Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code

  title={Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code},
  author={Sergey Bravyi and Martin Suchara and Alexander Vargo},
  journal={Physical Review A},
We describe two implementations of the optimal error correction algorithm known as the maximum likelihood decoder (MLD) for the 2D surface code with a noiseless syndrome extraction. First, we show how to implement MLD exactly in time $O(n^2)$, where $n$ is the number of code qubits. Our implementation uses a reduction from MLD to simulation of matchgate quantum circuits. This reduction however requires a special noise model with independent bit-flip and phase-flip errors. Secondly, we show how… Expand
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