Elastic scattering on a quantum computer

Scattering experiments are crucial for unveiling the internal structure of quantum systems. Classical computation of these many-body systems employs Monte Carlo simulations in Euclidean time, often plagued by the fermionic sign problem and usually confined to analyzing static properties. Quantum computing is emerging as the world's future technology capable of overcoming these limitations through unitary evolution in Minkowski time. In this pioneering work, we present a novel method for computing two-particle scattering phase shifts on quantum computers. Our method utilizes the Busch formula, which relates the phase shifts to the relative energy of scattering particles confined within a harmonic trap. We have modified the traditional Variational Quantum Eigensolver (VQE) by incorporating the relaxation method to accurately estimate the energy eigenvalues and eigenfunctions. We also use Schmidt decomposition to optimize the quantum circuitry, reducing the required measurements to a mere 2-qubit setup, from an initial tens of qubits, thus substantially reducing errors in current noisy quantum processors. This quantum computational approach to elastic scattering not only fosters exploration into the dynamic properties of quantum systems but also indicates potential advancements in the computations of complex many-body interactions.