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arXiv · 2112.12757

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

Laurens Lootens·Bram Vancraeynest-De Cuiper·Norbert Schuch·Frank Verstraete
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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.

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Laurens Lootens, Bram Vancraeynest-De Cuiper, Norbert Schuch, Frank Verstraete. 2021-12-23. Mapping between Morita equivalent string-net states with a constant depth quantum circuit. https://doi.org/10.1103/physrevb.105.085130

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