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We propose an error correction procedure based on a cellular automaton, thesweep rule, which is applicable to a broad range of codes beyond topologicalquantum codes. For simplicity, however, we focus on the three-dimensional (3D)toric code on the rhombic dodecahedral lattice with boundaries and prove thatthe resulting local decoder has a non-zero error threshold. We also numericallybenchmark the performance of the decoder in the setting with measurement errorsusing various noise models. We find that this error correction procedure isremarkably robust against measurement errors and is also essentiallyinsensitive to the details of the lattice and noise model. Our work constitutesa step towards finding simple and high-performance decoding strategies for awide range of quantum low-density parity-check codes.

Cellular automaton decoders for topological quantum codes with noisy measurements and beyond