Elastic scattering on a quantum computer

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 it to 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 two-qubit circuits, thus reducing the noise in quantum measurements. Calculations in multiparticle systems with many-body interactions would benefit from this reduction of qubits in noisy quantum processors.