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

• URL: http://arxiv.org/abs/2112.12757v2
• Date: Sat, 19 Feb 2022 20:28:58 GMT
• Title: Mapping between Morita equivalent string-net states with a constant depth quantum circuit
• Authors: Laurens Lootens, Bram Vancraeynest-De Cuiper, Norbert Schuch, Frank Verstraete
• Abstract summary: We construct a constant depth quantum circuit that maps between Morita equivalent string-net models. The circuit does not only act on the ground state subspace, but acts unitarily on the full Hilbert space when supplemented with ancillas.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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