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We construct an infinite-dimensional analog of the HaPPY code as a growingseries of stabilizer codes defined respective to their Hilbert spaces. TheHilbert spaces are related by isometric maps, which we define explicitly. Weconstruct a Hamiltonian that is compatible with the infinite-dimensional HaPPYcode and further study the stabilizer of our code, which has an inherentfractal structure. We use this result to study the dynamics of the code and mapa nontrivial bulk Hamiltonian to the boundary. We find that the image of themapping is scale invariant, but does not create any long-range entanglement inthe boundary, therefore failing to reproduce the features of a CFT. This resultshows the limits of the HaPPY code as a model of the AdS/CFT correspondence,but also hints that the relevance of quantum error correction in quantumgravity may not be limited to the CFT context.

The infinite-dimensional HaPPY code: entanglement wedge reconstruction and dynamics