It is believed that not all quantum systems can be simulated efficiently using classical computational resources. This notion is supported by the fact that it is not known how to express the partition function in a sign-free manner in quantum Monte Carlo (QMC) simulations for a large number of important problems. The answer to the question-whether there is a fundamental obstruction to such a si...

In physically-based image synthesis, the path space of light transport paths is usually explored by stochastic sampling. The two main families of algorithms are Monte Carlo/quasi-Monte Carlo sampling and Markov chain Monte Carlo. While the former is known for good uniform discovery of important regions, the latter facilitates efficient exploration of local effects. We introduce a hybrid samplin...

The numerical value of a universal quantity associated with the quantum critical regime, namely χuc2/T, for two-dimensional (2D) dimerized spin-1/2 antiferromagnet is calculated using Monte Carlo simulations (QMC). Here χu, c, and T are uniform susceptibility, spin-wave velocity, temperature, respectively. By simulating large lattices at moderately low temperatures, we find χuc2/T∼0.32. Our est...

We propose a quasi-Monte Carlo (QMC) scheme for the simulation of the general dynamics equation (GDE) for aerosols. The mass distribution is approximated by a fixed number of weighted numerical particles. Time is discretized and a splitting approach is used. Coagulation is simulated with a stochastic particle method using quasi-random points. In addition, the particles are reordered by increasi...

The uniform electron gas (UEG) is one of the key models for understanding warm dense matter—an exotic, highly compressed state matter between solid and plasma phases. difficulty in modelling UEG arises from need to simultaneously account Coulomb correlations, quantum effects, exchange as well finite temperature. most accurate results so far were obtained Monte Carlo (QMC) simulations with a var...

Various strategies to implement efficiently quantum Monte Carlo (QMC) simulations for large chemical systems are presented. These include: (i) the introduction of an efficient algorithm to calculate the computationally expensive Slater matrices. This novel scheme is based on the use of the highly localized character of atomic Gaussian basis functions (not the molecular orbitals as usually done)...

In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty quantification problems in subsurface flow. We extend the convergence analysis in [Graham et al., Numer. Math. 2014] to multilevel Quasi-Monte Carlo finite element discr...

Quasi-Monte Carlo (QMC) methods have been successfully used to compute high-dimensional integrals arising in many applications, especially in finance. To understand this success and the possible potential limitations of QMC, this paper focuses on quantitative measures of the quality of a point set in high dimensions. We introduce the order-`, superposition and truncation discrepancies, which me...

Quasi-Monte Carlo (QMC) methods exhibit a faster convergence rate than that of classic Monte Carlo methods. This feature has made QMC prevalent in image synthesis, where it is frequently used for approximating the value of spherical integrals (e.g., illumination integral). The common approach for generating QMC sampling patterns for spherical integration is to resort to unit square low discrepa...

Quantum Monte Carlo (QMC) is among the most accurate methods for solving the time independent Schrödinger equation. Unfortunately, the method is very expensive and requires a vast array of computing resources in order to obtain results of a reasonable convergence level. On the other hand, the method is not only easily parallelizable across CPU clusters, but as we report here, it also has a high...