Pauli stabilizer models of twisted quantum doubles

• URL: http://arxiv.org/abs/2112.11394v4
• Date: Thu, 15 Dec 2022 00:13:53 GMT
• Title: Pauli stabilizer models of twisted quantum doubles
• Authors: Tyler D. Ellison, Yu-An Chen, Arpit Dua, Wilbur Shirley, Nathanan Tantivasadakarn, Dominic J. Williamson
• Abstract summary: We construct a Pauli stabilizer model for every two-dimensional Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer model on four-dimensional qudits that belongs to the double semion phase of matter.
• Score: 2.554567149842799
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct a Pauli stabilizer model for every two-dimensional Abelian topological order that admits a gapped boundary. 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 $\mathbb{Z}_4$ toric code, where the condensation is implemented by making certain two-body measurements. We rigorously verify the topological order of the DS stabilizer model by identifying an explicit finite-depth quantum circuit (with ancillary qubits) that maps its ground state subspace to that of a DS string-net model. We show that the construction of the DS stabilizer Hamiltonian generalizes to all twisted quantum doubles (TQDs) with Abelian anyons. This yields a Pauli stabilizer code on composite-dimensional qudits for each such TQD, implying that the classification of topological Pauli stabilizer codes extends well beyond stacks of toric codes - in fact, exhausting all Abelian anyon theories that admit a gapped boundary. We also demonstrate that symmetry-protected topological phases of matter characterized by type I and type II cocycles can be modeled by Pauli stabilizer Hamiltonians by gauging certain 1-form symmetries of the TQD stabilizer models.

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