Classical Holographic Codes

TL;DR

This paper introduces classical holographic codes modeled as probabilistic networks in hyperbolic space, demonstrating features similar to AdS/CFT correspondence, including a Ryu-Takayanagi-like formula and bulk-boundary mappings.

Contribution

It presents the first classical analog of holographic codes, connecting probabilistic network models with holographic principles and error correction concepts.

Findings

Existence of classical holographic codes with hyperbolic network structure

Demonstration of a Ryu-Takayanagi-like formula in classical setting

Insights into bulk reconstruction and boundary representations

Abstract

In this work, we introduce classical holographic codes. These can be understood as concatenated probabilistic codes and can be represented as networks uniformly covering hyperbolic space. In particular, classical holographic codes can be interpreted as maps from bulk degrees of freedom to boundary degrees of freedom. Interestingly, they are shown to exhibit features similar to those expected from the AdS/CFT correspondence. Among these are a version of the Ryu-Takayanagi formula and intriguing properties regarding bulk reconstruction and boundary representations of bulk operations. We discuss the relation of our findings with expectations from AdS/CFT and, in particular, with recent results from quantum error correction.