Fast erasure decoder for a class of quantum LDPC codes

Title: Fast erasure decoder for a class of quantum LDPC codes

Abstract: In this work, we propose a decoding algorithm for correcting erasures with hypergraph product (HGP) codes, one of the most popular families of quantum LDPC codes. The algorithm we propose is a generalization of the classical peeling decoder adapted to quantum HGP codes. Our numerical simulations show that our decoder provides a close approximation of the maximum likelihood (ML) decoder which can be implemented in $O(N^2)$ bit operations, where $N$ is the length of the quantum code. This is a significant computational improvement over the ML Gaussian decoder, which has complexity $O(N^3)$.

Biography: Nicholas Connolly is a postdoctoral researcher at INRIA Paris and a member of the COSMIQ team. He is currently studying quantum error correction under the direction of Anthony Leverrier and Nicolas Delfosse. Nicholas Connolly completed his doctorate in mathematics in 2021 at the University of Iowa in the United States with a dissertation topic in knot theory.