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.