Efficient soft-output decoders for the surface code

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.