Fast erasure decoder for hypergraph product codes

Understand

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.