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About 10,000 papers for “Monte Carlo algorithm”

Tunneling hybrid Monte-Carlo algorithm

Maarten Golterman, Yigal Shamir · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology · 2007

The Hermitian Wilson kernel used in the construction of the domain-wall and overlap Dirac operators has exceptionally small eigenvalues that make it expensive to reach high-quality chiral symmetry for domain-wall fermions, or high precision in the case of the overlap operator. An efficient way of suppressing such eigenmodes consists of including a positive power of the determinant of the Wilson kernel in the Boltzmann weight, but doing this also suppresses tunneling between topological sectors. Here we propose a modification of the hybrid Monte-Carlo algorithm which aims to restore tunneling between topological sectors by excluding the lowest eigenmodes of the Wilson kernel from the molecular-dynamics evolution, and correcting for this at the accept/reject step. We discuss the implications of this modification for the acceptance rate.

Cited by 6Open access

A noisy Monte Carlo algorithm

Leyu Lin, K. F. Liu, J. Sloan · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 2000

We propose a Monte Carlo algorithm to promote the Kennedy-Kuti linear accept-reject algorithm which accommodates unbiased stochastic estimates of the probability to an exact one. This is achieved by adopting the Metropolis accept-reject steps for both the dynamical and noise configurations. We test it on the five state model and obtain desirable results even for the case with large noise. We also discuss its application to lattice QCD with stochastically estimated fermion determinants.

Cited by 43Open access

A polynomial hybrid Monte Carlo algorithm

Jansen, K. (European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.), Frezzotti, R. (Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)), Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany) · OpenGrey (Institut de l'Information Scientifique et Technique) · 1997

We present a simulation algorithm for dynamical fermions that combines the multiboson technique with the hybrid Monte Carlo algorithm. We find that the algorithm gives a substantial gain over the standard methods in practical simulations. We point out the ability of the algorithm to treat fermion zero modes in a clean and controllable manner. (orig.)

Cited by 0

Quantum computing quantum Monte Carlo algorithm

Yukun Zhang, Yifei Huang, Jinzhao Sun et al. · arXiv (Cornell University) · 2022

Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates these two methods, inheriting their distinct features in efficient representation and manipulation of quantum states and overcoming their limitations. We first introduce non-stoquasticity indicators (NSIs) and their upper bounds, which measure the sign problem, the most notable limitation of QMC. We show that our algorithm could greatly mitigate the sign problem, which decreases NSIs with the assistance of quantum computing. Meanwhile, the use of quantum Monte Carlo also increases the expressivity of shallow quantum circuits, allowing more accurate computation that is conventionally achievable only with much deeper circuits. We numerically test and verify the method for the N$_2$ molecule (12 qubits) and the Hubbard model (16 qubits). Our work paves the way to solving practical problems with intermediate-scale and early-fault tolerant quantum computers, with potential applications in chemistry, condensed matter physics, materials, high energy physics, etc.

Cited by 10Open access

Another Monte Carlo Renormalization Group Algorithm

John P. Donohue · ArXiv.org · 2004

A Monte Carlo Renormalization Group algorithm is used on the Ising model to derive critical exponents and the critical temperature. The algorithm is based on a minimum relative entropy iteration developed previously to derive potentials from equilibrium configurations. This previous algorithm is modified to derive useful information in an RG iteration. The method is applied in several dimensions with limited success. Required accuracy has not been achieved, but the method is interesting.

Cited by 0Open access

Accelerating the hybrid Monte Carlo algorithm

Ali Khan, A., Bakeyev, T., Gockeler, M. et al. · University of Regensburg Publication Server (University of Regensburg) · 2003

An algorithm for separating the high- and low-frequency molecular dynamics modes in Hybrid Monte Carlo simulations of gauge theories with dynamical fermions is presented. The separation is based on splitting the pseudo-fermion action into two parts, as was initially proposed by Hasenbusch. We propose to introduce different evolution time-scales for each part. We test our proposal in realistic simulations of two-flavor O(a) improved Wilson fermions. A speed-up of more than a factor of three compared to the standard HMC algorithm is observed in a typical run.

