Quantum simulation of scattering in the quantum Ising model

Understand

We discuss real time evolution for the quantum Ising model in one spatial dimension with $N_s$ sites.

• In the limit where the nearest neighbor interactions $J$ in the spatial directions are small, there is a simple physical picture where qubit states can be interpreted as approximate particle occupations.
• Using exact diagonalization, for initial states with one or two particles, we show that for small $J$, discrete Bessel functions provide very accurate expressions for the evolution of the occupancies corresponding to initial states with one and two particles.
• Boundary conditions play an important role when the evolution time is long enough.