Pauli topological stabilizer codes from twisted quantum doubles

We construct a Pauli stabilizer code for every two-dimensional Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer code, defined on four-dimensional qudits, belonging to the double semion (DS) phase of matter. We find an explicit finite-depth quantum circuit (with ancillary qubits) that maps the ground state subspace of the DS stabilizer code to that of the DS string-net model. The DS stabilizer code is constructed by condensing an emergent boson in a Z₄ toric code, which can be implemented by making certain two-body measurements. We show that the construction of the DS stabilizer code generalizes to all twisted quantum doubles with Abelian anyons, yielding models defined on composite-dimensional qudits. Our work thus extends the classification of Pauli topological stabilizer codes beyond stacks of toric codes. We also demonstrate that certain symmetry-protected topological phases can be modeled by Pauli stabilizer codes by gauging 1-form symmetries of the twisted quantum double stabilizer codes.