Pipelined correlated minimum weight perfect matching of the surface code

Alexandru Paler1,2 and Austin G. Fowler3

1Aalto University, Espoo 02150, Finland
2University of Texas at Dallas, Richardson, TX 75080, USA
3Google Inc., Santa Barbara, 93117 CA, USA

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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.

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Cited by

[1] Luka Skoric, Dan E. Browne, Kenton M. Barnes, Neil I. Gillespie, and Earl T. Campbell, "Parallel window decoding enables scalable fault tolerant quantum computation", Nature Communications 14 1, 7040 (2023).

[2] Samuel C. Smith, Benjamin J. Brown, and Stephen D. Bartlett, "Local Predecoder to Reduce the Bandwidth and Latency of Quantum Error Correction", Physical Review Applied 19 3, 034050 (2023).

[3] Antonio deMarti iOlius, Josu Etxezarreta Martinez, Patricio Fuentes, and Pedro M. Crespo, "Performance enhancement of surface codes via recursive minimum-weight perfect-match decoding", Physical Review A 108 2, 022401 (2023).

[4] F. Battistel, C. Chamberland, K. Johar, R. W. J. Overwater, F. Sebastiano, L. Skoric, Y. Ueno, and M. Usman, "Real-time decoding for fault-tolerant quantum computing: progress, challenges and outlook", Nano Futures 7 3, 032003 (2023).

[5] György P. Gehér, Campbell McLauchlan, Earl T. Campbell, Alexandra E. Moylett, and Ophelia Crawford, "Error-corrected Hadamard gate simulated at the circuit level", arXiv:2312.11605, (2023).

[6] Gyorgy P. Geher, Ophelia Crawford, and Earl T. Campbell, "Tangling schedules eases hardware connectivity requirements for quantum error correction", arXiv:2307.10147, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-02-27 12:07:30) and SAO/NASA ADS (last updated successfully 2024-02-27 12:07:31). The list may be incomplete as not all publishers provide suitable and complete citation data.