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Numerical and analytical bounds on threshold error rates for hypergraph-product codes
Alexey A. Kovalev, Sanjay Prabhakar, Ilya Dumer, Leonid P. Pryad · 2018-04-06 · via cs.IT updates on arXiv.org

We study analytically and numerically decoding properties of finite rate hypergraph-product quantum LDPC codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several non-trival lower and upper bounds for the decodable region are constructed analytically by analyzing the properties of the homological difference, equal minus the logarithm of the maximum-likelihood decoding probability for a given syndrome. Numerical results include an upper bound for the decodable region from specific heat calculations in associated Ising models, and a minimum weight decoding threshold of approximately 7%.

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