Comparison of fault-tolerant thresholds for planar qudit geometries

 

 

 

 

 

We introduce and analyze a new type of decoding algorithm called General Color Clustering (GCC), based on renormalization group methods, to be used in qudit color codes. The performance of this decoder is analyzed under depolarizing and generalized bit flip noise models, and is used to obtain the first fault-tolerant 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…

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