  A systematic approach to dualities in symmetric (1+1)d quantum lattice models
has recently been proposed in terms of module categories over the symmetry
fusion categories. By characterizing the non-trivial way in which dualities
intertwine closed boundary conditions and charge sectors, these can be
implemented by unitary matrix product operators. In this manuscript, we explain
how to turn such duality operators into unitary linear depth quantum circuits
via the introduction of ancillary degrees of freedom that keep track of the
various sectors. The linear depth is consistent with the fact that these
dualities change the phase of the states on which they act. When supplemented
with measurements, we show that dualities with respect to symmetries encoded
into nilpotent fusion categories can be realised in constant depth. The
resulting circuits can for instance be used to efficiently prepare short- and
long-range entangled states or map between different gapped boundaries of
(2+1)d topological models.
