Machine Learning Message-Passing for the Scalable Decoding of QLDPC Codes

We present Astra, a novel and scalable decoder using graph neural networks. Our decoder works similarly to solving a Sudoku puzzle of constraints represented by the Tanner graph. 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). Without using any post-processing, Astra achieves higher thresholds and better logical error rates when compared to BP+OSD, 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. Astra+OSD is faster than BP+OSD. We show that with decreasing physical error rates, Astra+OSD makes progressively fewer calls to OSD when compared to BP+OSD, even in the context of extrapolated decoding. Astra (+OSD) achieves orders of magnitude lower logical error rates for BB codes compared to BP (+OSD). The source code is open-sourced at https: //github. com/arshpreetmaan/astra.