Scalable Graph Neural Network Decoders for Quantum LDPC Codes*

Decoding quantum low density parity checks (QLDPC) codes shares similarities with the decoding of classical LDPC codes. In general, QLDPC decoding requires post-processing which is a time consuming procedure. Neural network (NN) decoders, with their constant time execution, have also been proposed for QLDPC codes. However, their training is very time consuming and once trained, a NN decoder cannot extrapolate (ie. train on a lower distance, and use it for larger distances) and can only be used on that particular code distance on which it was trained on. We present a novel graph-NN decoder which is trained on the Tanner graph of the QLDPC code. We benchmark our decoder on depolarizing noise and decode surface QECCs of distance 3, 5 and 7. We illustrate the extrapolation capabilities of our graph-NN decoder, and present numerical evidence that it achieves thresholds comparable to decoders using belief propagation combined with ordered statistics post-processing.