  The significance of topological phases has been widely recognized in the
community of condensed matter physics. The well controllable quantum systems
provide an artificial platform to probe and engineer various topological
phases. The adiabatic trajectory of a quantum state describes the change of the
bulk Bloch eigenstates with the momentum, and this adiabatic simulation method
is however practically limited due to quantum dissipation. Here we apply the
`shortcut to adiabaticity' (STA) protocol to realize fast adiabatic evolutions
in the system of a superconducting phase qubit. The resulting fast adiabatic
trajectories illustrate the change of the bulk Bloch eigenstates in the
Su-Schrieffer-Heeger (SSH) model. A sharp transition is experimentally
determined for the topological invariant of a winding number. Our experiment
helps identify the topological Chern number of a two-dimensional toy model,
suggesting the applicability of the fast adiabatic simulation method for
topological systems.
