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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…
Quantum nanosystems involve the coupled dynamics of fermions or bosons across multiple scales in space and time. Examples include quantum dots, superconducting or magnetic nanoparticles, molecular wires, and graphene nanoribbons. The number…
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…
We develop a formalism and present an algorithm for optimization of the trial wave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. We take advantage of a basic property of the walker configuration distribution…
Quantum Monte Carlo (QMC) methods offer exact solutions for quantum many-body systems but face severe limitations in fermionic systems like atomic nuclei due to the sign problem. While sign-problem-free QMC algorithms exist and provide…
Treating the fermionic ground state problem as a constrained stochastic optimization problem, a formalism for fermionic quantum Monte Carlo is developed that makes no reference to a trial wavefunction. Exchange symmetry is enforced by…
Fixed node diffusion quantum Monte Carlo (FN-DMC) is an increasingly used computational approach for investigating the electronic structure of molecules, solids, and surfaces with controllable accuracy. It stands out among equally accurate…
We propose neural control variates (NCV) for unbiased variance reduction in parametric Monte Carlo integration. So far, the core challenge of applying the method of control variates has been finding a good approximation of the integrand…
Variational methods have proven to be excellent tools to approximate ground states of complex many body Hamiltonians. Generic tools like neural networks are extremely powerful, but their parameters are not necessarily physically motivated.…
mVMC (many-variable Variational Monte Carlo) is an open-source software based on the variational Monte Carlo method applicable for a wide range of Hamiltonians for interacting fermion systems. In mVMC, we introduce more than ten thousands…
This study explores the application of neural network variational Monte Carlo (NN-VMC) for the computation of low-lying excited states in molecular systems. Our focus lies on the implementation and evaluation of two distinct methodologies,…
Solving the quantum many-body Schr\"odinger equation is a fundamental and challenging problem in the fields of quantum physics, quantum chemistry, and material sciences. One of the common computational approaches to this problem is Quantum…
We investigate the use of variational wave-functions that mimic stochastic recurrent neural networks, specifically, unrestricted Boltzmann machines, as guiding functions in projective quantum Monte Carlo (PQMC) simulations of quantum spin…
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…
Solving the Schr\"{o}dinger equation for interacting many-body quantum systems faces computational challenges due to exponential scaling with system size. This complexity limits the study of important phenomena in materials science and…
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…
Solving the Schr\"odinger equation is key to many quantum mechanical properties. However, an analytical solution is only tractable for single-electron systems. Recently, neural networks succeeded at modeling wave functions of many-electron…
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…
We propose a general framework for finding the ground state of many-body fermionic systems by using feed-forward neural networks. The anticommutation relation for fermions is usually implemented to a variational wave function by the Slater…
Deep neural networks have been extremely successful as highly accurate wave function ans\"atze for variational Monte Carlo calculations of molecular ground states. We present an extension of one such ansatz, FermiNet, to calculations of the…