Josu Etxezarreta Martinez

Real-time decoding is a fundamental necessity for building fault-tolerant quantum computers. In this work, we introduce decoding with alternating graph sparsification (DAWG), an ensemble based approach that combines Tanner graph sparsification with ensembling belief-propagation (BP) decoders. The DAWG decoder runs BP decoders over the full detector error model Tanner graph for certain iterations to then transfer the posteriors to a sparsified graph in which additional rounds of BP are run. Each of the decoders in the ensemble uses a different transfer matrix to map the posterior information to the sparsified graph. We use the serial schedule for the minimum-sum BP decoders used and, thus, employ Vibe decoding ideas by randomizing the schedules of each of them. The performance of the DAWG decoder is then numerically studied for bivariate bicycle codes and color codes encoded with superdense circuits. Furthermore, we compare compare its performance with other state-of-the-art decoding approaches showing the superiority of our proposal. Importantly, the DAWG decoder shows a similar performance as Relay belief-propagation when combined with an additional post-processor over uncorrelated detector error models. It also shows similar performance as Vibe decoding for superdense color code circuits. Crucially, the post-processors are called a negligible amount of times and an order of magnitude less times than standard Vibe decoding for relevant physical error rates, indicating that the introduced latency by them is not an issue to overcome the backlog problem.