Fast erasure decoder for hypergraph product codes

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 $O(N^2)$ bit operations where $N$ is the length of the quantum code. A probabilistic version of this decoder can be implemented in $O(N^{1.5})$ bit operations.