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 does not only act on the ground state subspace, but acts unitarily on the full Hilbert space when supplemented with ancillas.

arXiv comment11+2 pages, v2: updated section III.B

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• Towards Non-Invertible Anomalies from Generalized Ising Models
• Invertible bimodule categories and generalized Schur orthogonality
• Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model
• Decoherence and wavefunction deformation of $D_4$ non-Abelian topological order
• Efficient Preparation of Solvable Anyons with Adaptive Quantum Circuits
• Duality via Sequential Quantum Circuit in the Topological Holography Formalism
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• Noninvertible Gauge Symmetry in (2+1)d Topological Orders: A String-Net Model Realization
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