  The Kibble-Zurek mechanism (KZM) predicts the density of topological defects
produced in the dynamical processes of phase transitions in systems ranging
from cosmology to condensed matter and quantum materials. The similarity
between KZM and the Landau-Zener transition (LZT), which is a standard tool to
describe the dynamics of some non-equilibrium physics in contemporary physics,
is being extensively exploited. Here we demonstrate the equivalence between KZM
in the Ising model and LZT in a superconducting qubit system. We develop a
time-resolved approach to study quantum dynamics of LZT with nano-second
resolution. By using this technique, we simulate the key features of KZM in the
Ising model with LZT, e.g., the boundary between the adiabatic and impulse
regions, the freeze-out phenomenon in the impulse region, especially, the
scaling law of the excited state population as the square root of the quenching
rate. Our results supply the experimental evidence of the close connection
between KZM and LZT, two textbook paradigms to study the dynamics of the
non-equilibrium phenomena.
