  We test a method for computing the static quark-antiquark potential in
lattice QCD, which is not based on Wilson loops, but where the trial states are
formed by eigenvector components of the covariant lattice Laplace operator. The
runtime of this method is significantly smaller than the standard Wilson loop
calculation, when computing the static potential not only for on-axis, but also
for many off-axis quark-antiquark separations, i.e., when a fine spatial
resolution is required. We further improve the signal by using multiple
eigenvector pairs, weighted with Gaussian profile functions of the eigenvalues,
providing a basis for a generalized eigenvalue problem (GEVP), as it was
recently introduced to improve distillation in meson spectroscopy. We show
results with the new method for the static potential with dynamical fermions
and demonstrate its efficiency compared to traditional Wilson loop
calculations. The method presented here can also be applied to compute hybrid
or tetra-quark potentials and to static-light systems.
