Quantum error correction code decoder and associated methods

A method of decoding syndrome data of a quantum error correction code is disclosed comprising receiving position data representing the locations of defects from the syndrome data in a decoding graph, receiving dimension data of the decoding graph, determining the respective location of each of the plurality of defects in the decoding graph based on the position data and the dimension data and decoding the syndrome data using the determined respective location of each of the plurality of defects. The position data may encode an index value representing the location of each defect, it may comprise an index value list. The index values may be vertex values, one vertex value for each vertex of the decoding graph. The dimension data may comprise first and second values across different, preferably orthogonal, dimensions. The dimension data may comprise a third value for a third decoding graph dimension which may be orthogonal to the first and/or second decoding graph dimensions. The quantum error correction code may be a planar surface code. The syndrome data may comprise defects associated with a plurality of rounds of quantum error correction. The decoding graph dimensions may be different for different sets of rounds error correction.