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## "Nested Topological Order", Hector Bombin, Miguel Martin-Delgado, 2011

*Reviewed August 21, 2023*

*Citation:* Bombin, H., and M. A. Martin-Delgado. "Nested topological order." New Journal of Physics 13.12 (2011): 125001.

*Web:* https://arxiv.org/abs/0803.4299

*Tags:* Abelian-anyons, Kitaev-quantum-double, Error-correcing-codes, Defects/boundaries, Universal-scheme

This paper discusses a first example of domain walls and islands in generalized surface code models,
nd the power of passing quantum information across the boundaries.

The context is that of symmetry breaking,
where there can be small islands of a topological phase in which the symmetry has broken down into a quotient of a subgroup of the gauge group.

Braiding these islands has non-trivial effects, and having more islands increases the ground state degeneracy.
Hence, this sort of "nested topological order" gives a new paradigm of topological quantum computation.