In a seminal paper on quantum computation of scattering amplitudes, Jordan, Lee and Preskill motivate their work by stating that perturbative series for real-time evolution 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 expansionswith finite radius of convergence for lambda phi four theories. We discuss the complex singularities and compare the computational resources needed.