Enhanced Feedback Iterative Decoding of Sparse Quantum Codes

TL;DR

This paper introduces an enhanced belief propagation decoding method for sparse quantum codes that leverages additional stabilizer information, resulting in improved decoding performance without extra measurement overhead.

Contribution

A novel feedback adjustment strategy for belief propagation decoding that utilizes stabilizer information beyond syndromes, improving quantum code decoding accuracy.

Findings

Superior decoding performance over standard BP algorithms for depolarizing channels

No additional measurement overhead required for the enhanced decoding method

Effective use of stabilizer information improves quantum error correction

Abstract

Decoding sparse quantum codes can be accomplished by syndrome-based decoding using a belief propagation (BP) algorithm.We significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard BP algorithm. In our feedback procedure, we exploit much of the information from stabilizers, not just the syndrome but also the values of the frustrated checks on individual qubits of the code and the channel model. Furthermore we show that our decoding algorithm is superior to belief propagation algorithms using only the syndrome in the feedback procedure for all cases of the depolarizing channel. Our algorithm does not increase the measurement overhead compared to the previous method, as the extra information comes for free from the requisite stabilizer measurements.