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A generalized diffusion Monte Carlo method for solving the many-body Schr\"odinger equation on curved manifolds is introduced and used to perform a `fixed-phase' simulation of the fractional quantum Hall effect on the Haldane sphere. This…
Neural network quantum state (NNQS) has emerged as a promising candidate for quantum many-body problems, but its practical applications are often hindered by the high cost of sampling and local energy calculation. We develop a…
Accurate numerical solutions for the Schr\"odinger equation are of utmost importance in quantum chemistry. However, the computational cost of current high-accuracy methods scales poorly with the number of interacting particles. Combining…
Quantum Monte Carlo is an efficient technique for finding the ground-state energy and related properties of small molecules. A major challenge remains in accurate determination of a molecule's geometry, i.e. the optimal location of its…
We present an overview of the variational and diffusion quantum Monte Carlo methods as implemented in the CASINO program. We particularly focus on developments made in the last decade, describing state-of-the-art quantum Monte Carlo…
Excited states of molecules lie in the heart of photochemistry and chemical reactions. The recent development in quantum computational chemistry leads to inventions of a variety of algorithms that calculate the excited states of molecules…
Recently the general form of a translation-covariant quantum Boltzmann equation has been derived which describes the dynamics of a tracer particle in a quantum gas. We develop a stochastic wave function algorithm that enables full…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
Computer simulation plays a central role in modern day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost. Molecular crystals are a class of…
The Variational Monte Carlo method has recently seen important advances through the use of neural network quantum states. While more and more sophisticated ans\"atze have been designed to tackle a wide variety of quantum many-body problems,…
Coupled cluster theory is a vital cornerstone of electronic structure theory and is being applied to ever-larger systems. Stochastic approaches to quantum chemistry have grown in importance and offer compelling advantages over traditional…
We present a variational Monte Carlo (VMC) method that works equally well for the ground and the excited states of a quantum system. The method is based on the minimization of the variance of energy, as opposed to the energy itself in…
We investigate Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions. Several variants of the basic techniques are studied, including limiting the variations in the weighting factors which arise in…
Quantum Monte Carlo is one of the most promising approaches for dealing with large-scale quantum many-body systems. It has played an extremely important role in understanding strongly correlated physics. However, two fundamental problems,…
Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
The Markov chain Monte Carlo (MCMC) method is used to evaluate the imaginary-time path integral of a quantum oscillator with a potential that includes both a quadratic term and a quartic term whose coupling is varied by several orders of…
State-average calculations based on mixture of states are increasingly being exploited across chemistry and physics as versatile procedures for addressing excitations of quantum many-body systems. If not too many states should need to be…
The wave-function Monte-Carlo method, also referred to as the use of "quantum-jump trajectories", allows efficient simulation of open systems by independently tracking the evolution of many pure-state "trajectories". This method is ideally…
We develop a hybrid Monte Carlo method to efficiently compute the physical observables from the samplings of the Laughlin and the Moore-Read wave functions of fractional quantum Hall (FQH) systems. With the advancements in methodology,…