Error-Correcting Codes in TQFT on Multispheres

TL;DR

This paper explores how topological quantum field theories (TQFT) inherently function as error-correcting codes, enabling information recovery despite local decoherence by leveraging their nonlocal, redundant, and entangled states.

Contribution

It introduces a topological framework for deriving erasure error correction protocols in TQFTs, demonstrating their robustness in information storage and retrieval.

Findings

TQFT states serve as natural error-correcting codes due to their topological properties.

Information can be recovered even after parts of the system are corrupted.

Protocols based on space connectivity enable successful error correction.

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.