Related papers: Numerical path integration with Coulomb potential
We develop Monte Carlo methods for sampling random states and corresponding bit strings in qubit systems. To this end, we derive exact probability density functions that yield the Porter-Thomas distribution in the limit of large systems. We…
The discrete time path integral Monte Carlo (PIMC) with a one-particle density matrix approximation is applied to study the quantum phase transition in the coupled double-well chain. To improve the convergence properties, the exact action…
Relativistic generalization of Path Integral Monte-Carlo method has been proposed and some possible applications have been discussed.
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
In low-temperature high-density plasmas quantum effects of the electrons are becoming increasingly important. This requires the development of new theoretical and computational tools. Quantum Monte Carlo methods are among the most…
The multilevel Monte Carlo path simulation method introduced by Giles ({\it Operations Research}, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different…
We review a family of local algorithms that permit the simulation of charged particles with purely local dynamics. Molecular dynamics formulations lead to discretizations similar to those of ``particle in cell'' methods in plasma physics.…
A real-time path integral Monte Carlo approach is developed to study the dynamics in a many-body quantum system until reaching a nonequilibrium stationary state. The approach is based on augmenting an exact reduced equation for the…
We describe a novel simulation method that eliminates the slowing-down problem in the Monte Carlo simulations of imaginary-time path integrals near the continuum limit. This method combines a stochastic blocking procedure with the multigrid…
Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of…
We present a method to compute real-time path integrals numerically, by Monte-Carlo sampling on near-Lefschetz thimbles. We present a collection of tools based on the Lefschetz thimble methods, which together provide an alternative to…
Long ranged electrostatic interactions are time consuming to calculate in molecular dynamics and Monte-Carlo simulations. We introduce an algorithmic framework for simulating charged particles which modifies the dynamics so as to allow…
Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical…
An indirect, hybrid Monte Carlo discretization of general relativistic kinetic theory suitable for the development of numerical schemes for radiation transport is presented. The discretization is based on surface flux estimators obtained…
This tutorial paper introduces quantum approaches to Monte Carlo computation with applications in computational finance. We outline the basics of quantum computing using Grover's algorithm for unstructured search to build intuition. We then…
Path integral Monte Carlo with Green's function analysis allows the sampling of quantum mechanical properties of molecules at finite temperature. While a high-precision computation of the energy of the Born-Oppenheimer surface from path…
We propose numerical integration methods for Choquet integrals where the capacities are given by distortion functions of an underlying probability measure. It relies on the explicit representation of the integrals for step functions and can…
We present a path-integral Monte Carlo estimator for calculating the dipole polarizability of interacting Coulomb plasma in the long-wavelength limit, i.e., the optical region. We present comprehensive details and method validation studies…
We provide a new paradigm for quantum simulation that is based on path integration that allows quantum speedups to be observed for problems that are more naturally expressed using the path integral formalism rather than the conventional…
Sampling-based approaches are widely used in systems without analytic models to estimate risk or find optimal control. However, gathering sufficient data in such scenarios can be prohibitively costly. On the other hand, in many situations,…