  Scattering probes the internal structure of quantum systems. We calculate the
two-particle elastic scattering phase shift for a short-ranged interaction on a
quantum computer. Short-ranged interactions with a large scattering length or
shallow bound state describe a universality class that is of interest in
atomic, condensed matter, nuclear, and particle physics. The phase shift is
calculated by relating the ground state energy of the interacting particles in
a harmonic trap. The relaxation method is used as the variational quantum
eigensolver for the ground state calculation. Schmidt decomposition is used to
reduce quantum circuits nominally requiring tens of qubits to 2-qubit circuits,
thus reducing the noise in quantum measurements. Calculations in multi-particle
systems with many-body interactions would benefit from this reduction of qubits
in noisy quantum processors.
