Learning the generating functional for variance reduction in lattice QCD

2026-06-14

AI Summary

This work addresses the challenge of excessive variance in computing N-point correlation functions in lattice quantum chromodynamics by introducing, for the first time, a method that combines normalizing flows with the generating functional of quantum field theory. By modeling derivatives of the source operator within this framework, the authors systematically construct low-variance estimators for correlation functions. The approach is universally applicable to arbitrary bosonic operators and asymptotically approaches the theoretically optimal noise-free estimator. Numerical experiments on glueball correlators and Wilson loops demonstrate variance reductions of up to three orders of magnitude, substantially enhancing both computational efficiency and precision.

Abstract

The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators. We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary $N$-point correlation functions of bosonic operators in lattice gauge field theory calculations by encoding a representation of the generating functional. We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework. We demonstrate this methodology with applications to calculations of glueball correlation functions and Wilson loops in Quantum Chromodynamics and Yang-Mills theory. The results show up to three orders of magnitude variance reduction.

Problem

• variance reduction
• lattice QCD
• correlation functions
• generating functional
• glueball

Innovation

• generating functional
• normalizing flows
• variance reduction
• lattice QCD
• correlation functions