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The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
Markov chain Monte Carlo (MCMC) algorithms are based on the construction of a Markov chain with transition probabilities leaving invariant a probability distribution of interest. In this work, we look at these transition probabilities as…
We investigate fractional moments and expectations of power means of complex-valued random variables by using fractional calculus. We deal with both negative and positive orders of the fractional derivatives. The one-dimensional…
Owing to their favorable scaling with dimensionality, Monte Carlo (MC) methods have become the tool of choice for numerical integration across the quantitative sciences. Almost invariably, efficient MC integration schemes are strictly…
Silica is an abundant component of the Earth whose crystalline polymorphs play key roles in its structure and dynamics. As the simplest silicates, understanding pure silica is a prerequisite to understanding the rocky part of the Earth, its…
We show that recently developed quantum Monte Carlo methods, which provide accurate vertical transition energies for single excitations, also successfully treat double excitations. We study the double excitations in medium-sized molecules,…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…
Fixed-node diffusion Monte Carlo (FNDMC) is a stochastic quantum many-body method that has a great potential in electronic structure theory. We examine how FNDMC satisfies exact constraints, linearity and derivative discontinuity of total…
Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in…
Computational methods both open the frontiers of economic analysis and serve as a bottleneck in what can be achieved. We are the first to study whether Quantum Monte Carlo (QMC) algorithm can improve the runtime of economic applications and…
Variational Monte Carlo (VMC) is a powerful and fast-growing method for optimizing and evolving parameterized many-body wave functions, especially with modern neural-network quantum states. In practice, however, the stochastic estimators…
Diagrammatic Monte Carlo (DiagMC) is a numeric technique that allows one to calculate quantities specified in terms of diagrammatic expansions, the latter being a standard tool of many-body quantum statistics. The sign problem that is…
We analyze here in some detail, the derivation of the Particle and Monte Carlo methods of plasma simulation, such as Particle in Cell (PIC), Monte Carlo (MC) and Particle in Cell / Monte Carlo (PIC/MC) from formal manipulation of transport…
The HMC algorithm, combining the advantages of molecular dynamics and Monte-Carlo methods, is the most efficient algorithm to simulate QCD including the effects of sea quarks. In the standard approach momentum fields are generated with a…
Variational quantum Monte Carlo calculations are reported for the bulk GaAs semiconductor in order to present values for the ground-state energy, the lattice constant, the bulk modulus, and some derived properties. The statistical accuracy…
This paper introduces the first quantum computing framework for Stochastic Quantum Power Flow (SQPF) analysis in power systems. The proposed method leverages quantum states to encode power flow distributions, enabling the use of Quantum…
We present high-accuracy correlated calculations of small Si$_x$H$_y$ molecular systems both in the ground and excited states. We employ quantum Monte Carlo (QMC) together with a variety of many-body wave function approaches based on basis…
In recent years, the combination of precise quantum Monte Carlo (QMC) methods with realistic nuclear interactions and consistent electroweak currents, in particular those constructed within effective field theories (EFTs), has lead to new…
Particle-in-cell methods with stochastic collision models are commonly used to simulate collisional plasma dynamics, with applications ranging from hypersonic flight to semiconductor manufacturing. Code verification of such methods is…
We investigate Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions. Several variants of the basic techniques are studied, including limiting the variations in the weighting factors which arise in…