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 a sign problem, and is insensitive to critical slowing down. The algorithm is used to compute with and without a sign problem, a toy U (1) gauge theory model, and the Ising model. The effect of Rₙ-gate synthesis errors on a future fault-tolerant quantum computer is investigated.