Mapping between Morita-equivalent string-net states with a constant depth quantum circuit
Laurens Lootens, Bram Vancraeynest-De Cuiper, Norbert Schuch, Frank Verstraete
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.
Topics & Concepts
Morita equivalenceString (physics)Pure mathematicsMathematicsConstant (computer programming)Subspace topologyPhysicsTopology (electrical circuits)Discrete mathematicsMathematical analysisComputer scienceMathematical physicsCombinatoricsProgramming languageQuantum and electron transport phenomenaQuantum many-body systemsAlgebraic structures and combinatorial models