  The Kibble-Zurek mechanism is the paradigm to account for the nonadiabatic
dynamics of a system across a continuous phase transition. Its study in the
quantum regime is hindered by the requisite of ground state cooling. We report
the experimental quantum simulation of critical dynamics in the
transverse-field Ising model by a set of Landau-Zener crossings in
pseudo-momentum space, that can be probed with high accuracy using a single
trapped ion. We test the Kibble-Zurek mechanism in the quantum regime in the
momentum space and find the measured scaling of excitations is in accordance
with the theoretical prediction.
