  We present a locality preserving unitary mapping from fermions to qubits on a
2D torus whilst accounting for the mapping of topological sectors. Extending
the work of Shukla et al. [Phys. Rev. B 101, 155105], an explicit intertwiner
is constructed in the form of a projected entangled pair operator. By encoding
the information about the charge sectors (and if applicable the twisted
boundary conditions) in ancillary qubit(s), the intertwiner becomes a unitary
operator which exchanges boundary conditions and charge sectors.
