Comparison of memory thresholds for planar qudit geometries

Abstract

We introduce and analyze a new type of decoding algorithm called general color clustering, based on renormalization group methods, to be used in qudit color codes. The performance of this decoder is analyzed under a generalized bit-flip error model, and is used to obtain the first memory threshold estimates for qudit 6-6-6 color codes. The proposed decoder is compared with similar decoding schemes for qudit surface codes as well as the current leading qubit decoders for both sets of codes. We find that, as with surface codes, clustering performs sub-optimally for qubit color codes, giving a threshold of $5.6 \% $ compared to the $8.0 \% $ obtained through surface projection decoding methods. However, the threshold rate increases by up to 112% for large qudit dimensions, plateauing around $11.9 \% $ . All the analysis is performed using https://github.com/jacobmarks/QTop , a new open-source software for simulating and visualizing topological quantum error correcting codes.

Keywords

• quantum
• error correction
• color codes
• qudit
• fault-tolerant
• 03.67.Mn