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Variational Bayes (VB) is a popular tool for Bayesian inference in statistical modeling. Recently, some VB algorithms are proposed to handle intractable likelihoods with applications such as approximate Bayesian computation. In this paper,…
We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove…
The optimization of neural wave functions in variational Monte Carlo crucially relies on a robust convergence criterion. While the energy variance is theoretically a definitive measure, its practical application as a primary convergence…
Many probabilistic models of interest in scientific computing and machine learning have expensive, black-box likelihoods that prevent the application of standard techniques for Bayesian inference, such as MCMC, which would require access to…
Obtaining accurate solutions to the Schr\"odinger equation is the key challenge in computational quantum chemistry. Deep-learning-based Variational Monte Carlo (DL-VMC) has recently outperformed conventional approaches in terms of accuracy,…
We revisit the accuracy of the variational Monte Carlo (VMC) method by taking an example of ground state properties for the one-dimensional Hubbard model. We start from the variational wave functions with the Gutzwiller and long-range…
The VB-QMC method is presented in this chapter. It consists of using in quantum Monte Carlo (QMC) approaches with a wave function expressed as a usually short expansion of classical Valence-Bond (VB) structures supplemented by a Jastrow…
The fixed node diffusion Monte Carlo (DMC) method has attracted interest in recent years as a way to calculate properties of solid materials with high accuracy. However, the framework for the calculation of properties such as total…
Neural network parametrizations have increasingly been used to represent the ground and excited states in variational Monte Carlo (VMC) with promising results. However, traditional VMC methods only optimize the wave function in regions of…
This paper considers the problem of sampling from non-logconcave distribution, based on queries of its unnormalized density. It first describes a framework, Denoising Diffusion Monte Carlo (DDMC), based on the simulation of a denoising…
Variational Monte Carlo (VMC) is a powerful and fast-growing method for optimizing and evolving parameterized many-body wave functions, especially with modern neural-network quantum states. In practice, however, the stochastic estimators…
We investigate the use of different variational principles in quantum Monte Carlo, namely energy and variance minimization, prompted by the interest in the robust and accurate estimate of electronic excited states. For two prototypical,…
We propose to compute physical properties by Monte Carlo calculations using conditional expectation values. The latter are obtained on top of the usual Monte Carlo sampling by partitioning the physical space in several subspaces or…
Conditional Monte Carlo (CMC) has been widely used for sensitivity estimation with discontinuous integrands as a standard simulation technique. A major limitation of using CMC in this context is that finding conditioning variables to ensure…
The parameter derivative of the expectation value of the energy, $\partial E/\partial p$, is a key ingredient in variational quantum Monte Carlo (VMC) wave function optimization methods. In some cases, a na\"ive Monte Carlo estimate of this…
We develop a formalism to directly evaluate the matrix of force constants within a Quantum Monte Carlo calculation. We utilize the matrix of force constants to accurately relax the positions of atoms in molecules and determine their…
We present a new unbiased algorithm that estimates the expected value of f(U) via Monte Carlo simulation, where U is a vector of d independent random variables, and f is a function of d variables. We assume that f does not depend equally on…
Expectation values of physical quantities may accurately be obtained by the evaluation of integrals within Many-Body Quantum mechanics, and these multi-dimensional integrals may be estimated using Monte Carlo methods. In a previous…
We propose a new variational Monte Carlo (VMC) method with an energy variance extrapolation for large-scale shell-model calculations. This variational Monte Carlo is a stochastic optimization method with a projected correlated condensed…
Variational Monte Carlo (VMC) methods are used to sample classically from distributions corresponding to quantum states which have an efficient classical description. VMC methods are based on performing a number of steps of a Markov chain…