2021
DOI: 10.48550/arxiv.2110.14691
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Understanding holographic error correction via unique algebras and atomic examples

Jason Pollack,
Patrick Rall,
Andrea Rocchetto

Abstract: 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 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. Finally, leveraging a connection between correctable and private systems we prove the uni… Show more

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