  We show that topological equivalence classes of circles in a two-dimensional
square lattice can be used to design dynamical decoupling procedures to protect
qubits attached on the edges of the lattice. Based on the circles of the
topologically trivial class in the original and the dual lattices, we devise a
procedure which removes all kinds of local Hamiltonians from the dynamics of
the qubits while keeping information stored in the homological degrees of
freedom unchanged. If only the linearly independent interaction and
nearest-neighbor two-qubit interactions are concerned, a much simpler procedure
which involves the four equivalence classes of circles can be designed. This
procedure is compatible with Eulerian and concatenated dynamical decouplings,
which make it possible to implement the procedure with bounded-strength
controls and for a long time period. As an application, it is shown that our
method can be directly generalized to finite square lattices to suppress
uncorrectable errors in surface codes.
