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Hierarchical Evaluation of Correlated-Noise Decoders for Room- Temperature Photonic Quantum Computing: From Scale-Invariance Verification to Residual-Subtraction and GNN Decoders

Tomohiro Tani

Published May 12, 2026• 0 citations
Publisher

Abstract

Room-temperature continuous-variable (CV) photonic quantum computers are affected by inter-mode correlated displacement noise arising from a shared pump laser, violating the independent-noise assumptions underlying standard quantum error correction decoders. Here, we systematically evaluate four decoding strategies under correlated noise and establish a decoder hierarchy across code distances d = 3, 5, and 7. We first show that V_eff-recalibration MWPM is exactly equivalent to vanilla MWPM, confirmed by 100% agreement over 170,000 shots, reflecting the intrinsic scale invariance of minimum-weight perfect matching. To overcome this limitation, we introduce residual-subtraction MWPM, which estimates and removes the common-mode component from residual syndromes, adapting classical telecom common-mode rejection to quantum error correction. This method achieves up to 41.8× improvement at d = 5 and 19.0× at d = 7. We further develop a lightweight graph neural network (GNN) decoder with only 4,033 parameters (~2,500× smaller than AlphaQubit), which learns the correlation structure directly and achieves up to 33.4× improvement. A single GNN trained on mixed correlation strengths generalizes to unseen noise conditions, retaining a 20.8× advantage at out-of-distribution ρ = 0.20. Under independent noise (ρ = 0), both correlation-aware approaches degrade relative to MWPM, confirming that their advantage derives specifically from exploiting shared-noise structure. Across ~920,000 fully reproducible simulations, our results identify practical decoder strategies for correlated CV photonic hardware and demonstrate that explicitly modeling shared-noise structure can substantially improve fault-tolerant performance.

DOI
10.5281/zenodo.20137037

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Room-temperature continuous-variable (CV) photonic quantum computers are affected by inter-mode correlated displacement noise arising from a shared pump laser, violating the independent-noise assumptions underlying standard quantum error correction decoders. Here, we systematically evaluate four decoding strategies under correlated noise and establish a decoder hierarchy across code distances d = 3, 5, and 7. We first show that V_eff-recalibration MWPM is exactly equivalent to vanilla MWPM, confirmed by 100% agreement over 170,000 shots, reflecting the intrinsic scale invariance of minimum-weight perfect matching. To overcome this limitation, we introduce residual-subtraction MWPM, which estimates and removes the common-mode component from residual syndromes, adapting classical telecom common-mode rejection to quantum error correction. This method achieves up to 41.8× improvement at d = 5 and 19.0× at d = 7. We further develop a lightweight graph neural network (GNN) decoder with only 4,033 parameters (~2,500× smaller than AlphaQubit), which learns the correlation structure directly and achieves up to 33.4× improvement. A single GNN trained on mixed correlation strengths generalizes to unseen noise conditions, retaining a 20.8× advantage at out-of-distribution ρ = 0.20. Under independent noise (ρ = 0), both correlation-aware approaches degrade relative to MWPM, confirming that their advantage derives specifically from exploiting shared-noise structure. Across ~920,000 fully reproducible simulations, our results identify practical decoder strategies for correlated CV photonic hardware and demonstrate that explicitly modeling shared-noise structure can substantially improve fault-tolerant performance.
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.
Continuous-variable (CV) GKP quantum error correction produces high-precision analog residual syndromes rather than binary outcomes, yet these residuals have primarily been treated only as decoding inputs. Here, we show that GKP residuals are mathematically equivalent to pilot signals in telecommunications, enabling quantum error correction (QEC) itself to function as a real-time hardware-state sensor for room-temperature photonic quantum computers. Using the wrapped Gaussian residual distribution, we derive the Fisher information for effective displacement-noise variance (V_{\mathrm{eff}}) estimation and quantitatively compare CV analog syndromes against discrete-variable (DV) binary syndromes under an equal syndrome-measurement budget. CV systems provide 4.5–17.5× greater Fisher information for (V_{\mathrm{eff}}) estimation from QEC syndromes, with the advantage increasing at higher squeezing where DV information saturates. For a (d=7) surface code with 686 modes per QEC cycle, wrapped-Gaussian maximum-likelihood estimation achieves approximately 3% (V_{\mathrm{eff}}) accuracy within only three QEC cycles ((\sim 21,\mu\mathrm{s})), whereas DV syndrome-only estimation remains near 28% error even after 100 cycles under the same measurement budget due to the intrinsic information bottleneck of sparse binary events. We further evaluate online anomaly detection using false-alarm-rate-calibrated CUSUM tests. CV systems detect subtle (+0.2,\mathrm{dB}) degradations 1.9× faster than DV systems while maintaining perfect detection across all simulated trials, whereas DV detection rates fall to 91% under identical conditions. We additionally identify a fundamental scale-invariance limitation of adaptive minimum-weight perfect matching (MWPM): uniform recalibration of decoder weights leaves the matching solution unchanged even with perfect (V_{\mathrm{eff}}) estimation. This explains why accurate global noise estimation alone yields minimal decoding improvement unless channel asymmetry is present. Across approximately 11.5 million fully reproducible simulated shots, these results establish a high-bandwidth analog-information advantage (“14-bit advantage”) of CV-QEC residuals as a telemetry channel for autonomous monitoring, diagnostics, and preventive maintenance. More broadly, they demonstrate that QEC in CV photonic systems is not only an error-correction mechanism, but also an intrinsic real-time sensor for hardware-state estimation and adaptive system control in room-temperature quantum computing.
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.
Abstract One of the critical requirements for fault-tolerant quantum computation is fast and reliable decoding,Minimum-weight perfect matching (MWPM) is a reliable surface-code decoder,but it will face long decoding time when decoding instances grow. Neural-network decoders was used to solve this problem, but large models often require costly retraining when the code distance or noise model changes.In this work, we propose a two-stage decoder that combines pretrained graph neural network (GNN) residual pre-decoding with global MWPM cleanup.The GNN receives a detector graph generated by the established decoding backend and assigns confidence scores to local correction candidates.Two staggered layers of parallel local windows process confidence corrections.The residual syndrome is passed to the NVIDIA-accelerated MWPM backend.On matched batches of 32,768 samples, the complete method reduced the logical failure rate by 6.25% to 18.01% relative to Pure MWPM for code distances d=3,5,7 and 9 at physical error rates p = 0.007 to 0.013. At d=3,it decoded 3.48x – 4.38x faster over p=0.003 to 0.021. We also trained separate GNN residual pre-decoders for four circuit-level noise models over 160 code-distance/error-rate configurations and obtained 2.25x to 5.41x speedups in every case.The logical-failure benefit depended on the noise model,but the pace is all improving. Our work can accelerate surface-code decoding pace and extend to others noise models.
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.
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=5d=3, d=5d=3,d=5, andd=7d=7d=7. Under depolarizing noise, both FFNN and GNN achieve lower logical error rates than MWPM, with GNN yielding up to 28% improvement atd=7d=7d=7. GNN achieves pseudothresholds of 0.1084, 0.1311, and 0.1441 ford=3,d=5d=3, d=5d=3,d=5, andd=7d=7d=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.