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

TL;DR

DGR addresses critical weaknesses of MWPM decoders by using decoding-history statistics to dynamically re-weight the decoding graph in two ways: alignment re-weighting to track noise drift and correlation re-weighting to leverage edge correlations. The alignment step uses an occurrence tracer to update edge weights, while the correlation step builds a co-occurrence matrix and performs a second MWPM with either a heuristic formula or an NN-based re-weighter to refine results; both are designed to incur zero quantum overhead and operate in parallel on classical hardware. Empirically, DGR yields substantial logical-error-rate reductions across surface and honeycomb codes, with average improvements of $3.6\times$ to $1.7\times$ depending on regime, and worst-case improvements exceeding $5000\times$, while correlation re-weighting adds further gains (~$1.2$–$1.4\times$). The approach demonstrates strong robustness to large drift and complex correlations, providing a scalable, plug-and-play enhancement to MWPM for near-term quantum hardware.

Abstract

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.

Figures (19)

• Figure 1: Compare traditional decoding method with our proposed decoding graph re-weighting (DGR). DGR leverages decoding statistics to dynamically re-weight the decoding graph for high-fidelity quantum error correction.
• Figure 2: Surface code and its decoding graph.
• Figure 3: Noise drift with in short-term and long-term.
• Figure 4: Re-decoding with correlation re-weighting to identify the correct errors.
• Figure 5: The overview of the proposed decoding graph re-weighting flow, including conditional correlation re-weighting to capture edge correlation and periodic alignment re-weighting to align the probability.