  We present an efficient and general method to compute vortex-pinning
interactions - which arise in neutron stars, superconductors, and trapped cold
atoms - at arbitrary separations using real-time dynamics. This method
overcomes uncertainties associated with matter redistribution by the vortex
position and the related choice of ensemble that plague the typical approach of
comparing energy differences between stationary pinned and unpinned
configurations: uncertainties that prevent agreement in the literature on the
sign and magnitude of the vortex-nucleus interaction in the crust of neutron
stars. We demonstrate and validate the method with Gross-Pitaevskii-like
equations for the unitary Fermi gas, and demonstrate how the technique of
adiabatic state preparation with time-dependent simulation can be used to
calculate vortex-pinning interactions in fermionic systems such as the
vortex-nucleus interaction in the crust of neutron stars.
