Related papers: Path integral Monte Carlo method for the quantum a…

Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…

We introduce the energy-stepping Monte Carlo (ESMC) method, a Markov chain Monte Carlo (MCMC) algorithm based on the conventional dynamical interpretation of the proposal stage but employing an energy-stepping integrator. The…

High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…

A simple and efficient method for quantum Monte Carlo simulation is presented, based on discretization of the action in the path integral, and a Gaussian averaging of the potential, which works well e.g. with the Coulomb potential.

We present a probabilistic generative model for timing deviations in expressive music performance. The structure of the proposed model is equivalent to a switching state space model. The switch variables correspond to discrete note…

In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…

Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…

Quantum Monte Carlo (QMC) methods such as Variational Monte Carlo, Diffusion Monte Carlo or Path Integral Monte Carlo are the most accurate and general methods for computing total electronic energies. We will review methods we have…

Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster…

The path integral of a quantum system with an exact symmetry can be written as a sum of functional integrals each giving the contribution from quantum states with definite symmetry properties. We propose a strategy to compute each of them,…

In this paper, we consider the Markov-Chain Monte Carlo (MCMC) approach for random sampling of combinatorial objects. The running time of such an algorithm depends on the total mixing time of the underlying Markov chain and is unknown in…

Monte Carlo methods -- such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers -- provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in…

We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition…

Markov chain Monte Carlo (MCMC) methods provide consistent of integrals as the number of iterations goes to infinity. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using…

The tunneling decay event of a metastable state in a fully connected quantum spin model can be simulated efficiently by path integral quantum Monte Carlo (QMC) [Isakov $et~al.$, Phys. Rev. Lett. ${\bf 117}$, 180402 (2016).]. This is because…

The Markov chain Monte Carlo method is a versatile tool in statistical physics to evaluate multi-dimensional integrals numerically. For the method to work effectively, we must consider the following key issues: the choice of ensemble, the…

Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…

In statistical analysis, Monte Carlo (MC) stands as a classical numerical integration method. When encountering challenging sample problem, Markov chain Monte Carlo (MCMC) is a commonly employed method. However, the MCMC estimator is biased…

We apply a Bayesian data analysis scheme known as the Markov Chain Monte Carlo (MCMC) to the tomographic reconstruction of quantum states. This method yields a vector, known as the Markov chain, which contains the full statistical…

Particle Markov Chain Monte Carlo methods are used to carry out inference in non-linear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform…