  We propose a method for the tomographic reconstruction of qubit states for a
general class of solid state systems in which the Hamiltonians are represented
by spin operators, e.g., with Heisenberg-, $XXZ$-, or XY- type exchange
interactions. We analyze the implementation of the projective operator
measurements, or spin measurements, on qubit states. All the qubit states for
the spin Hamiltonians can be reconstructed by using experimental data.
