In this paper, the degenerate ground states of Z2 topological order on a plane with holes (the so-called surface codes) are used as the protected code subspace to build a topological quantum computer by tuning their quantum tunneling e ect. Using a designer Hamiltonian-the Kitaev toric-code model as an example, we study quantum tunneling e ects of the surface codes and obtain its e ective theory. Finally, we show how to do topological quantum computation including the initialization, the unitary transformation and the measurement.