We propose a decoder for the correction of erasures with hypergraph product codes, which form one of the most popular families of quantum LDPC codes. Our numerical simulations show that this decoder provides a close approximation of the maximum likelihood decoder that can be implemented in O(N2) bit operations where N is the length of the quantum code. A probabilistic version of this decoder can be implemented in O(N1.5) bit operations.
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Connolly et al. (2024) studied this question.
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