Machine learning message-passing for the scalable decoding of QLDPC codes

We present Astra, a novel and scalable decoder using graph neural networks. In general, Quantum Low Density Parity Check (QLDPC) decoding is based on Belief Propagation (BP, a variant of message-passing) and requires time intensive post-processing methods such as Ordered Statistics Decoding (OSD). Our decoder works on the Tanner graph, similarly to BP. Without using any post-processing, Astra achieves higher thresholds and better Logical Error Rates (LER) compared to BPOSD, both for surface codes trained up to distance 11 and Bivariate Bicycle (BB) codes trained up to distance 18. Moreover, we can successfully extrapolate the decoding functionality: we decode high distances (surface code up to distance 25 and BB code up to distance 34) by using decoders trained on lower distances. Extrapolated Astra achieves better LER than BPOSD for BB codes. Astra(+OSD) achieves orders of magnitude lower logical error rates for BB codes compared to BP(+OSD).