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.