# Improving Polynomial-filtered Hybrid Monte Carlo With Hasenbusch

## TL;DR

This paper compares and combines polynomial filtering with Hasenbusch preconditioning in Hybrid Monte Carlo for lattice QCD, demonstrating a speedup and easier tuning on a small lattice with Wilson fermions.

## Contribution

It introduces a novel combination of polynomial and Hasenbusch filters, improving efficiency and simplifying parameter tuning in HMC simulations.

## Key findings

- Combined filters outperform standard Hasenbusch filters in speed.
- The new method simplifies the tuning process.
- Speedup observed on a small lattice with Wilson fermions.

## Abstract

The predominant method for generating Lattice QCD configurations is Hybrid Monte Carlo (HMC). In order to speed up this generation, a wide range of preconditioning techniques that modify the lattice action have been devised. This work compares the performance of the well-known Hasenbusch preconditioning technique with the polynomial filtering technique on a small $16^3 \times 32$ lattice with two flavours of Wilson fermions at a pion mass $M_{\pi} \sim 400~\mathrm{MeV}$. We explore a novel method of combining polynomial and Hasenbusch filters, revealing a speedup when compared to the standard two Hasenbusch filters. This comes with the added advantage of simplified tuning.