Quantum Computer Measurements of Phase Shifts Using Wavepacket Edge Time Delays

We present a method to extract the phase shifts using a wavepacket edge time delay resulting from a comparison of the real time evolution with and without a potential interaction. This calculation is tested on a quantum computer using real-time simulation of a transverse Ising model in one spatial dimension. Using a 4 site system a wavepacket was constructed to have a localization that simulates a distinct scattering event in space both inside and outside a potential. A time evolution operator describing the progression of the system was constructed and transmission and reflection coefficients were calculated based on the identified quantum Fourier transformed momentum states. A detailed analysis of the of the phase shift calculations for both the IBM Q machines and data from a University of Maryland ion trap quantum computer show the platform independence of the methodology.