Decoding stabilizer codes such as the surface and toric codes involves evaluating free-energy differences in a disordered statistical mechanics model, in which the randomness comes from the observed pattern of error syndromes. We study the statistical distribution of logical failure rates across observed syndromes in the toric code, and show that, within the coding phase, logical failures are predominantly caused by exponentially unlikely syndromes. Therefore, postselecting on not seeing these exponentially unlikely syndrome patterns offers a scalable accuracy gain. In general, the logical error rate can be suppressed from $p_f$ to $p_f^b$, where $b\ge 2$ in general; in the specific case of the toric code with perfect syndrome measurements, we find numerically that $b=3.1\left(1\right)$. Our analysis extends directly to code families for which the relevant free-energy or decoder-confidence variable obeys a large-deviation principle.

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• Quantum error correction
• Large deviation & rare event statistics