Quantum mean estimation for lattice field theory

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 sign problem, and is insensitive to critical slowing down. The used compute $\pi$ with without toy U(1) gauge theory model, Ising model. effect $R_{Z}$-gate synthesis errors future fault-tolerant computer investigated.