8,137 research outputs found
Computing the Absolute Gibbs Free Energy in Atomistic Simulations: Applications to Defects in Solids
The Gibbs free energy is the fundamental thermodynamic potential underlying
the relative stability of different states of matter under constant-pressure
conditions. However, computing this quantity from atomic-scale simulations is
far from trivial. As a consequence, all too often the potential energy of the
system is used as a proxy, overlooking entropic and anharmonic effects. Here we
discuss a combination of different thermodynamic integration routes to obtain
the absolute Gibbs free energy of a solid system starting from a harmonic
reference state. This approach enables the direct comparison between the free
energy of different structures, circumventing the need to sample the transition
paths between them. We showcase this thermodynamic integration scheme by
computing the Gibbs free energy associated with a vacancy in BCC iron, and the
intrinsic stacking fault free energy of nickel. These examples highlight the
pitfalls of estimating the free energy of crystallographic defects only using
the minimum potential energy, which overestimates the vacancy free energy by
60% and the stacking-fault energy by almost 300% at temperatures close to the
melting point
Quantum rejection sampling
Rejection sampling is a well-known method to sample from a target
distribution, given the ability to sample from a given distribution. The method
has been first formalized by von Neumann (1951) and has many applications in
classical computing. We define a quantum analogue of rejection sampling: given
a black box producing a coherent superposition of (possibly unknown) quantum
states with some amplitudes, the problem is to prepare a coherent superposition
of the same states, albeit with different target amplitudes. The main result of
this paper is a tight characterization of the query complexity of this quantum
state generation problem. We exhibit an algorithm, which we call quantum
rejection sampling, and analyze its cost using semidefinite programming. Our
proof of a matching lower bound is based on the automorphism principle which
allows to symmetrize any algorithm over the automorphism group of the problem.
Our main technical innovation is an extension of the automorphism principle to
continuous groups that arise for quantum state generation problems where the
oracle encodes unknown quantum states, instead of just classical data.
Furthermore, we illustrate how quantum rejection sampling may be used as a
primitive in designing quantum algorithms, by providing three different
applications. We first show that it was implicitly used in the quantum
algorithm for linear systems of equations by Harrow, Hassidim and Lloyd.
Secondly, we show that it can be used to speed up the main step in the quantum
Metropolis sampling algorithm by Temme et al.. Finally, we derive a new quantum
algorithm for the hidden shift problem of an arbitrary Boolean function and
relate its query complexity to "water-filling" of the Fourier spectrum.Comment: 19 pages, 5 figures, minor changes and a more compact style (to
appear in proceedings of ITCS 2012
Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models
Mainstream machine-learning techniques such as deep learning and
probabilistic programming rely heavily on sampling from generally intractable
probability distributions. There is increasing interest in the potential
advantages of using quantum computing technologies as sampling engines to speed
up these tasks or to make them more effective. However, some pressing
challenges in state-of-the-art quantum annealers have to be overcome before we
can assess their actual performance. The sparse connectivity, resulting from
the local interaction between quantum bits in physical hardware
implementations, is considered the most severe limitation to the quality of
constructing powerful generative unsupervised machine-learning models. Here we
use embedding techniques to add redundancy to data sets, allowing us to
increase the modeling capacity of quantum annealers. We illustrate our findings
by training hardware-embedded graphical models on a binarized data set of
handwritten digits and two synthetic data sets in experiments with up to 940
quantum bits. Our model can be trained in quantum hardware without full
knowledge of the effective parameters specifying the corresponding quantum
Gibbs-like distribution; therefore, this approach avoids the need to infer the
effective temperature at each iteration, speeding up learning; it also
mitigates the effect of noise in the control parameters, making it robust to
deviations from the reference Gibbs distribution. Our approach demonstrates the
feasibility of using quantum annealers for implementing generative models, and
it provides a suitable framework for benchmarking these quantum technologies on
machine-learning-related tasks.Comment: 17 pages, 8 figures. Minor further revisions. As published in Phys.
Rev.
Monte Carlo Hamiltonian from Stochastic Basis
In order to extend the recently proposed Monte Carlo Hamiltonian to many-body
systems, we suggest to concept of a stochastic basis. We apply it to the chain
of coupled anharmonic oscillators. We compute the spectrum of excited
states in a finite energy window and thermodynamical observables free energy,
average energy, entropy and specific heat in a finite temperature window.
Comparing the results of the Monte Carlo Hamiltonian with standard Lagrangian
lattice calculations, we find good agreement. However, the Monte Carlo
Hamiltonian results show less fluctuations under variation of temperature.Comment: revised version, new figures. Text (LaTeX), 4 Figs. (eps), style fil
Hydrodynamics of the interacting Bose gas in the Quantum Newton Cradle setup
Describing and understanding the motion of quantum gases out of equilibrium
is one of the most important modern challenges for theorists. In the
groundbreaking Quantum Newton Cradle experiment [Kinoshita, Wenger and Weiss,
Nature 440, 900, 2006], quasi-one-dimensional cold atom gases were observed
with unprecedented accuracy, providing impetus for many developments on the
effects of low dimensionality in out-of-equilibrium physics. But it is only
recently that the theory of generalized hydrodynamics has provided the adequate
tools for a numerically efficient description. Using it, we give a complete
numerical study of the time evolution of an ultracold atomic gas in this setup,
in an interacting parameter regime close to that of the original experiment. We
evaluate the full evolving phase-space distribution of particles. We simulate
oscillations due to the harmonic trap, the collision of clouds without
thermalization, and observe a small elongation of the actual oscillation period
and cloud deformations due to many-body dephasing. We also analyze the effects
of weak anharmonicity. In the experiment, measurements are made after release
from the one-dimensional trap. We evaluate the gas density curves after such a
release, characterizing the actual time necessary for reaching the asymptotic
state where the integrable quasi-particle momentum distribution function
emerges.Comment: v1: 7+10 pages, 3+7 figures. v2: references added, pictures with
refined discretization. v3: addition of discussion of integrability breaking
by trap + small improvement
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