  An attempt is made to quantum simulate the topological classification, such
as winding number, geometric phase and symmetry properties for a quantum
simulated Kitaev chain. We find, {\alpha} (ratio between the spin-orbit
coupling and magnetic field) and the range of momentum space of consideration,
which plays a crucial role for the topological classification. We show
explicitly that the topological quantum phase transition does not occurs at k =
0 limit for the quantum simulated Kitaev chain. We observe that the
quasi-particle mass of the Majorana mode plays the significant role in
topological quantum phase transition. We also show that the symmetry properties
of simulated Kitaev chain is the same with original Kitaev chain. The exact
solution of simulated Kitaev chain is given. This work provides a new
perspective on new emerging quantum simulator and also for the topological
state of matter.
