Splitting decoders for correcting hypergraph faults

Understand

The surface code is one of the most popular quantum error correction codes.

• It comes with efficient decoders, such as the Minimum Weight Perfect Matching (MWPM) decoder and the Union-Find (UF) decoder, allowing for fast quantum error correction.
• For a general linear code or stabilizer code, the decoding problem is NP-hard.
• What makes it tractable for the surface code is the special structure of faults and checks: Each X and Z fault triggers at most two checks.