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Efficient soft-output decoders for the surface code

Quantum Physics 2024-06-04 v2

Abstract

Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work, we construct efficient soft-output decoders for the surface code derived from the Minimum-Weight Perfect Matching and Union-Find decoders. We show that soft-output decoding can improve the performance of a "hierarchical code," a concatenated scheme in which the inner code is the surface code, and the outer code is a high-rate quantum low-density parity-check code. Alternatively, the soft-output decoding can improve the reliability of fault-tolerant circuit sampling by flagging those runs that should be discarded because the probability of a logical error is intolerably large.

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Cite

@article{arxiv.2405.07433,
  title  = {Efficient soft-output decoders for the surface code},
  author = {Nadine Meister and Christopher A. Pattison and John Preskill},
  journal= {arXiv preprint arXiv:2405.07433},
  year   = {2024}
}

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