Related papers: Efficient simulation and calibration of general HJ…

Simulating quantum circuits (QC) on high-performance computing (HPC) systems has become an essential method to benchmark algorithms and probe the potential of large-scale quantum computation despite the limitations of current quantum…

Accurately and efficiently estimating system performance under uncertainty is paramount in power system planning and operation. Monte Carlo simulation is often used for this purpose, but convergence may be slow, especially when detailed…

Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability.…

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…

Quantum computing offers an alternative paradigm for addressing combinatorial optimization problems compared to classical computing. Despite recent hardware improvements, the execution of empirical quantum optimization experiments at scales…

Various strategies to implement efficiently 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…

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…

We provide algorithms for efficiently addressing quantum memory in parallel. These imply that the standard circuit model can be simulated with low overhead by the more realistic model of a distributed quantum computer. As a result, the…

Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) approach that exhibits favourable exploration properties in high-dimensional models such as neural networks. Unfortunately, HMC has limited use in large-data regimes and…

In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More…

Performing exact Bayesian inference for complex models is computationally intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are expensive for large datasets and…

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…

We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…

Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations…

Sampling-based inference has seen a surge of interest in recent years. Hamiltonian Monte Carlo (HMC) has emerged as a powerful algorithm that leverages concepts from Hamiltonian dynamics to efficiently explore complex target distributions.…

We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…

Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…

In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same…

Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining…

The development of efficient exact and approximate algorithms for probabilistic inference is a long-standing goal of artificial intelligence research. Whereas substantial progress has been made in dealing with purely discrete or purely…