Pipelined correlated minimum weight perfect matching of the surface code

Abstract

We describe a pipeline approach to decoding the surface code using minimum weight perfect matching, including taking into account correlations between detection events. An independent no-communication parallelizable processing stage reweights the graph according to likely correlations, followed by another no-communication parallelizable stage for high confidence matching. A later general stage finishes the matching. This is a simplification of previous correlated matching techniques which required a complex interaction between general matching and re-weighting the graph. Despite this simplification, which gives correlated matching a better chance of achieving real-time processing, we find the logical error rate practically unchanged. We validate the new algorithm on the fully fault-tolerant toric, unrotated, and rotated surface codes, all with standard depolarizing noise. We expect these techniques to be applicable to a wide range of other decoders.

References in corpus (4)

• Surface codes: Towards practical large-scale quantum computation
• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological fault-tolerance in cluster state quantum computation
• Optimal error correction in topological subsystem codes

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