Topological quantum computation with gapped boundaries and boundary defects
Iris Cong, Zhenghan Wang · Contemporary mathematics - American Mathematical Society · 2020
We survey some recent work on topological quantum computation with gapped boundaries and boundary defects: First, we review the Hamiltonians for gapped boundaries in quantum double models when the gapped boundaries correspond to subgroups with trivial cocycles. Then, the categorical formulation that excitations of gapped boundaries correspond to objects in dual categories, and defects between two gapped boundaries correspond to objects in functor categories is discussed. Finally, we list some open problems.