Quantum Error Correction Decoding

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15 papers0 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

Sep 16, 2026

Securing quantum error correction against misleading advice from AI agents

Can an attacker turn influence over an artificial intelligence (AI) adviser into a harmful quantum error-correction update? We identify an ambiguity in passive syndrome records that obstructs recovery selection, then show how additional calibration measurements support certified recovery updates under uncertainty and drift. In an odd-distance square toric code with error-free preparation, syndrome measurements, and recovery operations, opposite coherent

X

rotations produce identical passive syndrome-history distributions. Yet a fixed phase correction can help at one sign and harm at the other. A terminal logical measurement on known encoded calibration states supplies the missing sign information. A separate evaluator accepts an update only when calibration uncertainty and a justified drift bound certify improvement over the current recovery, without assuming that the adviser recommends correctly. In simulated advice attacks, calibration-confidence checks reject harmful proposals while retaining beneficial updates under honest advice. We derive sufficient limits on calibration age that require improvement through deployment. In matched simulations, a validated channel-specific bound retains more beneficial updates than the general bound after accounting for evaluation time, while preventing the tested harmful activations under the stated drift assumption. A separate surface-code experiment includes stochastic circuit faults and noise changing during acquisition. Deterministic controllers achieve at least as many beneficial updates with the same observations. Violating the drift assumption permits harmful acceptance in the toric experiment. The results identify information required for recovery selection, establish conditional guarantees against harmful updates, and quantify the recovery improvements forgone through conservative acceptance.

A. Barış Özgüler

AI Agent Reliability Quantum Error Correction AI Agent Security Quantum Error Correction Decoding

Sep 3, 2026

A Sim-to-Real Study of Surface-Code Decoder Benchmarking

Quantum error-correction decoders are typically benchmarked against synthetic circuit-level noise, under the assumption that a decoder's ranking under such noise transfers to hardware and improves as the noise model becomes more realistic. The Willow processor, the first to operate below the surface-code threshold, allows us to test this assumption. We rank a panel of six decoders using a four-rung ladder of noise models with increasing fidelity, evaluated against real data across three code distances, two bases, and fifteen round counts. Rank agreement with hardware appears once the noise model gives each operation type its own error rate. Calibrating the model to the device improves absolute error rates but not rank agreement. We additionally provide the first independent evaluation of NVIDIA's Ising pre-decoder on hardware, at code distances below its training receptive field and via a mapping onto the lattice on which it was trained. Under these conditions, it holds no accuracy-latency advantage: another panel decoder matches or improves on it in both per-cycle error rate and decode latency in 278 of the 280 evaluations. We release the full pipeline and the per-shot outcome of every evaluation, so future decoders and devices can be compared.

Shay J. Manor, Leila S. Erhili, Yassine Jebbouri

Department of Computer Science, Purdue University, West Lafayette, IN 47907 USA · Department of Computer Science, Columbia University, New York, NY 10027 USA · Data Science Institute, Columbia University, New York, NY 10027 USA

Quantum Error Correction Quantum Error Correction Decoding

Aug 16, 2026

Machine Learning Approaches to Decoding Topological Quantum Codes

Decoding is an essential component of quantum error correction (QEC), translating stabilizer measurement outcomes into corrective actions that suppress logical errors and preserve logical quantum information. Building fault-tolerant architectures requires increasing the code distance, which in turn places growing demands on decoding accuracy, scalability, and practical deployability. While a wide range of decoding algorithms have been proposed and demonstrated, achieving reliable, scalable, and real-time decoding remains a significant challenge. Machine-learning (ML) approaches are particularly well suited to this setting, as quantum error decoding is fundamentally a problem of processing large volumes of classical data with complex spatiotemporal correlations. This chapter surveys ML-based methods for quantum error decoding, with a focus on topological codes and an emphasis on architectural principles, practical performance, and real-time considerations. We first frame decoding as a learning problem and outline key paradigms, including discriminative, generative, and reinforcement-learning formulations. We then introduce the neural network building blocks that underpin most contemporary neural decoders and discuss how these components can be integrated to balance expressivity, scalability, and latency. Building on this architectural perspective, we review recent progress and benchmarks in neural decoding for memory experiments, and discuss real-time decoding, open challenges, and future directions toward scalable fault-tolerant quantum computing.

