Degenerate Quantum LDPC Codes With Good Finite Length Performance

By Pavel Panteleev, Gleb Kalachev. Quantum, 2019

408 citations recorded by the source corpus.

We study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel. Only degenerate codes with the maximal stabilizer weight much smaller than their minimum distance are considered. It is shown that with the help of OSD-like post-processing the performance of the standard belief propagation (BP) decoder on many QLDPC codes can be improved by several orders of magnitude. Using this new BP-OSD decoder we study the performance of several known classes of degenerate QLDPC codes including hypergraph product codes, hyperbicycle codes, homological product codes, and Haah's cubic codes. We also construct several interesting examples of short generalized bicycle codes. Some of them have an additional property that their syndromes are protected by small BCH codes, which may be useful for the fault-tolerant syndrome measurement. We also propose a new large family of QLDPC codes that contains the class of hypergraph product codes, where one of the used parity-check matrices is square. It is shown that in some cases such codes have better performance than hypergraph product codes. Finally, we demonstrate that the performance of the proposed BP-OSD decoder for some of the constructed codes is better than for a relatively large surface code decoded by a near-optimal decoder.

Subfields: Artificial Intelligence, Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/187f60cd014b587361d832d1bb213a8111c7e838

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Citations in the corpus

High-threshold and low-overhead fault-tolerant quantum memory (2023, methodology): “Our numerical experiments are based on the belief propagation with an ordered statistics decoder (BP-OSD) proposed by Panteleev and Kalachev 36 .”
Asymptotically good Quantum and locally testable classical LDPC codes (2021, background): “It is also interesting to note that the codes that were actually used to get the main results in [6, 27, 44] are from a more restricted class of lifted product codes, which were previously studied in [43] under the name GHP codes and shown to have surprisingly good practical error-correcting perform”