Local Jordan-Wigner transformations and topological sectors on the torus

We present a locality preserving unitary mapping from fermions to qubits on a two-dimensional torus while accounting for the mapping of topological sectors. Extending the work of Shukla [], 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.