@article{d5d29b44d2b74bda86a24c0c9e7bdbbd,
title = "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 not only acts on the ground state subspace but also acts unitarily on the full Hilbert space when supplemented with ancillas. ",
author = "Laurens Lootens and {Vancraeynest-De Cuiper}, Bram and Norbert Schuch and Frank Verstraete",
note = "Funding Information: We are grateful to Nick Bultinck for inspiring discussions and to Jacob Bridgeman for insightful comments on invertible bimodule categories and tube algebras. This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme [Grant Agreements No. 647905 (QUTE) and No. 863476 (SEQUAM)], and the Research Foundation Flanders via Grants No. G087918N and No. G0E1820N. L.L. is supported by a Ph.D. fellowship from the Research Foundation Flanders (FWO). B.V.-D.C. is supported by a Ph.D. fellowship from Bijzonder Onderzoeksfonds (BOF). Publisher Copyright: {\textcopyright} 2022 American Physical Society. Copyright: Copyright 2022 Elsevier B.V., All rights reserved.",
year = "2022",
month = feb,
day = "17",
doi = "10.1103/PhysRevB.105.085130",
language = "English",
volume = "105",
journal = "Physical Review B",
issn = "2469-9950",
publisher = "AMER PHYSICAL SOC",
number = "8",
}