Pipelined correlated minimum weight perfect matching of the surface code

TL;DR

This paper introduces a simplified, pipelined decoding algorithm for the surface code that efficiently incorporates correlations in detection events, maintaining low logical error rates and enabling real-time processing.

Contribution

A novel pipelined decoding approach for the surface code that simplifies correlated matching while preserving performance and enabling parallel processing.

Findings

Logical error rate remains practically unchanged.

Decoding process is fully parallelizable and suitable for real-time applications.

Validated on various surface code configurations with standard depolarizing noise.

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.