Scattering in the Ising model with the quantum Lanczos algorithm ^*

Abstract Time evolution and scattering simulation in phenomenological models are of great interest for testing validating the potential near-term quantum computers to simulate field theories. Here, we one-particle propagation two-particle one-dimensional transverse Ising model 3 4 spatial sites with periodic boundary conditions on a computer. We use Lanczos algorithm obtain all energy levels corresponding eigenstates system. simplify computation by taking advantage symmetries These results enable us compute one- transition amplitudes, particle numbers sites, magnetization as functions time. The circuits were executed various IBM Q superconducting hardware. experimental very good agreement values obtained using exact diagonalization.