“Local topological quantum codes and topological holography”
Topologically ordered quantum states give quantum error correction codes via the Topological Quantum Order (TQO) axioms. We will discuss a generalization of the TQO axioms called the Local Topological Order (LTO) axioms for abstract quantum spin systems on a lattice. Using our axioms, we produce a net of algebras on a codimension 1 sublattice called the boundary algebra. The local representation theory of DHR bimodules of the boundary algebra recovers the topological order of the bulk in all known examples satisfying the LTO axioms, giving a holographic perspective on topological quantum codes. This is joint work with Corey Jones, Pieter Naaijkens, and Daniel Wallick [arXiv:2307.12552].
Host: Mark Gonzalez, Joseph Lap, Xinping Yang