  We consider an inverse spectral problem on a quantum graph associated with
the square lattice. Assuming that the potentials on the edges are compactly
supported and symmetric, we show that the Dirichlet-to-Neumann map for a
boundary value problem on a finite part of the graph uniquely determines the
potentials. We obtain a reconstruction procedure, which is based on the
reduction of the differential Schr\"odinger operator to a discrete one. As a
corollary of the main results, it is proved that the S-matrix for all energies
in any given open set in the continuous spectrum uniquely specifies the
potentials on the square lattice.
