Tensor Networks with a Twist: Anyon-permuting domain walls and defects in PEPS

Abstract

We study the realization of anyon-permuting symmetries of topological phases on the lattice using tensor networks. Working on the virtual level of a projected entangled pair state, we find matrix product operators (MPOs) that realize all unitary topological symmetries for the toric and color codes. These operators act as domain walls that enact the symmetry transformation on anyons as they cross. By considering open boundary conditions for these domain wall MPOs, we show how to introduce symmetry twists and defect lines into the state.

11 pages, 6 figures, 2 appendices, v2 published version

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Restrictions on Transversal Encoded Quantum Gate Sets
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Fault-tolerant logical gates in quantum error-correcting codes

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• Lifting topological codes: Three-dimensional subsystem codes from two-dimensional anyon models
• Low-overhead quantum computing with the color code
• Electric-magnetic duality and ${\mathbb{Z}}_2$ symmetry enriched Abelian lattice gauge theory
• A 3D lattice defect and efficient computations in topological MBQC
• Weak Hopf tube algebra for domain walls between 2d gapped phases of Turaev-Viro TQFTs
• Tunable anyonic permeability across ${\mathbb{Z}}_2$ spin liquid junctions