  We discuss technical aspects and first results of a lattice QCD study of the
$a_0(980)$ state. We employ various interpolating operators of quark-antiquark,
mesonic molecule, diquark-antidiquark and two-meson type. Both connected and
disconnected contributions including diagrams with closed fermion loops are
computed. To keep statistical errors small, it is essential to optimize the
computation of these diagrams by choosing that combination of techniques most
appropriate for each type of diagram from the correlation matrix of
interpolating operators. We illustrate, how this can be done, by discussing
certain diagrams in detail. We also present preliminary results corresponding
to a $4\times 4$ submatrix computed with 2+1 flavors of clover fermions.
