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.
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.
Quantum computers can solve selected problems more efficiently than classical computers, but current devices are limited by high physical error rates. Quantum Error Correction (QEC) mitigates this by encoding many physical qubits into a logical qubit, with the surface code among the most widely studied approaches. Since syndrome measurements are produced continuously, the decoder must process them fast enough to avoid becoming a system bottleneck, making real-time decoding essential for fault-tolerant quantum computing. While most state-of-the-art real-time decoders rely on Minimum-Weight Perfect Matching (MWPM), we instead use a high-accuracy Graph Neural Network (GNN) that trades higher computational cost for lower logical error rates. To make this GNN practical for real-time decoding, we apply algorithm-hardware co-design. We reduce complexity through hardware-guided pruning and retraining, producing two hardware-friendly models that reduce parameter count by 3.1× and 6.5×. These target, respectively, an average decoding latency of one syndrome cycle and a worst-case latency within one syndrome cycle. We further reduce hardware cost using input-graph filtering and post-training quantization. Based on these optimized models, we propose an FPGA-based architecture for low-latency inference and real-time decoding. Evaluated on surface codes up to distance 7 under circuit-level noise at physical error rate p=10−3, our decoder outperforms MWPM in decoding accuracy for both average-latency and max-latency settings. It reduces logical error rate by 40% at 1μs average latency, and by 13% under a strict 1μs deadline.
Efficient and realistic error decoding is crucial for fault-tolerant quantum computation (FTQC) on near-term devices. While decoding is a classical post-processing task, its effectiveness depends on accurately modeling quantum noise, which is hardware-dependent. In particular, correlated bit-flip (X) and phase-flip (Z) errors often arise under circuit-level noise. We introduce the Iterative Reweighting Minimum-Weight Perfect Matching (IRMWPM) decoder, which systematically incorporates such correlations to enhance quantum error correction. Our method leverages fault-detection patterns to guide reweighting: correlated X and Z detection events are identified, and their conditional probabilities update weights on the primal and dual lattices. This iterative procedure improves handling of realistic error propagation in a hardware-agnostic yet noise-aware manner. We prove that IRMWPM converges in finite time while preserving the distance guarantee of MWPM. Numerical results under circuit-level noise show substantial improvements. For distances ≥17 and physical error rates ≤0.001, IRMWPM reduces logical error rates by over 20x with only a few iterations. It also raises the accuracy threshold from 1% to 1.16%, making it practical for near-term real-time decoding. Extrapolated estimates suggest that to reach logical error rate 10−16, IRMWPM requires distance d=31, while standard MWPM needs d=50, implying a major reduction in qubit overhead.
Realizing the full potential of quantum computation requires Quantum Error Correction (QEC). QEC reduces error rates by encoding logical information across redundant physical qubits, enabling errors to be detected and corrected. A common decoder used for this task is Minimum Weight Perfect Matching (MWPM) a graph-based algorithm that relies on edge weights to identify the most likely error chains. In this work, we propose a data-driven decoder named Neural Minimum Weight Perfect Matching (NMWPM). Our decoder utilizes a hybrid architecture that integrates Graph Neural Networks (GNNs) to extract local syndrome features and Transformers to capture long-range global dependencies, which are then used to predict dynamic edge weights for the MWPM decoder. To facilitate training through the non-differentiable MWPM algorithm, we formulate a novel proxy loss function that enables end-to-end optimization. Our findings on the toric code under depolarizing noise demonstrate thresholds of 17.9% and 10.95%, nearing the 18.9% and 11.0% maximum likelihood bounds, highlighting the advantage of hybrid decoders that combine the predictive capabilities of neural networks with the algorithmic structure of classical matching.
Quantum devices suffer from high error rates, which makes them ineffective for running practical applications. Quantum computers can be made fault tolerant using Quantum Error Correction (QEC), which protects quantum information by encoding logical qubits using data qubits and parity qubits. The data qubits collectively store the quantum information and the parity qubits are measured periodically to produce a syndrome, which is decoded by a classical decoder to identify the location and type of errors. To prevent errors from accumulating and causing a logical error, decoders must accurately identify errors in real-time, necessitating the use of hardware solutions because software decoders are slow. Ideally, a real-time decoder must match the performance of the Minimum-Weight Perfect Matching (MWPM) decoder. However, due to the complexity of the underlying Blossom algorithm, state-of-the-art real-time decoders either use lookup tables, which are not scalable, or use approximate decoding, which significantly increases logical error rates.
Quantum error correction (QEC) is crucial for achieving fault-tolerant quantum computing by addressing errors in noisy qubits. The surface code, a leading QEC framework, traditionally employs the Minimum Weight Perfect Matching (MWPM) decoder. We present a step-by-step methodology that formulates surface code decoding as a supervised machine learning classification problem within a two-level framework, where low-level modules address physical qubit errors and highlevel modules correct logical errors. We implement Feedforward Neural Networks (FFNN) and Graph Neural Networks (GNN), which are individually employed to perform low-level physical qubit error correction and high-level logical error correction for rotated surface codes of distancesd=3,d=5, andd=7. Under depolarizing noise, both FFNN and GNN achieve lower logical error rates than MWPM, with GNN yielding up to 28% improvement atd=7. GNN achieves pseudothresholds of 0.1084, 0.1311, and 0.1441 ford=3,d=5, andd=7, surpassing MWPM's 0.0914, 0.1024, and 0.1126. Crossover points further indicate GNN's robustness at higher noise levels (e.g., 0.1632 vs. 0.1291 for MWPM). By learning error distributions in a two-level setting, both FFNN and GNN outperform MWPM, demonstrating their potential as scalable, high-performance decoders for near-term quantum devices.
Abstract Quantum error-correction decoders must convert noisy syndrome records into logical decisions while operating under strict latency and reliability constraints. Minimum-weight perfect matching (MWPM) remains a strong baseline for surface-code decoding because it is fast, interpretable, and exact for its graphlike optimization problem [1–8]. However, the graphlike independent-error approximation can become mismatched when syndrome records contain temporal drift, measurement corruption, crosstalk, bursts, or mixtures of mechanisms [9–18]. We introduce SAGE-QEC, a failure-aware selective decoder that retains nominal PyMatching as its default decision and learns when an observable syndrome structure warrants an alternative candidate. SAGE-QEC uses train-frozen structure thresholds, a candidate ranker, validation-only policy selection, and a paired blind evaluation. Across 45 simulator conditions, SAGE-QEC reduced the aggregate logical error rate from 27.1285% for PyMatching to 24.8320%, corresponding to an 8.47% relative reduction. The campaign used rotated surface-code memory circuits at distances 3, 5, and 7, nominal circuit parameters 0.002, 0.003, and 0.005, five seeds, and four test regimes withheld from training: Burst-3, Temporal Drift, Crosstalk, and Mixed Noise. The test set contained 81,000 paired shots. All twelve distance-by-regime aggregate comparisons favored SAGE-QEC in the executed campaign, with paired bootstrap intervals below zero for SAGE-QEC minus PyMatching. The result is evidence of a reproducible simulator-level improvement, not a claim of universal decoder superiority. SAGE-QEC currently uses logical-output proxy candidates rather than a complete physical correction search, and its intervention rate remains high under distribution shift. It has not yet been compared with a fully calibrated correlated-noise space-time PyMatching baseline or hardware calibration data. We therefore characterize SAGE-QEC as a strong qualification-stage prototype and release a complete audit protocol for the next industrial validation stage.