Message passing in fault tolerant quantum error correction

TL;DR

This paper introduces a message passing error correction scheme for the nine-qubit Bacon-Shor code, significantly reducing logical failure rates by utilizing classical information across concatenation levels.

Contribution

It develops a novel message passing error correction method for fault-tolerant quantum computing, improving error correction efficiency over traditional approaches.

Findings

Corrects all cases with four physical errors at two levels of concatenation.

Reduces logical failure rate proportionally to the reciprocal of physical error rate.

Demonstrates improved fault tolerance in quantum error correction schemes.

Abstract

Inspired by Knill's scheme for message passing error detection, here we develop a scheme for message passing error correction for the nine-qubit Bacon-Shor code. We show that for two levels of concatenated error correction, where classical information obtained at the first level is used to help interpret the syndrome at the second level, our scheme will correct all cases with four physical errors. This results in a reduction of the logical failure rate relative to conventional error correction by a factor proportional to the reciprocal of the physical error rate.