Belief propagation as a partial decoder

TL;DR

This paper introduces a two-stage quantum decoder combining belief propagation and conventional methods, significantly improving speed and accuracy in surface code error correction under circuit noise.

Contribution

A novel two-stage decoding approach that accelerates quantum error correction and enhances logical accuracy compared to traditional methods.

Findings

Speeds up the MWPM decoding stage by 2-4 times.

Raises the error correction threshold from 0.94% to 1.02%.

Reduces bandwidth requirements for decoding.

Abstract

One of the fundamental challenges in enabling fault-tolerant quantum computation is realising fast enough quantum decoders. We present a new two-stage decoder that accelerates the decoding cycle and boosts accuracy. In the first stage, a partial decoder based on belief propagation is used to correct errors that occurred with high probability. In the second stage, a conventional decoder corrects any remaining errors. We study the performance of our two-stage decoder with simulations using the surface code under circuit-level noise. When the conventional decoder is minimum-weight perfect matching, adding the partial decoder decreases bandwidth requirements, increases speed and improves logical accuracy. Specifically, we observe partial decoding consistently speeds up the minimum-weight perfect matching stage by between $2$x-$4$x on average depending on the parameter regime, and raises the threshold from $0.94\%$ to $1.02\%$.