Changwon Lee, Tak Hur, Jeongwoo Jae +1

Department of Statistics and Data Science, Yonsei University, Seoul 03722, Republic of Korea · R&D center, Samsung SDS, Seoul 05510, Republic of Korea · Department of Applied Statistics, Yonsei University, Seoul 03722, Republic of Korea +1

Quantum Error Correction Decoding Neural Decoding Quantum Error Correction

Jul 30, 2026

QAdapt: A Noise-Adaptive Neural Pre-Decoding Framework for Quantum Error Correction

Fault-tolerant quantum computing (FTQC) relies on quantum error correction to suppress physical errors and preserve logical information at scale. In practice, however, performance is constrained not only by physical noise but also by the latency of classical decoders processing rapidly generated syndrome data. This challenge is exacerbated by hardware noise that is strong, heterogeneous, and nonstationary, as well as by the simulation-to-hardware distribution shift that can substantially degrade fixed neural decoders. We present QAdapt, a noise-adaptive neural pre-decoding framework for surface-code quantum error correction. QAdapt captures local spatiotemporal correlations in syndrome data, sequentially adapts to evolving noise conditions while mitigating catastrophic forgetting, and forwards the residual syndrome to a conventional global decoder. Across 110 synthetic out-of-distribution noise configurations for rotated surface-code memory circuits, QAdapt consistently reduces the logical error rate relative to the neural pre-decoding baseline. On Google's Willow benchmark data, without target-domain fine-tuning, it achieves reductions of up to 5.79 percent in logical error rate and 9.32 percent in backend decoding latency on the residual syndrome. These results demonstrate that QAdapt provides a practical and decoder-compatible approach to improving the robustness and backend decoding efficiency of quantum error correction under evolving hardware noise.

Ran Miao, Rui Luo, Xiaohan Shan +1

Beijing Zhongke Qhub Technology Co., Ltd. (Qhub), Beijing, China · Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China · Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

Distribution Shift Neural Decoding Quantum Error Correction Quantum Error Correction Decoding

Jul 12, 2026

MDQEC-QAS: Meta-Decoding for Quantum Error Correction with Hardware-Aware VQC Search and Confidence-Gated Recovery

We propose a unified meta-decoding framework for quantum error correction that learns syndrome-to-recovery mappings across multiple stabilizer codes and noise settings, without requiring separate decoders for each configuration. The benchmark includes FiveQubit, Steane, Planar3x3, and Planar5x5 codes, four noise families, and five evaluation regimes: interpolation, unseen-p transfer, unseen-noise transfer, few-shot unseen-code adaptation, and few-shot held-out-size adaptation. We compare a classical Meta-MLP teacher-trained baseline with variational quantum circuit (VQC) meta-decoders selected through hardware-aware quantum architecture search over qubit count, circuit depth, and entangling topology. The Meta-MLP achieves teacher-label accuracies of 0.9993, 0.9118, 0.9342, 0.6304, and 0.7548 across the five regimes, while the hardware-aware VQC achieves 0.9400, 0.8495, 0.8415, 0.5678, and 0.7143. However, logical-level evaluation shows that high teacher-label accuracy alone is insufficient in the most challenging Planar5x5 setting. During interpolation, the raw logical-failure ratios relative to the teacher are 12.08 and 25.91 for the Meta-MLP and VQC, respectively, whereas confidence-gated fallback reduces them to 1.71 and 1.11. These results support confidence-aware selective recovery rather than unconditional teacher replacement.

Prashant Kumar Choudhary, Nouhaila Innan, Muhammad Shafique +1

Department of Physics, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, India · eBRAIN Lab, Division of Engineering, New York University Abu Dhabi (NYUAD), Abu Dhabi, UAE · Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, NYUAD, Abu Dhabi, UAE

Variational Quantum Circuits Selective Prediction Meta-Learning Neural Decoding Quantum Error Correction Quantum Architecture Search+2

Jul 7, 2026

Latency-Constrained Hardware-Aware Quantum Error Correction Co-Design with Adaptive Confidence-Gated Neural Decoding for the Rotated Surface Code

