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arXiv:2610.01683

A Code-Agnostic Graph Neural Network Decoder from the Detection Error Model

Federico Alberto Astolfi, Guido Pupillo

quant-phSubmitted Oct 1, 2026• Announced Oct 2, 2026• 0 citations
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Abstract

We present POLYMECHANON, a graph neural network (GNN) decoder for quantum error correction whose only input is the detection error model (DEM) of a quantum code under a given noise model. We represent the DEM as a tripartite graph of detectors, error mechanisms and logical observables, where every input feature is computed by using the quantum code as data rather than design choice. In this way, the same architecture decodes in principle any stabiliser code, under any noise model that can be expressed as a detection error model, once trained on the DEM. We test this approach along four directions. Firstly, on the rotated surface code the decoder outperforms correlated MWPM under both phenomenological and circuit-level noise, with up to $25\%$ fewer logical failures. Secondly, on a family of high-rate qLDPC codes it matches BP+OSD on the smaller codes and surpasses it on the larger ones, with up to $16\%$ fewer logical failures on $[\![130,4,6]\!]$. Thirdly, its decoding time does not depend on the physical error rate, whereas that of BP+OSD grows with it: on $[\![130,4,6]\!]$ its effective cost per shot is of the order of a few ms on a single GPU against a few tens of milliseconds for BP+OSD on a single CPU core, and its fixed computational graph makes it a candidate for real-time decoding on neutral-atom processors. Finally, a single model trained across codes of different families outperforms uncorrelated MWPM on the graph-like codes seen during training and stays within $10\%$ of BP+OSD on the others, while it tends to fail to generalize to unseen codes, particularly larger ones. Its probabilistic output enables confidence-based post-selection, lowering the logical error rate by more than an order of magnitude on the surface code while keeping more than $90\%$ of the shots. Since only the DEM changes, new codes and noise models can be decoded without redesigning the decoder.

