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Efficient Near-Optimal Decoding of the Surface Code through Ensembling

Noah Shutty1, Michael Newman2, and Benjamin Villalonga1

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Phys. Rev. Lett. 136, 070603 – Published 19 February, 2026

DOI: https://doi.org/10.1103/77j6-32xx

Abstract

We introduce harmonization, an ensembling method that combines several “noisy” decoders to generate highly accurate decoding predictions. Harmonized ensembles of minimum weight perfect matching-based decoders achieve lower logical error rates than their individual counterparts on repetition and surface code benchmarks, approaching maximum-likelihood accuracy at large ensemble sizes. We can use the degree of consensus among the ensemble as a confidence measure for a layered decoding scheme, in which a small ensemble flags high-risk cases to be checked by a larger, more accurate ensemble. This layered scheme can realize the accuracy improvements of large ensembles with a relatively small constant factor of computational overhead. We conclude that harmonization provides a viable path toward highly accurate real-time decoding.

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Phys. Rev. Lett. 136, 070603– Published 19 February, 2026
  • Received 15 March 2024
  • Revised 19 February 2025
  • Accepted 8 September 2025
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