Efficient soft-output decoders for the surface code
Nadine Meister, Christopher A. Pattison, John Preskill

TL;DR
This paper develops efficient soft-output decoders for the surface code, enhancing fault-tolerant quantum memory and computation by providing probabilistic error estimates, which improve performance and reliability.
Contribution
It introduces novel soft-output decoders based on Minimum-Weight Perfect Matching and Union-Find for the surface code, enabling better error probability estimation.
Findings
Soft-output decoding improves hierarchical code performance.
Decoding enhances fault-tolerant circuit sampling reliability.
Probabilistic estimates help discard high-error runs.
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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Taxonomy
TopicsAdvanced Data Storage Technologies · Cellular Automata and Applications · Algorithms and Data Compression
