Enhanced Feedback Iterative Decoding of Sparse Quantum Codes

Abstract

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.

The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure

“…2012 Wang et al [96] Feedback mechanism was introduced in the context of the heuristic methods of [95] to further improve the performance.…”

“…short cycles and symmetric degeneracy error, which were further improved in [96]. The major contributions made in the context of QLDPC codes are summarized in Table III, while the most promising QLDPC construction methods are compared in Table IV 16 .…”

On the decoding of non-binary quantum low-density parity check codes

“…The error-correcting performance of a degenerate quantum error-correcting code can be improved by modifying a decoding algorithm properly [2], [3]. The degeneracy becomes more relevant when stabilizer operators of a quantum code have low weight [2], and therefore some quantum low-density parity check codes are highly degenerate.…”

“…By the way, the sumproduct algorithm itself does not consider the degeneracy. To exploit the degeneracy of binary quantum low-density parity check codes, two methods [2], [3] have been proposed, and the error-correcting performance by these methods is much better.…”

“…However, with this CSS decoding, the degeneracy problem cannot be dealt with properly. In this regard, we first proposes a non-binary quantum sum-product algorithm, and describe non-binary versions of the binary heuristic methods described in [2], [3] to deal with the degeneracy problem.…”