A renormalization group decoding algorithm for topological quantum codes

TL;DR

This paper introduces a faster, more versatile decoding algorithm for topological quantum codes, leveraging statistical physics techniques like renormalization groups and belief propagation to improve error correction efficiency.

Contribution

The authors develop a novel decoding algorithm that extends to a broader class of topological codes and outperforms previous methods in speed.

Findings

Decoding speed is improved over existing algorithms.

Applicable to a wider class of topological codes.

Uses statistical physics methods for decoding.

Abstract

Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we present a decoding algorithm for topological codes that is faster than previously known algorithms and applies to a wider class of topological codes. Our algorithm makes use of two methods inspired from statistical physics: renormalization groups and mean-field approximations. First, the topological code is approximated by a concatenated block code that can be efficiently decoded. To improve this approximation, additional consistency conditions are imposed between the blocks, and are solved by a belief propagation algorithm.