Related papers: Heavy-tailed random error in quantum Monte Carlo
Concentrating on zero temperature Quantum Monte Carlo calculations of electronic systems, we give a general description of the theory of finite size extrapolations of energies to the thermodynamic limit based on one and two-body correlation…
We perform \emph{ab initio} quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with linear response theory we are able to remove finite-size errors from the…
We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs when a functional of the solution to the model is below (or…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
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…
In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted…
The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio $s/d$, where $s$ and $d$ encode the…
Quantum Monte Carlo (QMC) methods have received considerable attention over the last decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling…
This paper addresses the key challenge of estimating the asymptotic covariance associated with the Markov chain central limit theorem, which is essential for visualizing and terminating Markov Chain Monte Carlo (MCMC) simulations. We focus…
A review of the Loop Algorithm, its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a Quantum Monte Carlo procedure which employs nonlocal changes of worldline configurations,…
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 particle-based algorithms, the effect of binary collisions is commonly described in a statistical way, using Monte Carlo techniques. It is shown that, in the relativistic regime, stringent constraints should be considered on the sampling…
We consider the one-dimensional quantum-statistical problem of interacting spin-less particles in an infinite deep potential valley and on a ring. Several limits for the applicability of the Quantum Monte Carlo (QMC) methods were revealed…
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 problem of estimating the probability p=P(g(X<0) is considered when X represents a multivariate stochastic input of a monotone function g. First, a heuristic method to bound p is formally described, involving a specialized design of…
We revisit the infinite variance problem in fermionic Monte Carlo simulations, which is widely encountered in areas ranging from condensed matter to nuclear and high-energy physics. The different algorithms, which we broadly refer to as…
Quantum computing using two optical coherent states as qubit basis states has been suggested as an interesting alternative to single photon optical quantum computing with lower physical resource overheads. These proposals have been…
We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…
When a system undergoes a quantum phase transition, the ground-state wave-function shows a change of nature, which can be monitored using the fidelity concept. We introduce two Quantum Monte Carlo schemes that allow the computation of…
We propose a method for eliminating the truncation error associated with any subspace diagonalization calculation. The new method, called stochastic error correction, uses Monte Carlo sampling to compute the contribution of the remaining…