Real-time decoding is a major bottleneck in scaling quantum error correction (QEC) from noisy intermediate-scale quantum (NISQ) devices to fault-tolerant quantum computing. We present an adaptive confidence-gated decoding framework for the rotated surface code that treats decoding as a two-stage inference problem. A lightweight feed-forward neural network performs fast-path decoding for the majority of syndrome measurements, while only low-confidence predictions are escalated to a minimum-weight perfect matching (MWPM) refinement stage. We benchmark the framework on rotated surface codes with distances

d \in \{3,5,7,9,11\}

under circuit-level depolarising noise using the Stim stabiliser simulator. The evaluation characterises logical accuracy, confidence-controlled accuracy-latency trade-offs, decoding throughput, per-shot latency, and decoding-graph resource scaling. Routing only 3.3%-6.2% of syndromes to the refinement stage improves logical accuracy from 99.21% for the neural-only baseline to 99.81% at a confidence threshold of 0.95 while incurring only a bounded increase in average decoding cost. Neural-decoder throughput saturates near

4.6 \times 10^{5}

samples s

^{-1}

at batch size 512 on commodity CPU hardware, indicating that the neural fast path is not the dominant throughput bottleneck beyond code distance

d=7

. We release the complete benchmarking pipeline, trained models, raw benchmark data, and source code, and explicitly distinguish the experimentally validated contributions from the broader hardware-aware QEC co-design roadmap, including hardware-constrained code discovery, GPU-accelerated inference, and multi-noise optimisation, which remain directions for future work.

Sumit Chongder

Department of Physics, Quantum Information and Computation, Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan 342037, India

Neural Decoding Quantum Error Correction Quantum Error Correction Decoding Error-Correcting Codes

Jun 25, 2026

Efficient foundation decoders for fault-tolerant quantum computing

Foundation decoders, a class of high-capacity neural decoders, are leading candidates for fault-tolerant quantum computing, with accurate and efficient decoding at large code distances. However, their construction often faces a steep scaling barrier, as larger code distances rapidly amplify the cost of syndrome generation and neural optimization. To address this bottleneck, here we devise neural transfer unification (NTU), a unified framework for efficient foundation decoders. A central feature of NTU is its ability to align decoding tasks across code distances via algebraic structures shared by scalable code families, which enables knowledge learned on smaller codes to accelerate large-scale decoder training. We instantiate NTU as NTU-Transformer, a transformer-based neural decoder tailored for planar surface codes and bivariate bicycle codes. For planar surface codes under circuit-level noise, NTU-Transformer outperforms correlation-aware matching on the

[\![361,1,19]\!]

code and further scales to the

[\![625,1,25]\!]

code, where it exceeds standard matching through transfer adaptation. For the bivariate bicycle code with

[\![72,12,6]\!]

, it surpasses Relay-BP in the low-physical-error regime. These results establish our proposal as a scalable route to amortized cross-distance training of foundation decoders for fault-tolerant quantum processors.

Ge Yan, Shanchuan Li, Shiyi Xiao +4

College of Computing and Data Science, Nanyang Technological University, Singapore · Department of Electrical Engineering and Computer Science, Tokyo University of Agriculture and Technology, Koganei, Tokyo, Japan · School of Artificial Intelligence, Shanghai Jiao Tong University, Shanghai, China +2

Neural Decoding Quantum Error Correction Quantum Error Correction Decoding Transfer Learning

May 17, 2026

Maximum Likelihood Decoding of Quantum Error Correction Codes

Quantum error correction (QEC) is indispensable for realizing fault-tolerant quantum computation, yet its effectiveness hinges critically on the classical decoding algorithm that interprets noisy syndrome measurements. Among all possible decoding strategies, maximum likelihood decoding (MLD) is provably optimal, since it identifies the logical group with largest likelihood by summing over all possible errors within logical class consistent with the observed syndrome. Despite its optimality, MLD is computationally intractable in general (#P-hard), motivating a rich landscape of exact and approximate algorithms. In this topical review, we provide a unified perspective on MLD by surveying recent advances through three complementary lenses: statistical mechanics, tensor networks, and artificial intelligence. From the statistical mechanics viewpoint, the MLD problem maps onto evaluating partition functions of disordered spin models, enabling exact solutions for certain codes and noise models as well as threshold estimation via phase-transition analysis. From the tensor network perspective, approximate contraction of tensor networks on the code's factor graph yields decoders that closely approach MLD accuracy with polynomial computational cost. From the artificial intelligence perspective, neural-network-based decoders, including autoregressive generative models and recurrent transformers, learn to approximate the MLD distribution from data, achieving high accuracy with the parallelism afforded by modern hardware accelerators. We discuss the connections among these three approaches, review their application to both simulated and experimental quantum hardware, and outline open challenges including real-time decoding, scalability to large code distances, and generalization to high-rate quantum low-density parity-check codes.

