Related papers: Optimum and efficient sampling for variational qua…
We explore to what extent path-integral quantum Monte Carlo methods can efficiently simulate the tunneling behavior of quantum adiabatic optimization algorithms. Specifically we look at symmetric cost functions defined over n bits with a…
The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks. A large number of solutions have been proposed to…
The mean of a random variable can be understood as a linear functional on the space of probability distributions. Quantum computing is known to provide a quadratic speedup over classical Monte Carlo methods for mean estimation. In this…
By considering the effect of varying the target radii and detector aperture width on the scattering angle in experimental Compton scattering, mathematical models were developed and subsequently incorporated into Monte Carlo simulations. By…
When dealing with difficult inverse problems such as inverse rendering, using Monte Carlo estimated gradients to optimise parameters can slow down convergence due to variance. Averaging many gradient samples in each iteration reduces this…
Space filling designs are central to studying complex systems in various areas of science. They are used for obtaining an overall understanding of the behaviour of the response over the input space, model construction and uncertainty…
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…
Compact and accurate wave functions can be constructed by quantum Monte Carlo methods. Typically, these wave functions consist of a sum of a small number of Slater determinants multiplied by a Jastrow factor. In this paper we study the…
Importance sampling is a promising variance reduction technique for Monte Carlo simulation based derivative pricing. Existing importance sampling methods are based on a parametric choice of the proposal. This article proposes an algorithm…
The main idea of this work is that the quantum-classical isomorphism is a suitable framework for a generalization of the notion of detailed balance. The quantum-classical isomorphism is used in order to develop a Monte Carlo simulation with…
The quantum Monte Carlo (QMC) is one of the most promising many-body electronic structure approaches. It employs stochastic techniques for solving the stationary Schr\" odinger equation and for evaluation of expectation values. The key…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
The theme of the present paper is numerical integration of $C^r$ functions using randomized methods. We consider variance reduction methods that consist in two steps. First the initial interval is partitioned into subintervals and the…
Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…
This is the documentation for generating random samples from the quantum state space in accordance with a specified distribution, associated with this webpage: http://tinyurl.com/QSampling . Ready-made samples (each with at least a million…
We discuss the improvement in the accuracy of a Monte Carlo integration that can be obtained by optimization of the `a-priori weights' of the various channels. These channels may be either the strata in a stratified-sampling approach, or…
We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining…
Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where…
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…
Variational Monte Carlo methods have recently been applied to the calculation of excited states; however, it is still an open question what objective function is most effective. A promising approach is to optimize excited states using a…