Disclosed herein is a computer-implemented
quantum error
correction method for decoding errors in a
quantum computer
system. The
quantum computer
system comprises a decoder apparatus and a register of
quantum devices, the decoder apparatus comprising a plurality of
processing elements (PEs). The method comprises receiving, at the decoder apparatus, syndrome data representative of an
error state of the
quantum devices in the register of
quantum devices, the syndrome data comprising a plurality of defects, wherein the syndrome data is representable as a decoding
hypergraph comprising a plurality of nodes connected by hyperedges representing error mechanisms associated with the plurality of quantum devices. The method further comprises performing, by the plurality of PEs, a clustering
algorithm, the clustering
algorithm comprising a plurality of steps, and wherein the clustering
algorithm grows and merges clusters of nodes based on the number of defects in each cluster until a final
cluster state is reached. The method further comprises determining, by the decoder apparatus, a correction for the
error state based on the final
cluster state; wherein each of the plurality of PEs is associated with a respective batch of nodes of the decoding
hypergraph, each batch containing a plurality of nodes. Each PE of the plurality of PEs performs one or more first steps of the plurality of steps of the clustering algorithm. Performing the one or more first steps by each PE comprises determining which nodes of the PE's associated batch of nodes are in a cluster, and performing, in respect of each of the nodes determined to be in a cluster, the one or more first steps of the clustering algorithm.