Decoding Quantum Error Correction Codes with Local Variation

TL;DR

This paper demonstrates that incorporating local information into decoding quantum error correction codes enhances resource efficiency, reducing the required code distance for a given logical error rate, especially near the threshold.

Contribution

It introduces a method to improve quantum error correction decoding by leveraging local information, leading to resource savings and better performance.

Findings

Resource efficiency improves with local information use.

Code distance reduction depends on proximity to error threshold.

Local information enhances decoding schemes for quantum codes.

Abstract

In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local information is taken into account during the decoding process: the code distance associated with a given logical error rate is reduced with a magnitude depending on the proximity of the physical error rate to the accuracy threshold of the code. We also briefly discuss an averaged approach with local information for table-lookup and localised decoding schemes, an expected breakdown of these effects for large-scale systems, and the importance of this resource reduction in the near-term.