  Simulations of scattering processes are essential in understanding the
physics of our universe. Computing relevant scattering quantities from ab
initio methods is extremely difficult on classical devices because of the
substantial computational resources needed. This work reports the development
of an algorithm that makes it possible to obtain phase shifts for generic
non-relativistic elastic scattering processes on a quantum computer. This
algorithm is based on extracting phase shifts from the direct implementation of
the real-time evolution. The algorithm is improved by a variational procedure,
making it more accurate and resistant to the quantum noise. The reliability of
the algorithm is first demonstrated by means of classical numerical simulations
for different potentials, and later tested on existing quantum hardware,
specifically on IBM quantum processors.
