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The Kibble-Zurek mechanism (KZM) predicts the density of topological defectsproduced in the dynamical processes of phase transitions in systems rangingfrom cosmology to condensed matter and quantum materials. The similaritybetween KZM and the Landau-Zener transition (LZT), which is a standard tool todescribe the dynamics of some non-equilibrium physics in contemporary physics,is being extensively exploited. Here we demonstrate the equivalence between KZMin the Ising model and LZT in a superconducting qubit system. We develop atime-resolved approach to study quantum dynamics of LZT with nano-secondresolution. By using this technique, we simulate the key features of KZM in theIsing model with LZT, e.g., the boundary between the adiabatic and impulseregions, the freeze-out phenomenon in the impulse region, especially, thescaling law of the excited state population as the square root of the quenchingrate. Our results supply the experimental evidence of the close connectionbetween KZM and LZT, two textbook paradigms to study the dynamics of thenon-equilibrium phenomena.

Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system