  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 effect. Using a designer Hamiltonian - the Kitaev toric-code model as
an example, we study quantum tunneling effects of the surface codes and obtain
its effective theory. Finally, we show how to do topological quantum
computation including the initialization, the unitary transformation and the
measurement.
