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Quantum hardware suffers from high error rates and noise, which makesdirectly running applications on them ineffective. Quantum Error Correction(QEC) is a critical technique towards fault tolerance which encodes the quantuminformation distributively in multiple data qubits and uses syndrome qubits tocheck parity. Minimum-Weight-Perfect-Matching (MWPM) is a popular QEC decoderthat takes the syndromes as input and finds the matchings between syndromesthat infer the errors. However, there are two paramount challenges for MWPMdecoders. First, as noise in real quantum systems can drift over time, there isa potential misalignment with the decoding graph's initial weights, leading toa severe performance degradation in the logical error rates. Second, while theMWPM decoder addresses independent errors, it falls short when encounteringcorrelated errors typical on real hardware, such as those in the 2Qdepolarizing channel.  We propose DGR, an efficient decoding graph edge re-weighting strategy withno quantum overhead. It leverages the insight that the statistics of matchingsacross decoding iterations offer rich information about errors on real quantumhardware. By counting the occurrences of edges and edge pairs in decodedmatchings, we can statistically estimate the up-to-date probabilities of eachedge and the correlations between them. The reweighting process includes twovital steps: alignment re-weighting and correlation re-weighting. The formerupdates the MWPM weights based on statistics to align with actual noise, andthe latter adjusts the weight considering edge correlations.  Extensive evaluations on surface code and honeycomb code under varioussettings show that DGR reduces the logical error rate by 3.6x on average-casenoise mismatch with exceeding 5000x improvement under worst-case mismatch.

DGR: Tackling Drifted and Correlated Noise in Quantum Error Correction via Decoding Graph Re-weighting