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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…

Solving the ground state of quantum many-body systems remains a fundamental challenge in physics and chemistry. Recent advancements in quantum hardware have opened new avenues for addressing this challenge. Inspired by the quantum-enhanced…

Variational optimization of neural-network representations of quantum states has been successfully applied to solve interacting fermionic problems. Despite rapid developments, significant scalability challenges arise when considering…

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively.…

Variational inference lies at the core of many state-of-the-art algorithms. To improve the approximation of the posterior beyond parametric families, it was proposed to include MCMC steps into the variational lower bound. In this work we…

A faithful description of chemical processes requires exploring extended regions of the molecular potential energy surface (PES), which remains challenging for strongly correlated systems. Transferable deep-learning variational Monte Carlo…

One of the open challenges in quantum computing is to find meaningful and practical methods to leverage quantum computation to accelerate classical machine learning workflows. A ubiquitous problem in machine learning workflows is sampling…

We propose an end-to-end integrated strategy to produce highly accurate quantum chemistry (QC) synthetic datasets (energies and forces) aimed at deriving Foundation Machine Learning models for molecular simulation. Starting from Density…

We provide theoretical convergence bounds for the variational Monte Carlo (VMC) method as applied to optimize neural network wave functions for the electronic structure problem. We study both the energy minimization phase and the supervised…

When combined with highly expressive ansatz functions such as neural quantum states, variational Monte Carlo (VMC) constitutes a versatile numerical approach to tackle the quantum many-body problem in and out of equilibrium. However, its…

Neural-network quantum states (NQS) offer a versatile and expressive alternative to traditional variational ans\"atze for simulating physical systems. Energy-based frameworks, like Hopfield networks and Restricted Boltzmann Machines,…

We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on…

Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption,…

Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining…

Monte Carlo (MC) simulations are essential computational approaches with widespread use throughout all areas of science. We present a method for accelerating lattice MC simulations using fully connected and convolutional artificial neural…

We investigate the challenge of classical simulation of unitary quantum dynamics with variational Monte Carlo approaches, addressing the instabilities and high computational demands of existing methods. By systematically analyzing the…

We introduce forward-backward stochastic differential equations, highlighting the connection between solutions of these and solutions of partial differential equations, related by the Feynman-Kac theorem. We review the technique of…

Sequential Monte Carlo (SMC), or particle filtering, is a popular class of methods for sampling from an intractable target distribution using a sequence of simpler intermediate distributions. Like other importance sampling-based methods,…

Variational Bayesian Monte Carlo (VBMC) is a recently introduced framework that uses Gaussian process surrogates to perform approximate Bayesian inference in models with black-box, non-cheap likelihoods. In this work, we extend VBMC to deal…

Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in some areas of application to quantum theories computational progress has been slow. Here we…