Toward a Union-Find Decoder for Quantum LDPC Codes
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Publication:5088459
DOI10.1109/TIT.2022.3143452zbMATH Open1497.81035arXiv2103.08049OpenAlexW4206182345MaRDI QIDQ5088459
Nicolas Delfosse, Vivien Londe, Michael E. Beverland
Publication date: 13 July 2022
Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)
Abstract: Quantum LDPC codes are a promising direction for low overhead quantum computing. In this paper, we propose a generalization of the Union-Find decoder as adecoder for quantum LDPC codes. We prove that this decoder corrects all errors with weight up to An^{alpha} for some A, {alpha} > 0 for different classes of quantum LDPC codes such as toric codes and hyperbolic codes in any dimension D geq 3 and quantum expander codes. To prove this result, we introduce a notion of covering radius which measures the spread of an error from its syndrome. We believe this notion could find application beyond the decoding problem. We also perform numerical simulations, which show that our Union-Find decoder outperforms the belief propagation decoder in the low error rate regime in the case of a quantum LDPC code with length 3600.
Full work available at URL: https://arxiv.org/abs/2103.08049
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