Perturbative boundaries of quantum advantage in lattice field theory

In a seminal paper on quantum computation of scattering amplitudes, Jordan, Lee and Preskill motivate their work by stating that perturbative series do not converge. 

However, when digitizations and truncations are introduced, this statement needs to be revisited. We show that finite harmonic digitizations lead to weak and strong coupling expansions

with finite radius of convergence for lambda phi four theories. We compare the computational resources needed. We also discuss converging perturbative methods used to describe 

analog simulators for the Abelian Higgs model based on configurable Rydberg atom arrays.