Error-Correcting Codes in TQFT on Multispheres

Abstract: Topological quantum field theories (TQFT) encode quantum correlations in topological features of spaces. In this work, we leverage this feature to explore how information encoded in TQFTs can be stored and retrieved in the presence of local decoherence affecting its physical carriers. TQFT states' inherent nonlocality, redundancy, and entanglement position them as natural error-correcting codes. We demonstrate that information recovery protocols can be derived from the principle that protected information must be uniformly distributed across the system and from interpreting correlations in terms of space connectivity. Specifically, we employ a topological framework to devise erasure error correction protocols, showing that information can be successfully recovered even when parts of the system are corrupted.