Scalable Surface-Code Decoders with Parallelization in Time

Abstract

Fast classical processing is essential for most quantum fault-tolerance architectures. We introduce a sliding-window decoding scheme that provides fast classical processing for the surface code through parallelism. Our scheme divides the syndromes in space-time into overlapping windows along the time direction, which can be decoded in parallel with any inner decoder. With this parallelism, our scheme can solve the backlog problem as the code scales up, even if the inner decoder is slow. When using minimum-weight perfect matching and union find as the inner decoders, we observe circuit-level thresholds of 0.68% and 0.55%, respectively, which are almost identical to those for the batch decoding.