Emergent Gravity in an Approximate Quantum Error Correction Code

It is known that the AdS/CFT correspondence is related to approximate quantum error correction codes. However, the exact manner in which gravity can arise in such codes remains largely unexplored. Here we construct an approximate quantum error correction code which can be represented as a holographic tensor network. In the "noiseless" limit, it admits a local log-depth decoding circuit and reproduces certain properties of holography, such as the Ryu-Takayanagi formula and subregion duality, much like other known holographic codes. However, the code becomes approximate when "coherent noise" is injected, allowing it to capture features analogous to those of gravity, such as back-reaction, subspace-dependence, and approximate bulk locality.  I will briefly explain what these features are and how they are manifested in the tensor network. The talk is based on (https://arxiv.org/abs/2010.05960).