IQI Weekly Seminar

Abstract: We construct an explicit and solvable toy model for the AdS/CFT correspondence in the form of an approximate quantum error correction code with a non-trivial center in the code subalgebra. Specifically, we use approximate Bacon-Shor codes and perfect tensors to construct a holographic tensor network that reproduces an analog of the Ryu-Takayanagi formula and features of the sub-region duality. We find that both the position of the Ryu-Takayanagi surface and its entropy contribution will depend on the bulk logical state, resembling the effects of gravitational back-reactions in AdS. We will also discuss examples where exact complementary error correction breaks down. This results in a bulk region that can not be perfectly reconstructed from either boundary subregions in a bipartition of the boundary physical qubits. In these instances, we find that the reconstruction of certain bulk operators from a boundary subregion becomes subspace-dependent.