Mapping between Morita equivalent string-net states with a constant depth quantum circuit
Quantum Physics
2022-02-22 v2 Strongly Correlated Electrons
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.
Cite
@article{arxiv.2112.12757,
title = {Mapping between Morita equivalent string-net states with a constant depth quantum circuit},
author = {Laurens Lootens and Bram Vancraeynest-De Cuiper and Norbert Schuch and Frank Verstraete},
journal= {arXiv preprint arXiv:2112.12757},
year = {2022}
}
Comments
11+2 pages, v2: updated section III.B