# Path optimization in 0+1 dimensional QCD at finite density

## TL;DR

This paper applies a neural network-based path optimization method to mitigate the sign problem in 0+1 dimensional QCD at finite density, demonstrating significant enhancement of the average phase factor.

## Contribution

It introduces the use of neural network-optimized integration paths in gauge theories to address the sign problem, marking a novel application in this context.

## Key findings

- Average phase factor exceeds 0.99 on optimized paths
- Results are consistent with and without gauge fixing
- First application of path optimization to gauge theories

## Abstract

We investigate the sign problem in 0+1 dimensional QCD at finite chemical potential by using the path optimization method. The SU(3) link variable is complexified to the SL(3,$\mathbb{C}$) link variable, and the integral path is represented by a feedforward neural network. The integral path is then optimized to weaken the sign problem. The average phase factor is enhanced to be greater than 0.99 on the optimized path. Results with and without diagonalized gauge fixing are compared and proven to be consistent. This is the first step of applying the path optimization method to gauge theories.