  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. We discuss a Trotter
procedure to implement the evolution on existing quantum computers and discuss
the error associated with the Trotter step size. We discuss the effects of gate
and measurement errors on the evolution of one and two particle states using 4
and 8 qubits circuits approximately corresponding to existing or near term
quantum computers.
