Comparison of memory thresholds for planar qudit geometries

Abstract

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 code capacity depolarizing noise, 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. We find that, as with surface codes, clustering performs sub-optimally for qubit color codes, giving a threshold of $9.75\%$ compared to the $11.4\%$ obtained through surface projection decoding methods. However, the threshold rate increases by up to $75\%$ for large qudit dimensions, plateauing around $17.1\%$. All the analysis is performed using QTop, a new open-source software for simulating and visualizing topological quantum error correcting codes.

Replaced with the published version, small typos corrected, any comments are welcome! QTop software available at https://github.com/jacobmarks/QTop

References in corpus (6)

• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological Quantum Distillation
• Single-shot fault-tolerant quantum error correction
• Universal transversal gates with color codes - a simplified approach
• A fast fault-tolerant decoder for qubit and qudit surface codes
• Generalized Color Codes Supporting Non-Abelian Anyons

Cited by in corpus (4)

• Neural ensemble decoding for topological quantum error-correcting codes
• Fault-Tolerant Computing with Single Qudit Encoding
• Non-Pauli errors can be efficiently sampled in qudit surface codes
• Quantum computation with charge-and-color permuting twists in qudit color codes