Topological Quantum Computation with Gapped Boundaries

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This paper studies fault-tolerant quantum computation with gapped boundaries.

• We first introduce gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories using their Hamiltonian realizations.
• We classify the elementary excitations on the boundary, and systematically describe the bulk-to-boundary condensation procedure.
• We also provide a commuting Hamiltonian to realize defects between boundaries in any quantum double model.