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

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.

Automated summary

The study constructs a constant depth quantum circuit for mapping between Morita-equivalent string-net models. The circuit, with its constant depth and unitarity, is unable to alter the topological order, thereby demonstrating that Morita-equivalent string nets are in the same phase.