Real-time quantum calculations of phase shifts using wave packet time
  delays
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.
Erik Gustafson Yingyue Zhu Patrick Dreher Norbert M. Linke Yannick Meurice