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

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