Comments
19 pages, 8 figures, 6 tables

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We present POLYMECHANON, a graph neural network (GNN) decoder for quantum error correction whose only input is the detection error model (DEM) of a quantum code under a given noise model. We represent the DEM as a tripartite graph of detectors, error mechanisms and logical observables, where every input feature is computed by using the quantum code as data rather than design choice. In this way, the same architecture decodes in principle any stabiliser code, under any noise model that can be expressed as a detection error model, once trained on the DEM. We test this approach along four directions. Firstly, on the rotated surface code the decoder outperforms correlated MWPM under both phenomenological and circuit-level noise, with up to 25%25\%25% fewer logical failures. Secondly, on a family of high-rate qLDPC codes it matches BP+OSD on the smaller codes and surpasses it on the larger ones, with up to 16%16\%16% fewer logical failures on [ ⁣[130,4,6] ⁣][\![130,4,6]\!][[130,4,6]]. Thirdly, its decoding time does not depend on the physical error rate, whereas that of BP+OSD grows with it: on [ ⁣[130,4,6] ⁣][\![130,4,6]\!][[130,4,6]] its effective cost per shot is of the order of a few ms on a single GPU against a few tens of milliseconds for BP+OSD on a single CPU core, and its fixed computational graph makes it a candidate for real-time decoding on neutral-atom processors. Finally, a single model trained across codes of different families outperforms uncorrelated MWPM on the graph-like codes seen during training and stays within 10%10\%10% of BP+OSD on the others, while it tends to fail to generalize to unseen codes, particularly larger ones. Its probabilistic output enables confidence-based post-selection, lowering the logical error rate by more than an order of magnitude on the surface code while keeping more than 90%90\%90% of the shots. Since only the DEM changes, new codes and noise models can be decoded without redesigning the decoder.
Graph neural network (GNN) decoders for quantum error correction have historically been locked to specific code families. The POLYMECHANON preprint [1,2] proposes a decoder whose sole input is the detection error model (DEM) — a tripartite graph of detectors, error mechanisms, and logical observables — making the code data rather than an architectural design choice. This paper provides an independent, arithmetic-first assessment of that claim. We convert the reported headline numbers into concrete quantities: a 25% reduction in logical failures versus correlated MWPM on the rotated surface code corresponds to an improvement factor of 0.75, which under the standard scaling ansatz p_L ∝ (p/p_th)^⌈d/2⌉ is equivalent to a relative pseudo-threshold improvement of ≈10.06% at d = 5 and ≈7.46% at d = 7; a 16% reduction on the [[130,4,6]] qLDPC code corresponds to a factor of 0.84 and an equivalent threshold improvement of ≈5.98%. The reported latency advantage ("a few ms per shot on a single GPU" versus "a few tens of ms" for BP+OSD on a CPU core) would bound the speedup in [4×, 25×], midpoint ≈10×, with an explicit hardware-asymmetry caveat — but this latency analysis is conditional on claims not verifiable in the available abstract record of [1,2]. We derive DEM graph sizes for canonical cases (441 detectors, 1,337 mechanisms, 2,681 edges at d = 8, R = 8 under stated conventions), prove a cheap non-isomorphism certificate between surface-code and qLDPC DEMs via part-size vectors, and show that the claimed post-selection result (>10× error reduction at >90% shot retention) would arithmetically require discarded shots to fail at ≈9.1× the base rate — a strong, testable separability condition, conditional on a claim not verifiable in the available abstract record of [1,2]. We identify size-generalization, DEM fidelity, and hardware-fair latency comparison as the principal open risks, and propose falsification experiments for each. ## 1. Introduction Fault-tolerant quantum Full text and updates: papers.qnfo.org/papers/code-agnostic-graph-neural-network-decoding-from-detection-error-models-a-reconc/
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 3.1×3.1\times3.1× and 6.5×6.5\times6.5×. 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=10−3p=10^{-3}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 1μs1μs1μs average latency, and by 13% under a strict 1μs1μs1μs deadline.
Quantum error correction is essential to achieve fault-tolerant quantum computation in the presence of noisy qubits. Among the most promising approaches to quantum error correction is the surface code, thanks to a scalable two-dimensional architecture, only nearest-neighbor interactions, and a high error threshold. Decoding the surface code, i.e. finding the most likely error chain given a syndrome measurement outcome is a computationally complex task. Traditional decoders rely on classical algorithms, which, especially for larger systems, can be slow and may not always converge to the optimal solution. This thesis presents a novel approach to decoding the surface code using graph neural networks. By mapping the syndrome measurements to a graph and performing graph classification, we find that the graph neural networks can predict the most likely error configuration with high accuracy. Our results show that the GNN-based decoder outperforms the classic minimum weight perfect matching (MWPM) decoder in terms of accuracy. With a phenomenological noise model with depolarizing noise and perfect syndrome measurements, our networks beat MWPM up to code-size 15 across all relevant error rates. Furthermore, the GNN is capable of surpassing MWPM under circuit-level noise up to code size 7. We also show that training the network on repetition code data from a recent experiment [Google Quantum AI, Nature 614, 676 (2023)] produces per-step error rates comparable to those achieved with a matching decoder specifically adapted to the error rates of the physical qubits. This indicates that graph neural network decoders are capable of learning the underlying error distribution on the qubits. Our findings advance the field of quantum error correction and provide a promising new direction for the development of efficient decoding algorithms.
Post-selection improves the logical reliability of quantum computation by rejecting shots which are likely to result in logical failure. We introduce graph neural networks that predict decoder failure without additional decoder executions, using only syndromes, and for high-rate quantum low-density parity-check (qLDPC) codes, existing belief-propagation posteriors. We evaluate rotated surface and bivariate bicycle (BB) code memories under uniform depolarising circuit-level noise. Retaining 90% of shots gives approximately 3700x and 740x reductions in logical error rates for [[72,12,6]] and [[144,12,12]] BB codes at realistic physical error rates. For the distance 5 surface code at physical noise p=0.003, our neural post-selector achieves logical error suppression comparable to the leading complementary gap method without running the decoder.
Fault-tolerant quantum computing critically relies on quantum error correction. We study surface-code decoding with diagonally correlated two-qubit Z\mathbf{Z}Z errors, a structured noise model that breaks assumptions leveraged by MinimumWeight Perfect Matching (MWPM). We develop a graph neural network (GNN) decoder based on learned message passing and benchmark it against a tuned MWPM baseline informed by the same noise statistics. In code-capacity simulations at code distances 3, 5, and 7, the GNN achieves consistently lower logical error rates than MWPM across the tested range of pair-error probabilities. The GNN correction threshold is about 2.5%, surpassing the 2.4% achieved by the MWPM baseline. These results indicate that data-driven message passing can adapt to complex, geometry-dependent noise without hand-crafted correlation models, thereby reducing reliance on manual model specification for quantum error correction.
Neural decoders for quantum error correction have achieved high accuracy on surface code memory experiments, but practical fault-tolerant computation requires decoders that transfer across devices, noise conditions, and logical operations. We introduce a modular graph-recurrent decoder designed for this setting. Built from reusable local syndrome encoders, it is pretrained in simulation and fine-tuned to hardware using a common pipeline, with only lightweight spatial aggregation adapted between experiments. The decoder performs competitively on conventional memory benchmarks, outperforming minimum-weight perfect matching (MWPM) at distances 3 and 5 on an IBM Nighthawk-generation processor and closely approaching AlphaQubit on Google's below-threshold hardware data. We then test the framework in two settings beyond memory decoding on the same IBM device. First, in an XXX-type stability experiment, we continuously tune the effective measurement error rate using a variable pre-readout rotation and train a single decoder jointly across the resulting noise range. It matches or outperforms MWPM across the sweep without requiring a separately calibrated decoder for each setting. Second, we decode a ZZZZZZ-merge lattice-surgery experiment between two distance-3 surface-code patches, improving the decoded correlation between the merge outcome and the final ZZZZZZ parity relative to MWPM on real hardware. Together, these experiments demonstrate neural decoding that is portable not only across hardware, but also across qualitatively different surface code observables and logical operations, using models trainable on single-GPU academic resources.