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Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…
Expectation values of physical quantities may accurately be obtained by the evaluation of integrals within Many-Body Quantum mechanics, and these multi-dimensional integrals may be estimated using Monte Carlo methods. In a previous…
We present a novel approach for improving particle filters for multi-target tracking. The suggested approach is based on drift homotopy for stochastic differential equations. Drift homotopy is used to design a Markov Chain Monte Carlo step…
We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…
Event-chain Monte Carlo (ECMC) accelerates the sampling of hard-sphere systems, and has been generalized to the potentials used in classical molecular simulation. Rather than imposing detailed balance on transition probabilities, the method…
We study the large-scale dynamics of event chain Monte Carlo algorithms in one dimension, and their relation to the true self-avoiding walk. In particular, we study the influence of stress, and different forms of interaction on the…
We present a new Monte Carlo scheme for the efficient simulation of multi-polymer systems. The method permits chains to be inserted into the system using a biased growth technique. The growth proceeds via the use of a retractable feeler,…
Multivariate normal (MVN) probabilities arise in myriad applications, but they are analytically intractable and need to be evaluated via Monte-Carlo-based numerical integration. For the state-of-the-art minimax exponential tilting (MET)…
A detailed description is provided of a new Worm Algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the…
We consider situations where the applicability of sequential Monte Carlo particle filters is compromised due to the expensive evaluation of the particle weights. To alleviate this problem, we propose a new particle filter algorithm based on…
We present a method based on the Path Integral Monte Carlo formalism for the calculation of ground-state time correlation functions in quantum systems. The key point of the method is the consideration of time as a complex variable whose…
We review efficient Monte Carlo methods for simulating quantum systems which couple to a dissipative environment. A brief introduction of the Caldeira-Leggett model and the Monte Carlo method will be followed by a detailed discussion of…
While kinetic Monte Carlo simulations can provide long-time simulations of the dynamics of physical and chemical systems, it is not yet possible in general to identify the inverse Monte Carlo attempt frequency with a physical timescale.…
Applications that require substantial computational resources today cannot avoid the use of heavily parallel machines. Embracing the opportunities of parallel computing and especially the possibilities provided by a new generation of…
From basic considerations of the Lie group that preserves a target probability measure, we derive the Barker, Metropolis, and ensemble Markov chain Monte Carlo (MCMC) algorithms, as well as variants of waste-recycling Metropolis-Hastings…
Quantum Monte Carlo (QMC) methods are one of the most important tools for studying interacting quantum many-body systems. The vast majority of QMC calculations in interacting fermion systems require a constraint to control the sign problem.…
The directed-loop quantum Monte Carlo method is generalized to the case of retarded interactions. Using the path integral, fermion-boson or spin-boson models are mapped to actions with retarded interactions by analytically integrating out…
We derive the improved estimators for general interactions and employ these for the continuous-time quantum Monte Carlo method. Using a worm algorithm we show how measuring higher-ordered correlators leads to an improved high-frequency…
Recently, a diffusion Monte Carlo algorithm was applied to the study of spin dependent interactions in condensed matter. Following some of the ideas presented therein, and applied to a Hamiltonian containing a Rashba-like interaction, a…
We prove that for any Monte Carlo algorithm of Metropolis type, the autocorrelation time of a suitable ``energy''-like observable is bounded below by a multiple of the corresponding ``specific heat''. This bound does not depend on whether…