but might elucidate
whether quantum annealing has a "`quantum advantage" over corresponding
classical algorithms like simulated annealing. Our results on a 496 qubit
D-Wave Two quantum annealing device are compared to recently-used
state-of-the-art thermal simulated annealing codes.Comment: 14 pages, 8 figures, 3 tables, way too many reference
Extreme Quantum Advantage for Rare-Event Sampling
We introduce a quantum algorithm for efficient biased sampling of the rare
events generated by classical memoryful stochastic processes. We show that this
quantum algorithm gives an extreme advantage over known classical biased
sampling algorithms in terms of the memory resources required. The quantum
memory advantage ranges from polynomial to exponential and when sampling the
rare equilibrium configurations of spin systems the quantum advantage diverges.Comment: 11 pages, 9 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/eqafbs.ht
The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
Among various algorithms designed to exploit the specific properties of
quantum computers with respect to classical ones, the quantum adiabatic
algorithm is a versatile proposition to find the minimal value of an arbitrary
cost function (ground state energy). Random optimization problems provide a
natural testbed to compare its efficiency with that of classical algorithms.
These problems correspond to mean field spin glasses that have been extensively
studied in the classical case. This paper reviews recent analytical works that
extended these studies to incorporate the effect of quantum fluctuations, and
presents also some original results in this direction.Comment: 151 pages, 21 figure
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