Related papers: Monte Carlo sampling from the quantum state space.…
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…
Quantum computing was so far mainly concerned with discrete problems. Recently, E. Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, which advantages quantum computing can bring…
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…
Rydberg atom arrays have emerged as a powerful platform to simulate a number of exotic quantum ground states and phase transitions. To verify these capabilities numerically, we develop a versatile quantum Monte Carlo sampling technique…
We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…
We review the method of stochastic error correction which eliminates the truncation error associated with any subspace diagonalization. Monte Carlo sampling is used to compute the contribution of the remaining basis vectors not included in…
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…
Quantum algorithms present a quadratically improved complexity over classical ones for certain sampling tasks. For instance, the Quantum Amplitude Estimation (QAE) algorithm promises to speedup the estimation of the mean of certain…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
Expectation values of physical quantities may accurately be obtained by the evaluation of integrals within Many-Body Quantum mechanics, and these multi-dimensional integrals may be estimated using Monte Carlo methods. In a previous…
For a wide class of applications of the Monte Carlo method, we describe a general sampling methodology that is guaranteed to converge to a specified equilibrium distribution function. The method is distinct from that of Metropolis in that…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
Consider a central problem in randomized approximation schemes that use a Monte Carlo approach. Given a sequence of independent, identically distributed random variables $X_1,X_2,\ldots$ with mean $\mu$ and standard deviation at most $c…
To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important…
We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018)), where the manifold is defined by…
Computations of chemical systems' equilibrium properties and non-equilibrium dynamics have been suspected of being a "killer app" for quantum computers. This review highlights the recent advancements of quantum algorithms tackling complex…
In statistical data assimilation one seeks the largest maximum of the conditional probability distribution $P(\mathbf{X},\mathbf{p}|\mathbf{Y})$ of model states, $\mathbf{X}$, and parameters,$\mathbf{p}$, conditioned on observations…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
Quantum Monte Carlo methods are first-principle approaches that approximately solve the Schr\"odinger equation stochastically. As compared to traditional quantum chemistry methods, they offer important advantages such as the ability to…
The preferential sampling of locations chosen to observe a spatio-temporal process has been identified as a major problem across multiple fields. Predictions of the process can be severely biased when standard statistical methodologies are…