Related papers: The Monte Carlo method in quantum field theory
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
Quantum-enhanced Markov chain Monte Carlo, an algorithm in which configurations are proposed through a measured quantum quench and accepted or rejected by a classical algorithm, has been proposed as a possible method for robust quantum…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
In lattice quantum field theory studies, parameters defining the lattice theory must be tuned toward criticality to access continuum physics. Commonly used Markov chain Monte Carlo (MCMC) methods suffer from critical slowing down in this…
We review the use of the path integral Monte Carlo (PIMC) methodology to the study of finite-size quantum clusters, with particular emphasis on recent applications to pure and impurity-doped He clusters. We describe the principles of PIMC,…
The Diffusion Monte Carlo method with constant number of walkers, also called Stochastic Reconfiguration as well as Sequential Monte Carlo, is a widely used Monte Carlo methodology for computing the ground-state energy and wave function of…
This paper shows how one can use Sequential Monte Carlo methods to perform what is typically done using Markov chain Monte Carlo methods. This leads to a general class of principled integration and genetic type optimization methods based on…
This book aims to provide a graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC) algorithms, as applied broadly in the Bayesian computational context. Most, if not all of these topics (stochastic gradient MCMC,…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
A Path Integral Monte Carlo method is used to investigate the thermodynamics of nuclear like systems. Systems composed of bosons or fermions interracting via a Lennard-Jones potential with periodic boundary conditions were simulated and the…
We perform a comprehensive analysis of the quantum-enhanced Monte Carlo method [Nature, 619, 282-287 (2023)], aimed at identifying the optimal working point of the algorithm. We observe an optimal mixing Hamiltonian strength and analyze the…
It is commonly admitted that non-reversible Markov chain Monte Carlo (MCMC) algorithms usually yield more accurate MCMC estimators than their reversible counterparts. In this note, we show that in addition to their variance reduction…
Adaptive Markov chain Monte Carlo (MCMC) algorithms, which automatically tune their parameters based on past samples, have proved extremely useful in practice. The self-tuning mechanism makes them `non-Markovian', which means that their…
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…
A theoretical investigation of quantum-transport phenomena in mesoscopic systems is presented. In particular, a generalization to ``open systems'' of the well-known semiconductor Bloch equations is proposed. The presence of spatial boundary…
The Metropolis-Hastings algorithm is a cornerstone of Markov Chain Monte Carlo methods, underpinning a wide range of applications in computational physics, Bayesian inference, and machine learning. Quantum variants of Metropolis-Hastings…
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…
High-dimensional multimodal sampling problems from lattice field theory (LFT) have become important benchmarks for machine learning assisted sampling methods. We show that GPU-accelerated particle methods, Sequential Monte Carlo (SMC) and…
This review paper, written for the second edition of the Handbook of Markov Chain Monte Carlo, provides an introduction to the study of convergence analysis for Markov chain Monte Carlo (MCMC), aimed at researchers new to the field. We…
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…