Kitaev's Z_d-Codes Threshold Estimates

TL;DR

This paper investigates the error correction threshold of Kitaev's Z_d toric code under generalized noise, developing new decoding methods based on a generalized renormalization group approach.

Contribution

It introduces a novel decoding technique for Z_d topological codes by generalizing the renormalization group method previously used for Z_2 codes.

Findings

Developed a generalized renormalization group decoding method.

Estimated the error correction threshold for Z_d codes.

Enhanced understanding of topological code robustness.

Abstract

We study the quantum error correction threshold of Kitaev's toric code over the group Z_d subject to a generalized bit-flip noise. This problem requires novel decoding techniques, and for this purpose we generalize the renormalization group method we previously introduced for Z_2 topological codes.