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The standard kinetic Monte Carlo algorithm is an extremely efficient method to carry out serial simulations of dynamical processes such as thin-film growth. However, in some cases it is necessary to study systems over extended time and…
Owing to their favorable scaling with dimensionality, Monte Carlo (MC) methods have become the tool of choice for numerical integration across the quantitative sciences. Almost invariably, efficient MC integration schemes are strictly…
The development of efficient numerical methods for kinetic equations with stochastic parameters is a challenge due to the high dimensionality of the problem. Recently we introduced a multiscale control variate strategy which is capable to…
We introduce and compare three different Monte Carlo determinantal algorithms that allow one to compute dynamical quantities, such as the self-energy, of fermionic systems in their thermodynamic limit. We show that the most efficient…
If a stochastic system during some periods of its evolution can be divided into non-interacting parts, the kinetics of each part can be simulated independently. We show that this can be used in the development of efficient Monte Carlo…
By precisely writing down the matrix element of the local Boltzmann operator, we have proposed a new path integral formulation for quantum field theory and developed a corresponding Monte Carlo algorithm. With current formula, the…
Leverage score sampling is crucial to the design of randomized algorithms for large-scale matrix problems, while the computation of leverage scores is a bottleneck of many applications. In this paper, we propose a quantum algorithm to…
We demonstrate that the multicanonical approach is not restricted to Monte Carlo simulations, but can also be applied to simulation techniques such as molecular dynamics, Langevin, and hybrid Monte Carlo algorithms. The effectiveness of the…
We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a novel…
A first-order, Monte Carlo ensemble method has been recently introduced for solving parabolic equations with random coefficients in [26], which is a natural synthesis of the ensemble-based, Monte Carlo sampling algorithm and the…
We present a general approach to greatly increase at little cost the efficiency of Monte Carlo algorithms. To each observable to be computed we associate a renormalized observable (improved estimator) having the same average but a different…
Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…
The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement…
In this article we offer some modification of Monte-Carlo method for multiple parametric integral computation and solving of a linear integral Fredholm equation of a second kind (well posed problem). We prove that the rate of convergence of…
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…
We review the path-integral quantum Monte Carlo method and discuss its implementation by multiworm algorithms. We analyze in details the features of the algorithms, and focus our attention on the computation of the $N$-body density matrix…
In this paper we present a dynamical Monte Carlo algorithm which is applicable to systems satisfying a clustering condition: during the dynamical evolution the system is mostly trapped in deep local minima (as happens in glasses, pinning…
Variational quantum metrology represents a powerful tool for optimizing generic estimation strategies, combining the principles of variational optimization with the techniques of quantum metrology. Such optimization procedures result…
This article aims to summarize recent and ongoing efforts to simulate continuous-variable quantum systems using flow-based variational quantum Monte Carlo techniques, focusing for pedagogical purposes on the example of bosons in the field…
Quantum Monte Carlo integration, a quantum algorithm for calculating expectations that provides a quadratic speed-up compared to its classical counterpart, is now attracting increasing interest in the context of its industrial and…