Hanyan Cao, Ge Yan, Yuxuan Du +1

1Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372, Singapore · College of Computing and Data Science, Nanyang Technological University, Singapore, Singapore · School of Physical and Mathematical Sciences, Nanyang Technological University,2026 Singapore, Singapore

Quantum Error Correction Quantum Error Correction Decoding Error-Correcting Codes

May 16, 2026

Sparse Mamba Decoder for Quantum Error Correction: Efficient Defect-Centric Processing of Surface Code Syndromes

Quantum error correction (QEC) is essential for building fault-tolerant quantum computers, requiring decoders that are simultaneously accurate, fast, and scalable. Most state-of-the-art neural decoders achieve high accuracy but process the full dense syndrome array of size

O(d^2 R)

regardless of the actual error rate, where d is the code distance and R is the number of measurement rounds. At physically relevant error rates (p ~ 0.1%), fewer than 5% of syndrome entries contain active detection events -- yet existing decoders process the entire syndrome volume. We introduce the Sparse Mamba Decoder (SMD), a defect-centric neural decoder that processes only the k active detection events using a 13-dimensional feature representation per defect and a Mamba state-space backbone, achieving

O(k)

complexity. Across depolarizing, uniform circuit-level, SI1000, and Google Sycamore experimental benchmarks, SMD reduces the MWPM logical error rate by up to 49% at

d \le 5

under SI1000 noise, runs 95-467x faster than the Tesseract near-MLD decoder and 232-463x faster than Belief Matching, and maintains nearly constant latency (24-57 us) across d = 3-9 under uniform circuit-level noise. On the Sycamore experimental dataset, the SMD ensemble matches or slightly surpasses the dense Mamba decoder of Varbanov et al. All results are obtained on commodity NVIDIA GPUs with 7.5-16M parameters, without specialized accelerators.

Samira Sayedsalehi, Nader Bagherzadeh, Maxim Shcherbakov +1

Department of Electrical Engineering and Computer Science University of California, Irvine, CA 92697, USA

Neural Decoding Quantum Error Correction Quantum Error Correction Decoding Error-Correcting Codes

May 12, 2026

Rethink the Role of Neural Decoders in Quantum Error Correction

Quantum error correction (QEC) is essential for enabling quantum advantages, with decoding as a central algorithmic primitive. Owing to its importance and intrinsic difficulty, substantial effort has been made to QEC decoder design, among which neural decoders have recently emerged as a promising data-driven paradigm. Despite this progress, practical deployment remains hindered by a fundamental accuracy-latency tradeoff, often on the microsecond timescale. To address this challenge, here we revisit neural decoders for surface-code decoding under explicit accuracy-latency constraints, considering code distances up to d=9 (161 physical qubits). We unify and redesign representative neural decoders into five architectural paradigms and develop an end-to-end compression pipeline to evaluate their deployability and performance on FPGA hardware. Through systematic experiments, we reveal several previously underexplored insights: (i) near-term decoding performance is driven more by data scale than architectural complexity; (ii) appropriate inductive bias is essential for achieving high decoding accuracy; and (iii) INT4 quantization is a prerequisite for meeting microsecond-scale latency requirements on FPGAs. Together, these findings provide concrete guidance toward scalable and real-time neural QEC decoding.

