Related papers: A Multi-level Algorithm for Quantum-impurity Model…
The Monte Carlo method is a thriving and mathematically beautiful numerical technique used extensively, nowadays, to deal with many demanding problems in diverse fields. Here, we present an iterative Monte Carlo algorithm to work out very…
We discuss the sign problem arising in Monte Carlo simulations of frustrated quantum spin systems. We show that for a class of ``semi-frustrated'' systems (Heisenberg models with ferromagnetic couplings $J_z(r) < 0$ along the $z$-axis and…
We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
Monte Carlo simulations are a powerful tool for elucidating the properties of complex systems across many disciplines. Not requiring any a priori knowledge, they are particularly well suited for exploring new phenomena. However, when…
We propose a multi-index algorithm for the Monte Carlo (MC) discretization of a linear, elliptic PDE with affine-parametric input. We prove an error vs. work analysis which allows a multi-level finite-element approximation in the physical…
Standard quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations but require a circuit depth that scales as inverse of the estimation error. In view of the shallow depth in near-term devices, the…
We present a Maximum Entropy method (MEM) for obtaining dynamical spectra from Quantum Monte Carlo data which have a sign problem. By relating the sign fluctuations to the norm of the spectra, our method properly treats the correlations…
Interacting single-level quantum dot connected to BCS superconducting leads represents a well-controllable system to study the interplay between the correlation effects and the electron pairing that can result in a $0-\pi$ (singlet-doublet)…
A versatile and efficient variational approach is developed to solve in- and out-of-equilibrium problems of generic quantum spin-impurity systems. Employing the discrete symmetry hidden in spin-impurity models, we present a new canonical…
The computational complexity of simulating quantum many-body systems generally scales exponentially with the number of particles. This enormous computational cost prohibits first principles simulations of many important problems throughout…
As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…
We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random coefficients. We focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter, and…
Nested Monte Carlo is widely used for risk estimation, but its efficiency is limited by the discontinuity of the indicator function and high computational cost. This paper proposes a nested Multilevel Monte Carlo (MLMC) method combined with…
Quantum Monte Carlo algorithms based on a world-line representation such as the worm algorithm and the directed loop algorithm are among the most powerful numerical techniques for the simulation of non-frustrated spin models and of bosonic…
We discuss the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification in subsurface flow modeling. We give a brief…
We use tensor network techniques to obtain high order perturbative diagrammatic expansions for the quantum many-body problem at very high precision. The approach is based on a tensor train parsimonious representation of the sum of all…
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…
In this paper we propose a general framework for the uncertainty quantification of quantities of interest for high-contrast single-phase flow problems. It is based on the generalized multiscale finite element method (GMsFEM) and multilevel…