Elastic scattering on a quantum computer

TL;DR

This paper demonstrates how to compute elastic scattering phase shifts of two particles with short-range interactions on a quantum computer, using variational methods and circuit reduction techniques to mitigate noise.

Contribution

It introduces a method to calculate scattering phase shifts on quantum computers by relating ground state energies to phase shifts, employing circuit reduction via Schmidt decomposition.

Findings

Successfully computed phase shifts using reduced qubit circuits.

Demonstrated the approach's potential for multi-particle systems.

Reduced quantum circuit complexity to improve measurement accuracy.

Abstract

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.