Universal Quantum Computation with Gapped Boundaries

Understand

This Letter discusses topological quantum computation with gapped boundaries of two-dimensional topological phases.

• Systematic methods are presented to encode quantum information topologically using gapped boundaries, and to perform topologically protected operations on this encoding.
• In particular, we introduce a new and general computational primitive of topological charge measurement and present a symmetry-protected implementation of this primitive.
• Throughout the Letter, a concrete physical example, the $\mathbb{Z}_3$ toric code ($\mathfrak{D}(\mathbb{Z}_3)$), is discussed.