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

Laurens Lootens (Corresponding author), Bram Vancraeynest-De Cuiper, Norbert Schuch, Frank Verstraete

Publications: Contribution to journalArticlePeer Reviewed

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.
Original languageEnglish
Article number085130
Number of pages12
JournalPhysical Review B
Volume105
Issue number8
DOIs
Publication statusPublished - 17 Feb 2022

Austrian Fields of Science 2012

  • 103025 Quantum mechanics
  • 103015 Condensed matter

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