Related papers: Monte Carlo sampling from the quantum state space.…
Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…
We propose a new type of Monte Carlo approach in numerical studies of quantum systems. Introducing a probability function which determines whether a state in the vector space survives or not, we can evaluate expectation values of powers of…
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo…
We propose quantum algorithms that provide provable speedups for Markov Chain Monte Carlo (MCMC) methods commonly used for sampling from probability distributions of the form $\pi \propto e^{-f}$, where $f$ is a potential function. Our…
This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computational science and engineering - notably, some of those arising…
We describe a number of strategies for minimizing and calculating accurately the statistical uncertainty in quantum Monte Carlo calculations. We investigate the impact of the sampling algorithm on the efficiency of the variational Monte…
In solving simulation-based stochastic root-finding or optimization problems that involve rare events, such as in extreme quantile estimation, running crude Monte Carlo can be prohibitively inefficient. To address this issue, importance…
Boson sampling is a promising candidate for quantum supremacy. It requires to sample from a complicated distribution, and is trusted to be intractable on classical computers. Among the various classical sampling methods, the Markov chain…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
Artificial Neural Networks were recently shown to be an efficient representation of highly-entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in Variational Monte Carlo, most…
Neural-network quantum states (NQS) offer a powerful and expressive ansatz for representing quantum many-body wave functions. However, their training via Variational Monte Carlo (VMC) methods remains challenging. It is well known that some…
One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
Standard Bayesian credible-region theory for constructing an error region on the unique estimator of an unknown state in general quantum-state tomography to calculate its size and credibility relies on heavy Monte~Carlo sampling of the…
Discrepancies play an important role in the study of uniformity properties of point sets. Their probability distributions are a help in the analysis of the efficiency of the Quasi Monte Carlo method of numerical integration, which uses…
A Monte Carlo method is presented to evaluate quantum states with many particles moving in the continuum. The scattering state is generated at each time by a Monte Carlo random sampling algorithm. The same calculation are repeated until the…
Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…
In the last fifteen the subset sampling method has often been used in reliability problems as a tool for calculating small probabilities. This method is extrapolating from an initial Monte Carlo estimate for the probability content of a…
The efficiency of a Markov chain Monte Carlo algorithm might be measured by the cost of generating one independent sample, or equivalently, the total cost divided by the effective sample size, defined in terms of the integrated…