Abstract: We construct a Pauli stabilizer model for every Abelian topological order that admits a gapped boundary in two spatial dimensions. Our primary example is a Pauli stabilizer model on four-dimensional qudits that belongs to the double semion (DS) phase of matter. The DS stabilizer Hamiltonian is constructed by condensing an emergent boson in a Z4 toric code. We show that the construction of the DS stabilizer Hamiltonian generalizes to all twisted quantum doubles (TQDs) with Abelian anyons. This construction yields a Pauli stabilizer code on composite-dimensional qudits and implies that the classification of topological Pauli stabilizer codes extends beyond stacks of toric codes—in fact, exhausting all Abelian anyon theories that admit a gapped boundary.
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