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There has been a rise in decoding quantum error correction codes with neuralnetwork based decoders, due to the good decoding performance achieved andadaptability to any noise model. However, the main challenge is scalability tolarger code distances due to an exponential increase of the error syndromespace. Note that, successfully decoding the surface code under realistic noiseassumptions will limit the size of the code to less than 100 qubits withcurrent neural network based decoders.  Such a problem can be tackled by a distributed way of decoding, similar tothe Renormalization Group (RG) decoders. In this paper, we introduce a decodingalgorithm that combines the concept of RG decoding and neural network baseddecoders. We tested the decoding performance under depolarizing noise withnoiseless error syndrome measurements for the rotated surface code and comparedagainst the Blossom algorithm and a neural network based decoder. We show thatsimilar level of decoding performance can be achieved between all testeddecoders while providing a solution to the scalability issues of neural networkbased decoders.

Decoding surface code with a distributed neural network based decoder