Mapping between Morita-equivalent string-net states with a constant depth quantum circuit
TLDR
In this article , a constant depth quantum circuit that maps between Morita-equivalent string-net models is constructed from an invertible bimodule category connecting the two input fusion categories.Abstract:
We construct a constant depth quantum circuit that maps between Morita-equivalent string-net models. Due to its constant depth and unitarity, the circuit cannot alter the topological order, which demonstrates that Morita-equivalent string nets are in the same phase. The circuit is constructed from an invertible bimodule category connecting the two input fusion categories of the relevant string-net models, acting as a generalized Fourier transform for fusion categories. The circuit not only acts on the ground state subspace but also acts unitarily on the full Hilbert space when supplemented with ancillas. read more
Citations
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References
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From subfactors to categories and topology I: Frobenius algebras in and Morita equivalence of tensor categories
TL;DR: Weak monoidal Morita equivalence of tensor categories, denoted A ≈ B, has been studied in this article, where it has been shown that A and B have equivalent quantum doubles (centers) and (if A, B are semisimple spherical or ∗ -categories) have equal dimensions and give rise the same state sum invariant of closed oriented 3-manifolds as recently defined by Barrett and Westbury.