  Time evolution and scattering simulation in phenomenological models are of
great interest for testing and validating the potential for near-term quantum
computers to simulate quantum field theories. Here, we simulate one-particle
propagation and two-particle scattering in the one-dimensional transverse Ising
model for 3 and 4 spatial sites with periodic boundary conditions on a quantum
computer. We use the quantum Lanczos algorithm to obtain all energy levels and
corresponding eigenstates of the system. We simplify the quantum computation by
taking advantage of the symmetries of the system. These results enable us to
compute one- and two-particle transition amplitudes, particle numbers for
spatial sites, and the transverse magnetization as functions of time. The
quantum circuits were executed on IBM 5-qubit superconducting hardware. The
experimental results with readout error mitigation are in very good agreement
with the values obtained using exact diagonalization.
