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

Quantum hardware suffers from high error rates and noise, which makes directly running applications on them ineffective. Quantum Error Correction (QEC) is a critical technique towards fault tolerance which encodes the quantum information distributively in multiple data qubits and uses syndrome qubits to check parity. Minimum-Weight-Perfect-Matching (MWPM) is a popular QEC decoder that takes the syndromes as input and finds the matchings between syndromes that infer the errors. However, there are two paramount challenges for MWPM decoders. First, as noise in real quantum systems can drift over time, there is a potential misalignment with the decoding graph's initial weights, leading to a severe performance degradation in the logical error rates. Second, while the MWPM decoder addresses independent errors, it falls short when encountering correlated errors typical on real hardware, such as those in the 2Q depolarizing channel. We propose DGR, an efficient decoding graph edge re-weighting strategy with no quantum overhead. It leverages the insight that the statistics of matchings across decoding iterations offer rich information about errors on real quantum hardware. By counting the occurrences of edges and edge pairs in decoded matchings, we can statistically estimate the up-to-date probabilities of each edge and the correlations between them. The reweighting process includes two vital steps: alignment re-weighting and correlation re-weighting. The former updates the MWPM weights based on statistics to align with actual noise, and the latter adjusts the weight considering edge correlations. Extensive evaluations on surface code and honeycomb code under various settings show that DGR reduces the logical error rate by 3.6x on average-case noise mismatch with exceeding 5000x improvement under worst-case mismatch.