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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…
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…
Variational wave functions used in the variational Monte Carlo (VMC) method are extensively improved to overcome the biases coming from the assumed variational form of the wave functions. We construct a highly generalized variational form…
Variational Monte Carlo (VMC) is an approach for computing ground-state wavefunctions that has recently become more powerful due to the introduction of neural network-based wavefunction parametrizations. However, efficiently training neural…
Neural-network quantum states (NQS) offer a powerful and expressive ansatz for representing quantum many-body wave functions. However, their training via Variational Monte Carlo (VMC) methods remains challenging. It is well known that some…
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…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
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…
An appropriate iterative scheme for the minimization of the energy, based on the variational Monte Carlo (VMC) technique, is introduced and compared with existing stochastic schemes. We test the various methods for the 1D Heisenberg ring…
Modern quantum Monte Carlo (QMC) methods often capture electron correlation through both explicitly correlating Jastrow factors and small to mid-sized configuration interaction (CI) expansions. Here, we study the additional optimization…
The variational quantum Monte Carlo (VQMC) method received significant attention in the recent past because of its ability to overcome the curse of dimensionality inherent in many-body quantum systems. Close parallels exist between VQMC and…
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,…
Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…
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…
Practitioners of Bayesian statistics have long depended on Markov chain Monte Carlo (MCMC) to obtain samples from intractable posterior distributions. Unfortunately, MCMC algorithms are typically serial, and do not scale to the large…
Approximate Bayesian inference for models with computationally expensive, black-box likelihoods poses a significant challenge, especially when the posterior distribution is complex. Many inference methods struggle to explore the parameter…
We develop a time-dependent variational Monte Carlo (t-VMC) method for quantum dynamics of strongly correlated electrons. The t-VMC method has been recently applied to bosonic systems and quantum spin systems. Here, we propose a…
The conventional tensor-network states employ real-space product states as reference wave functions. Here, we propose a many-variable variational Monte Carlo (mVMC) method combined with tensor networks by taking advantages of both to study…
We examine the application of the Variational Monte Carlo (VMC) method to a cluster model for halo nuclei. Particular attention is paid to the error estimate in the presence of correlations in the underlying random walk. We analyse the…
The use of neural network parametrizations to represent the ground state in variational Monte Carlo (VMC) calculations has generated intense interest in recent years. However, as we demonstrate in the context of the periodic Heisenberg spin…