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We investigate the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable…
Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…
Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious…
This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The…
Quantum Monte Carlo simulations are powerful and versatile tools for the quantum many-body problem. In addition to the usual calculations of energies and eigenstate observables, quantum Monte Carlo simulations can in principle be used to…
We introduce a novel many body method which combines two powerful many body techniques, viz., quantum Monte Carlo and coupled cluster theory. Coupled cluster wave functions are introduced as importance functions in a Monte Carlo method…
We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a novel…
Auxiliary-field quantum Monte Carlo methods enable the calculation of thermal and ground state properties of correlated quantum many-body systems in model spaces that are many orders of magnitude larger than those that can be treated by…
We investigate the inclusion of variable spins in electronic structure quantum Monte Carlo, with a focus on diffusion Monte Carlo with Hamiltonians that include spin-orbit interactions. Following our previous introduction of fixed-phase…
We investigate how the fixed-node diffusion Monte Carlo energy of solids depends on single-particle orbitals used in Slater--Jastrow wave functions. We demonstrate that the dependence can be significant, in particular in the case of 3d…
Quantum algorithms offer the potential for significant computational advantages; however, in many cases, it remains unclear how these advantages can be practically realized. Causal Set Theory is a discrete, Lorentz-invariant approach to…
Localized orbitals are important for modeling and interpreting complicated electronic structures of atoms and molecules in a chemically meaningful way. Here, we present the parameter-free procedure for transforming delocalized molecular…
We propose a new treatment for the quantum three-body problem. It is based on an expansion of the wave function on harmonic oscillator functions with different sizes in the Jacobi coordinates. The matrix elements of the Hamiltonian can be…
Quantum computing offers an alternative paradigm for addressing combinatorial optimization problems compared to classical computing. Despite recent hardware improvements, the execution of empirical quantum optimization experiments at scales…
We investigate in this work a recently proposed diagrammatic quantum Monte Carlo method --- the inchworm Monte Carlo method --- for open quantum systems. We establish its validity rigorously based on resummation of Dyson series. Moreover,…
A numerical integration method for guiding-center orbits of charged particles in toroidal fusion devices with three-dimensional field geometry is described. Here, high order interpolation of electromagnetic fields in space is replaced by a…
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…
We demonstrate how to determine numerically nearly exact orthonormal orbitals that are optimal for evaluation of the energy of arbitrary (correlated) states of atoms and molecules by minimization of the energy Lagrangian. Orbitals are…
Methods for electronic structure based on Gaussian and molecular orbital discretizations offer a well established, compact representation that forms much of the foundation of correlated quantum chemistry calculations on both classical and…
A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…