  The Kibble-Zurek mechanism provides a description of the topological
structure occurring in the symmetry breaking phase transitions, which may
manifest as the cosmological strings in the early universe or vortex lines in
the superfulid. A particularly intriguing analogy between Kibble-Zurek
mechanism and a text book quantum phenomenon, Landau-Zener transition has been
discovered, but is difficult to observe up to now. In recent years, there has
been broad interest in quantum simulations using different well-controlled
physical setups, in which full tunability allows access to unexplored parameter
regimes. Here we demonstrate a proof-of-principle quantum simulation of
Kibble-Zurek mechanism using a single electron charge qubit in double quantum
dot, set to behave as Landau-Zener dynamics. We measure the qubit states as a
function of driven pulse velocity and successfully reproduce Kibble-Zurek like
dependence of topological defect density on the quench rate. The high-level
controllability of semiconductor two-level system make it a platform to test
the key elements of topological defect formation process and shed a new insight
on the aspect of non-equilibrium phase transitions.
