Source-linked AI summary
Fast Decoders for Topological Quantum Codes
Guillaume Duclos-Cianci, David Poulin
TL;DR
Topological-code decoding requires rapid inference of error homology while accounting for degeneracy and correlated errors. The paper combines real-space renormalization with belief propagation to estimate free energies, achieving logarithmic parallel runtime and depolarizing thresholds up to 16.4%.
Problem
Efficient decoding must infer world-line homology rapidly, but minimum-weight perfect matching scales as ℓ^6 and minimizes energy rather than free energy.
Method
The paper uses overlapping-code real-space renormalization, brute-force decoding of small blocks, and belief propagation to impose self-consistency on shared-qubit probabilities.
Results
The algorithm runs in time log ℓ in parallel and reaches a depolarizing threshold of p ∼16.4%, exceeding the PMA.
Takeaways & Limitations
The method provides a versatile decoder for topologically ordered systems, including color codes, and supports fault-tolerant quantum information processing schemes.
Takeaways & Limitations
The PMA treats X and Z errors independently, although depolarizing noise correlates them through Y errors.
Abstract
from arXiv · showhide
We present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects. Such an algorithm is needed to preserve the quantum information stored in the ground space of a topologically ordered system and to decode topological error-correcting codes. For a system of linear size L, our algorithm runs in time log L compared to L^6 needed for the minimum-weight perfect matching algorithm previously used in this context and achieves a higher depolarizing error threshold.