# Polynomial complexity despite the fermionic sign

## TL;DR

This paper demonstrates that for certain Feynman diagrammatic Monte Carlo methods, the computational complexity grows only polynomially with inverse error, challenging the notion that the fermionic sign problem leads to exponential difficulty.

## Contribution

It shows that specific Monte Carlo approaches to fermionic problems can have polynomial complexity despite the sign problem, offering a new perspective on computational feasibility.

## Key findings

- Computational time increases polynomially with inverse error.
- Challenges the belief that the sign problem causes exponential complexity.
- Applicable to convergent Feynman diagrammatic series.

## Abstract

It is commonly believed that in quantum Monte Carlo approaches to fermionic many- body problems, the infamous sign problem generically implies prohibitively large computational times for obtaining thermodynamic-limit quantities. We point out that for convergent Feynman diagrammatic series evaluated with the Monte Carlo algorithm of [Rossi, arXiv:1612.05184], the computational time increases only polynomially with the inverse error on thermodynamic-limit quantities.