Related papers: Diffusion Monte Carlo with lattice regularization
We show how the Hamiltonian Monte Carlo algorithm can sometimes be speeded up by "splitting" the Hamiltonian in a way that allows much of the movement around the state space to be done at low computational cost. One context where this is…
We introduce a theoretical approach to study the quantum-dissipative dynamics of electronic excitations in macromolecules, which enables to perform calculations in large systems and cover long time intervals. All the parameters of the…
We formulate a path-integral Monte Carlo algorithm for simulating lattice systems consisting of fictitious particles governed by a generalized exchange statistics. This method, initially proposed for continuum systems, introduces a…
We consider how different choices of kinetic energy in Hamiltonian Monte Carlo affect algorithm performance. To this end, we introduce two quantities which can be easily evaluated, the composite gradient and the implicit noise. Results are…
We present a plane-wave (PW) implementation of the auxiliary-field quantum Monte Carlo (AFQMC) method within the projector augmented-wave (PAW) formalism in the Vienna ab initio Simulation Package (VASP). By employing an exact inversion of…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
We propose a method for the numerical computation of microcanonical expectation values--i.e. averages over energy eigenstates with the same eigenvalue-without any prior knowledge about the spectrum of the Hamiltonian. This is accomplished…
A general class of loop quantizations for anisotropic models is introduced and discussed, which enhances loop quantum cosmology by relevant features seen in inhomogeneous situations. The main new effect is an underlying lattice which is…
In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing…
We present an algorithmic framework for a variant of the quantum Monte Carlo operator-loop algorithm, where non-local cluster updates are constructed in a way that makes each individual loop smaller. The algorithm is designed to increase…
We present unbiased, finite--variance estimators of energy derivatives for real--space diffusion Monte Carlo calculations within the fixed--node approximation. The derivative $d_\lambda E$ is fully consistent with the dependence…
Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the…
It is natural to investigate if the quantization of an integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of natural Hamiltonians with constants of…
Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such…
Monte Carlo is one of the most useful methods to study the quantum Hall problems. In this paper, we introduce a fast lattice Monte Carlo method based on a mathematically exact reformulation of the torus quantum Hall problems from continuum…
We present a finite-temperature canonical-ensemble determinant quantum Monte Carlo algorithm that enforces an exact fermion number and enables stable simulations of correlated lattice fermions. We propose a stabilized QR update that reduces…
Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L1 Wasserstein) distance. The lower bound for the contraction rate is…
This work is motivated by the need to study the impact of data uncertainties and material imperfections on the solution to optimal control problems constrained by partial differential equations. We consider a pathwise optimal control…
We propose a new regularization scheme to study the bound state of two-nucleon systems in Lattice Effective Field Theory. Inspired by continuum EFT calculation, we study an exponential regulator acting on the leading-order (LO) and…
Because of their robustness, efficiency and non-intrusiveness, Monte Carlo methods are probably the most popular approach in uncertainty quantification to computing expected values of quantities of interest (QoIs). Multilevel Monte Carlo…