Cited by 0

A quasi-Monte Carlo Metropolis algorithm

Art B. Owen, Seth D. Tribble · Proceedings of the National Academy of Sciences · 2005

This work presents a version of the Metropolis-Hastings algorithm using quasi-Monte Carlo inputs. We prove that the method yields consistent estimates in some problems with finite state spaces and completely uniformly distributed inputs. In some numerical examples, the proposed method is much more accurate than ordinary Metropolis-Hastings sampling.

Cited by 65Open access

Dual Quantum Monte Carlo Algorithm for

Hardcore Bosons, G. G. Batrouni, H. Mabilat · 2008

We derive the exact dual representation of the bosonic Hubbard model which takes the form of conserved current loops. The hardcore limit, which corresponds to the quantum spin-1 2 Heisenberg antiferromagnet, is also obtained. In this limit, the dual partition function takes a particularly simple form which is very amenable to numerical simulations. In addition to the usual quantities that we can measure (energy, density-density correlation function and superfluid density) we can with this new algorithm measure efficiently the order parameter correlation function, 〈aia † j 〉, |i − j | ≥ 1. We demonstrate this with numerical tests in one dimension. 1

Cited by 0

Online sequential Monte Carlo EM algorithm

Olivier Cappé · 2009 IEEE/SP 15th Workshop on Statistical Signal Processing · 2009

Online (or recursive) estimation of fixed model parameters in general state-space models is a crucial but often difficult task. This paper is about likelihood-based point estimation, showing that an online EM (Expectation-Maximization) algorithm recently proposed for discrete hidden Markov models can be extended to more general settings, including non-linear non-Gaussian state-space models that necessitate the use of sequential Monte Carlo filtering approximations. The performance of the proposed online sequential Monte Carlo EM algorithm is illustrated on numerical examples.

Cited by 55

Accelerating the Hybrid Monte Carlo algorithm

Khan, A. Ali, Bakeyev, T., Göckeler, M. et al. · arXiv (Cornell University) · 2003

An algorithm for separating the high- and low-frequency molecular dynamics modes in Hybrid Monte Carlo simulations of gauge theories with dynamical fermions is presented. The separation is based on splitting the pseudo-fermion action into two parts, as was initially proposed by Hasenbusch. We propose to introduce different evolution time-scales for each part. We test our proposal in realistic simulations of two-flavor O(a) improved Wilson fermions. A speed-up of more than a factor of three compared to the standard HMC algorithm is observed in a typical run.

Cited by 0Open access

The Rational Hybrid Monte Carlo Algorithm

M. A. Clark · ArXiv.org · 2006

The past few years have seen considerable progress in algorithmic development for the generation of gauge fields including the effects of dynamical fermions. The Rational Hybrid Monte Carlo (RHMC) algorithm, where Hybrid Monte Carlo is performed using a rational approximation in place the usual inverse quark matrix kernel is one of these developments. This algorithm has been found to be extremely beneficial in many areas of lattice QCD (chiral fermions, finite temperature, Wilson fermions etc.). We review the algorithm and some of these benefits, and we compare against other recent algorithm developements. We conclude with an update of the Berlin wall plot comparing costs of all popular fermion formulations.

Cited by 2Open access

Multicanonical Monte Carlo ensemble growth algorithm

Graziano Vernizzi, Trung Dac Nguyen, Henri Orland et al. · Physical review. E · 2020

We present an ensemble Monte Carlo growth method to sample the equilibrium thermodynamic properties of random chains. The method is based on the multicanonical technique of computing the density of states in the energy space. Such a quantity is temperature independent, and therefore microcanonical and canonical thermodynamic quantities, including the free energy, entropy, and thermal averages, can be obtained by reweighting with a Boltzmann factor. The algorithm we present combines two approaches: The first is the Monte Carlo ensemble growth method, where a "population" of samples in the state space is considered, as opposed to traditional sampling by long random walks, or iterative single-chain growth. The second is the flat-histogram Monte Carlo, similar to the popular Wang-Landau sampling, or to multicanonical chain-growth sampling. We discuss the performance and relative simplicity of the proposed algorithm, and we apply it to known test cases.

Cited by 1Open access