# Quantum mean estimation for lattice field theory

## TL;DR

This paper applies quantum mean estimation to lattice field theories, achieving quadratic speedup over classical Monte Carlo methods, and explores its robustness against sign problems and errors in quantum gates.

## Contribution

It demonstrates the effectiveness of quantum mean estimation in lattice field theories, including models with sign problems and error analysis for fault-tolerant quantum computing.

## Key findings

- Quadratic advantage over Monte Carlo methods.
- Effective in presence of sign problems and critical slowing down.
- Analyzed impact of gate synthesis errors on quantum algorithms.

## Abstract

We demonstrate the quantum mean estimation algorithm on Euclidean lattice field theories. This shows a quadratic advantage over Monte Carlo methods which persists even in presence of a sign problem, and is insensitive to critical slowing down. The algorithm is used to compute $\pi$ with and without a sign problem, a toy U(1) gauge theory model, and the Ising model. The effect of $R_{Z}$-gate synthesis errors on a future fault-tolerant quantum computer is investigated.