Related papers: Numerical stability of force-gradient integrators …
We present initial results on Hessian-free force-gradient integrators for lattice field theories. Integrators of this framework promise to provide substantial performance enhancements, particularly for larger lattice volumes where…
We propose a new framework of Hessian-free force-gradient integrators that do not require the analytical expression of the force-gradient term based on the Hessian of the potential. Due to that the new class of decomposition algorithms for…
We study a novel class of numerical integrators, the adapted nested force-gradient schemes, used within the molecular dynamics step of the Hybrid Monte Carlo (HMC) algorithm. We test these methods in the Schwinger model on the lattice, a…
We show how the integrators used for the molecular dynamics step of the Hybrid Monte Carlo algorithm can be further improved. These integrators not only approximately conserve some Hamiltonian $H$ but conserve exactly a nearby shadow…
We discuss an instability in the leapfrog integration algorithm, widely used in current Hybrid Monte Carlo (HMC) simulations of lattice QCD. We demonstrate the instability in the simple harmonic oscillator (SHO) system where it is manifest.…
We investigate instability and reversibility within Hybrid Monte Carlo simulations using a non-perturbatively improved Wilson action. We demonstrate the onset of instability as tolerance parameters and molecular dynamics step sizes are…
Exponential integrators are a well-known class of time integration methods that have been the subject of many studies and developments in the past two decades. Surprisingly, there have been limited efforts to analyze their stability and…
The rich non-linear dynamics of the coupled oscillators (under second harmonic injection) can be leveraged to solve computationally hard problems in combinatorial optimization such as finding the ground state of the Ising Hamiltonian. While…
This review gives an overview on the research of algorithms for dynamical fermions used in large scale lattice QCD simulations. First a short overview on the state-of-the-art of ensemble generation at the physical point is given. Followed…
In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to…
A practical and simple stable method for calculating Fourier integrals is proposed, effective both at low and at high frequencies. An approach based on the fruitful idea of Levin, to use of the collocation method to approximate the slowly…
First results of a recently started simulation of full QCD with two flavours of sea-quarks at a coupling of $\beta = 5.6$ on a $16^3 \times 32$ lattice are presented. Emphasis is laid on the statistical significance that can be achieved by…
We study efficiency of higher order integrator schemes for the hybrid Monte Carlo (HMC) algorithm. Numerical tests are performed for Quantum Chromo Dynamics (QCD) with two flavors of Wilson fermions. We compare 2nd, 4th and 6th order…
Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments…
We propose a modification of the Hybrid-Monte-Carlo algorithm that allows for a larger step-size of the integration scheme at constant acceptance rate. The key ingredient is the splitting of the pseudo-fermion action into two parts. We test…
In this paper, we derive a variational integrator for certain highly oscillatory problems in mechanics. To do this, we take a new approach to the splitting of fast and slow potential forces: rather than splitting these forces at the level…
Hamiltonian Poisson integrators are Poisson integrators that admit a modified Hamiltonian. In this article, we illustrate the importance of the existence of a modified Hamiltonian for Poisson integrators in the context of integrable and…
We develop an implementation for a recently proposed Noisy Monte Carlo approach to the simulation of lattice QCD with dynamical fermions by incorporating the full fermion determinant directly. Our algorithm uses a quenched gauge field…
We propose various improvements of finite step-size updating for full QCD on the lattice that might turn finite step-size updating into a viable alternative to the hybrid Monte Carlo algorithm. These improvements are noise reduction of the…
We show how to improve the molecular dynamics step of Hybrid Monte Carlo, both by tuning the integrator using Poisson brackets measurements and by the use of force gradient integrators. We present results for moderate lattice sizes.