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.

翻译：我们提出了一种用于超图积码擦除校正的译码器，超图积码是最流行的量子LDPC码族之一。数值模拟表明，该译码器能以O(N^2)比特运算复杂度实现最大似然译码的近似逼近，其中N为量子码长。其概率化版本可在O(N^1.5)比特运算复杂度内实现。