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Hamiltonian Monte Carlo (HMC) is an efficient Bayesian sampling method that can make distant proposals in the parameter space by simulating a Hamiltonian dynamical system. Despite its popularity in machine learning and data science, HMC is…

Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in…

The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…

Quantum Monte Carlo (QMC) is a powerful method to calculate accurate energies and forces for molecular systems. In this work, we demonstrate how we can obtain accurate QMC forces for the fluxional ethanol molecule at room temperature by…

The auxiliary-field quantum Monte Carlo (AFMC) method is a powerful and widely used technique for ground-state and finite-temperature simulations of quantum many-body systems. We introduce several algorithmic improvements for…

In the present paper we examine the risk-sensitive and sampling issues associated with the problem of calculating generalized averages. By combining thermodynamic integration and Stationary Phase Monte Carlo techniques, we develop an…

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.…

We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…

We propose a flat-histogram Monte Carlo method to efficiently sample fractal landscapes such as escape time functions of open chaotic systems. This is achieved by using a random-walk step which depends on the height of the landscape via the…

We present an implementation of a Monte Carlo algorithm that generates points randomly and uniformly on a set of arbitrary surfaces. The algorithm is completely general and only requires the geometry modeling software to provide the…

Diagrammatic expansions are a central tool for treating correlated electron systems. At thermal equilibrium, they are most naturally defined within the Matsubara formalism. However, extracting any dynamic response function from a Matsubara…

Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…

A central challenge in analog quantum simulation is to characterize desirable physical properties of quantum states produced in experiments. However, in conventional approaches, the extraction of arbitrary information requires performing…

This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational challenges posed by quantum phase…

A Monte Carlo simulation on the basis of quantum trajectory approach is carried out for the measurement dynamics of a single electron spin resonance. The measured electron, which is confined in either a quantum dot or a defect trap, is…

Quantum annealing (QA) with a transverse field often fails to sample degenerate ground states fairly, limiting applicability to problems requiring diverse optimal solutions. Although Quantum Monte Carlo (QMC) is widely used to simulate QA,…

Modeling the dynamics of a quantum system connected to the environment is critical for advancing our understanding of complex quantum processes, as most quantum processes in nature are affected by an environment. Modeling a macroscopic…

We present a new approach to the study of equilibrium properties in many-body quantum physics. Our method takes inspiration from Density Matrix Quantum Monte Carlo and incorporates new crucial features. First of all, the dynamics is…

In this paper we present a new approach to control variates for improving computational efficiency of Ensemble Monte Carlo. We present the approach using simulation of paths of a time-dependent nonlinear stochastic equation. The core idea…

In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…