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Computing accurate yet efficient approximations to the solutions of the electronic Schr\"odinger equation has been a paramount challenge of computational chemistry for decades. Quantum Monte Carlo methods are a promising avenue of…
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…
We present a continuous-time Monte Carlo method for quantum impurity models, which combines a weak-coupling expansion with an auxiliary-field decomposition. The method is considerably more efficient than Hirsch-Fye and free of time…
Bayesian parametric analytic continuation (BPAC) is proposed for the analytic continuation of noisy imaginary-time Green's function data as, e.g., obtained by continuous-time quantum Monte Carlo simulations (CTQMC). Within BPAC, the…
In this paper, we propose a new analytic continuation method to extract real frequency spectral functions from imaginary frequency Green's functions of quantum many-body systems. This method is based on the pole representation of Matsubara…
We present VegasFlow, a new software for fast evaluation of high dimensional integrals based on Monte Carlo integration techniques designed for platforms with hardware accelerators. The growing complexity of calculations and simulations in…
The realization of novel technological opportunities given by computational and autonomous materials design requires efficient and effective frameworks. For more than two decades, aflow++ (Automatic-Flow Framework for Materials Discovery)…
A detailed description is provided of a new Worm Algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within 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…
Recently Han and Heary proposed an approach to steady-state quantum transport through mesoscopic structures, which maps the non-equilibrium problem onto a family of auxiliary quantum impurity systems subject to imaginary voltages. We employ…
Wave-function Monte Carlo methods are an important tool for simulating quantum systems, but the standard method cannot be used to simulate decoherence in continuously measured systems. Here we present a new Monte Carlo method for such…
We briefly review the principles, mathematical bases, numerical shortcuts and applications of fast random walk (FRW) algorithms. This Monte Carlo technique allows one to simulate individual trajectories of diffusing particles in order to…
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo…
Finite-temperature quantum field theories are formulated in terms of Green's functions and self-energies on the Matsubara axis. In multi-orbital systems, these quantities are related to positive semidefinite matrix-valued functions of the…
We used methods of Bayesian statistical inference and the principle of maximum entropy to analytically continue imaginary-time Green's function generated in quantum Monte Carlo simulations to obtain the real-time Green's functions. For test…
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…
Monte Carlo simulation is one of the most important tools in the study of diffusion processes. For constant diffusion coefficients, an appropriate Gaussian distribution of particle's steplengths can generate exact results, when compared…
The auxiliary-field quantum Monte Carlo (AFQMC) method provides a computational framework for solving the time-independent Schroedinger equation in atoms, molecules, solids, and a variety of model systems by stochastic sampling. We…
New model-independent compact representations of imaginary-time data are presented in terms of the intermediate representation (IR) of analytical continuation. This is motivated by a recent numerical finding by the authors [J. Otsuki et…
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…