Improved HDRG decoders for qudit and non-Abelian quantum error correction

Understand

Hard-decision renormalization group (HDRG) decoders are an important class of decoding algorithms for topological quantum error correction.

• Due to their versatility, they have been used to decode systems with fractal logical operators, color codes, qudit topological codes, and non-Abelian systems.
• In this work, we develop a method of performing HDRG decoding which combines strenghts of existing decoders and further improves upon them.
• In particular, we increase the minimal number of errors necessary for a logical error in a system of linear size $L$ from $\Theta(L^{2/3})$ to $\Omega(L^{1-\epsilon})$ for any $\epsilon>0$.