Mapping between Morita equivalent string-net states with a constant depth quantum circuit

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 does not only act on the ground state subspace, but acts unitarily on the full Hilbert space when supplemented with ancillas.

11+2 pages, v2: updated section III.B

References in corpus (6)

• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Explicit tensor network representation for the ground states of string-net models
• Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
• Topological Defects on the Lattice: Dualities and Degeneracies
• Generalized string-nets for unitary fusion categories without tetrahedral symmetry
• Tensor-product representations for string-net condensed states

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