Understanding holographic error correction via unique algebras and atomic examples

Understand

We introduce a fully constructive characterisation of holographic quantum error-correcting codes.

• That is, given a code and an erasure error we give a recipe to explicitly compute the terms in the RT formula.
• Using this formalism, we employ quantum circuits to construct a number of examples of holographic codes.
• Our codes have nontrivial holographic properties and are simpler than existing approaches built on tensor networks.