Deep Learning of Fermion Sign Fluctuations

TL;DR

This paper introduces a neural network-based approach to mitigate the fermion sign problem in quantum simulations by explicitly modeling and subtracting phase fluctuations, improving computational efficiency.

Contribution

It proposes a novel neural network method to parameterize phase fluctuations, enhancing existing techniques for alleviating the fermion sign problem.

Findings

Neural networks can effectively model phase fluctuations in fermionic systems.

Combining neural networks with contour deformation improves sign problem mitigation.

Performance improves with deeper neural network architectures.

Abstract

We describe a procedure for alleviating the fermion sign problem in which phase fluctuations are explicitly subtracted from the Boltzmann factor. Several ans\"atze for fluctuations are designed and compared. In the absence of a sufficiently high-quality ansatz, a neural network can be trained to parameterize the fluctuations. Demonstrating on the staggered Thirring model in $1+1$ dimensions, we examine the performance of this method as deeper neural networks are used, and in conjunction with the well-studied contour deformation methods.