Quantum mean estimation for lattice field theory
Erik Gustafson, Henry Lamm, Judah Unmuth-Yockey · Physical review. D/Physical review. D. · 2023
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 $\ensuremath{\pi}$ 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.