We perform high resolution simulations in a scenario where the Peccei-Quinn (PQ) symmetry is broken after inflation starting at the epoch before the PQ phase transition and ending at matter-radiation equality. We characterize the spectrum of primordial perturbations that are generated and comment on implications for efforts to detect axion dark matter (DM). We also measure the DM density at different simulated masses and argue that the correct DM density is obtained for an axion mass of 25.2 ± 11.0 µeV.