Self-inverse twists with invariant localisable charges in k stacked surface codes realize the kth level of a Tambara-Yamagami hierarchy whose braiding implements tensor products of S or CZ gates.
Nielsen and Isaac L
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A Hierarchy of Anyon Models Realised by Twists in Stacked Surface Codes
Self-inverse twists with invariant localisable charges in k stacked surface codes realize the kth level of a Tambara-Yamagami hierarchy whose braiding implements tensor products of S or CZ gates.