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A revised iterative method based on Green function defined by quadratures along a single trajectory is proposed to solve the low-lying quantum wave function for Schroedinger equation. Specially a new expression of the perturbed energy is…
The phase space slicing method of two cutoffs for next-to-leading-order Monte-Carlo style QCD corrections has been applied to many physics processes. The method is intuitive, simple to implement, and relies on a minimum of process dependent…
State-space models are commonly used to describe different forms of ecological data. We consider the case of count data with observation errors. For such data the system process is typically multi-dimensional consisting of coupled Markov…
In this study we present an optimization method based on the quantum Monte Carlo diagonalization for many-fermion systems. Using the Hubbard-Stratonovich transformation, employed to decompose the interactions in terms of auxiliary fields,…
A self-contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a…
The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
Variational wave function ansatze are an invaluable tool to study the properties of strongly correlated systems. We propose such a wave function, based on the theory of auxiliary fields and combining aspects of auxiliary-field quantum Monte…
An efficient multigrid Monte-Carlo algorithm for calculating the ground state of the hydrogen atom using path integral is presented. The algorithm uses a unigrid approach. The action integral near r=0 is modified so that the correct values…
We describe a path-integral ground-state quantum Monte Carlo method for light nuclei in continuous space. We show how to efficiently update and sample the paths with spin-isospin dependent and spin-orbit interactions. We apply the method to…
In this work we develop tools that enable the study of non-adiabatic effects with variational and diffusion Monte Carlo methods. We introduce a highly accurate wave function ansatz for electron-ion systems that can involve a combination of…
Inclusive semileptonic decays are discussed in the framework of heavy quark effective field theory by employing the short distance expansion in the effective theory. The lowest order term turns out to be the parton model; the higher order…
The concept of effective order is a popular methodology in the deterministic literature for the construction of efficient and accurate integrators for differential equations over long times. The idea is to enhance the accuracy of a…
Real-time calculations in tensor networks are strongly limited in time by entanglement growth, restricting the achievable frequency resolution of Green's functions, spectral functions, self-energies, and other related quantities. By…
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…
In this study, we develop an extended implicit moment method, namely, a coupled high-order low-order (HOLO) method and apply it to the electromagnetic Vlasov-Darwin model. The high-order (HO) system evolves particles in a manner that…
We present a formulation of the Constrained Path Monte Carlo (CPMC) method for fermions that uses trial wave-functions that include many-body effects. This new formulation allows us to implement a whole family of generalized mean-field…
We propose quantum algorithms for projective ground-state preparation and calculations of the many-body Green's functions directly in frequency domain. The algorithms are based on the linear combination of unitary (LCU) operations and…
Standard quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations but require a circuit depth that scales as inverse of the estimation error. In view of the shallow depth in near-term devices, the…
We provide quantitative inductive estimates for Green's functions of matrices with (sub)expoentially decaying off diagonal entries in higher dimensions. Together with Cartan's estimates and discrepancy estimates, we establish explicit…