Real-time quantum calculations of phase shifts using wave packet time delays

TL;DR

This paper introduces a quantum computing method to determine phase shifts in scattering processes by analyzing wave packet time delays during real-time evolution, suitable for noisy quantum devices.

Contribution

It presents a novel approach to extract phase shifts using real-time quantum evolution, applicable to current noisy quantum hardware and scalable to larger systems.

Findings

Successfully implemented in 1+1 dimensions on IBM quantum computers.

Demonstrated consistency with numerical results in quantum mechanics and quantum field theory.

Discussed finite volume effects and scalability for larger quantum computations.

Abstract

We present a method to extract the phase shift of a scattering process using the real-time evolution in the early and intermediate stages of the collision in order to estimate the time delay of a wave packet. This procedure is convenient when using noisy quantum computers for which the asymptotic out-state behavior is unreachable. We demonstrate that the challenging Fourier transforms involved in the state preparation and measurements can be implemented in $1+1$ dimensions with current trapped ion devices and IBM quantum computers. We compare quantum computation of the time delays obtained in the one-particle quantum mechanics limit and the scalable quantum field theory formulation with accurate numerical results. We discuss the finite volume effects in the Wigner formula connecting time delays to phase shifts. The results reported involve two- and four-qubit calculations, and we discuss the possibility of larger scale computations in the near future.