  Utilizing the Lehmann-Symanzik-Zimmermann reduction formula, we present a new
general framework for computing scattering amplitudes in quantum field theory
with quantum computers in a fully nonperturbative way. In this framework, one
only has to construct one-particle states of zero momentum, and no wave packets
of incoming particles are needed. The framework is able to incorporate
scatterings of bound states, and is ideal for scatterings involving a small
number of particles. We expect this framework to have particular advantages
when applied to exclusive hadron scatterings. As a proof of concept, by
simulations on classical hardware, we demonstrate that in the one-flavor
Gross-Neveu model, the fermion propagator, the connected fermion four-point
function, and the propagator of a fermion-antifermion bound state obtained from
our proposed quantum algorithm have the desired pole structure crucial to the
implementation of the Lehmann-Symanzik-Zimmermann reduction formula.
