Fast Decoders for Topological Quantum Codes

TL;DR

This paper introduces a new family of algorithms combining renormalization and belief propagation to efficiently decode topological quantum codes, significantly improving speed and error thresholds over previous methods.

Contribution

The authors develop a novel algorithm that reduces decoding time from polynomial to logarithmic in system size while enhancing error correction performance.

Findings

Decoding time scales as log L, much faster than previous methods.

Achieves higher depolarizing error thresholds.

Demonstrates improved efficiency for topological quantum code decoding.

Abstract

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.