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

Understand

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.