Ge Yan, Shanchuan Li, Yuxuan Du

College of Computing and Data Science, Nanyang Technological University, Singapore 639798, Singapore · Department of Electrical Engineering and Computer Science, Tokyo University of Agriculture & Technology, Koganei, Tokyo, 184-8588, Japan · School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639798, Singapore

Neural Decoding Quantum Error Correction Quantum Error Correction Decoding

Apr 9, 2026

Scalable Neural Decoders for Practical Fault-Tolerant Quantum Computation

Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have recently emerged as a promising route to efficient fault tolerance, current decoding algorithms do not allow one to realize the full potential of these codes in practical settings. Here, we introduce a convolutional neural network decoder that exploits the geometric structure of QEC codes, and use it to probe a novel "waterfall" regime of error suppression, demonstrating that the logical error rates required for large-scale fault-tolerant algorithms are attainable with modest code sizes at current physical error rates, and with latencies within the real-time budgets of several leading hardware platforms. For example, for the

[144, 12, 12]

Gross code, the decoder achieves logical error rates up to

\sim 17

x below existing decoders - reaching logical error rates

\sim 10^{-10}

at physical error

p=0.1\%

- with 3-5 orders of magnitude higher throughput. This decoder also produces well-calibrated confidence estimates that can significantly reduce the time overhead of repeat-until-success protocols. Taken together, these results suggest that the space-time costs associated with fault-tolerant quantum computation may be significantly lower than previously anticipated.

Andi Gu, J. Pablo Bonilla Ataides, Mikhail D. Lukin +1

Department of Physics, Harvard University, Cambridge, MA 02138, USA · Harvard Quantum Initiative, Harvard University, Cambridge, MA 02138, USA

Quantum LDPC Codes Quantum Error Correction Decoding Quantum Error Correction Neural Decoding Error-Correcting Codes Convolutional Neural Networks

Jan 1, 2026

Neural Minimum Weight Perfect Matching for Quantum Error Codes

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.

Yotam Peled, David Zenati, Eliya Nachmani

School of Electrical and Computer Engineering (ECE), Ben-Gurion University, Beer Sheva, Israel.

Neural Decoding Quantum Error Correction Combinatorial Optimization Quantum Error Correction Decoding

Dec 20, 2025

Evolutionary BP+OSD Decoding for Low-Latency Quantum Error Correction

Quantum error correction (QEC) for fault-tolerant quantum computing requires a balanced decoding solution that offers high performance, low complexity, and low latency. However, the de facto standard - belief propagation (BP) combined with ordered statistics decoding (OSD) - suffers from excessive iterations in the BP stage and high complexity in the OSD stage. To address these challenges, we propose an evolutionary BP (EBP) decoder optimized via a differential evolution (DE) algorithm. By leveraging the gradient-free nature of DE, we enable end-to-end optimization of the EBP+OSD structure to maximize overall performance. In addition, a multi-objective selection rule is introduced to suppress frequent OSD activation, significantly reducing complexity overhead. Simulation results on surface codes and quantum low-density parity-check (QLDPC) codes demonstrate that EBP+OSD simultaneously achieves both superior decoding performance and substantially lower complexity compared to conventional BP+OSD, particularly in stringent low-latency regimes.

Hee-Youl Kwak, Seong-Joon Park, Hyunwoo Jung +2

Department of Electrical, Electronic and Computer Engineering, University of Ulsan, Ulsan 44610, South Korea · Department of Electrical Engineering at Pohang University of Science and Technology (POSTECH), Pohang, Gyeongbuk 37673, South Korea · School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea +1

Quantum Error Correction Decoding Quantum Error Correction Quantum LDPC Codes

Oct 13, 2025

Qubit-centric Transformer for Surface Code Decoding

For reliable large-scale quantum computation, quantum error correction (QEC) is essential to protect logical information distributed across multiple physical qubits. Taking advantage of recent advances in deep learning, neural network-based decoders have emerged as a promising approach to improve the reliability of QEC. We propose the qubit-centric transformer (QCT), a novel and universal QEC decoder based on a transformer architecture with a qubit-centric attention mechanism. Our decoder transforms input syndromes from the stabilizer domain into qubit-centric tokens via a specialized embedding strategy. These qubit-centric tokens are processed through attention layers to effectively identify the underlying logical error. Furthermore, we introduce a graph-based masking method that incorporates the topological structure of quantum codes, enforcing attention toward relevant qubit interactions. Across various code distances for surface codes, QCT achieves state-of-the-art decoding performance, significantly outperforming existing neural decoders and the belief propagation (BP) with ordered statistics decoding (OSD) baseline. Notably, QCT achieves a high threshold of 18.1% under depolarizing noise, which closely approaches the theoretical bound of 18.9% and surpasses both the BP+OSD and the minimum-weight perfect matching (MWPM) thresholds. This qubit-centric approach provides a scalable and robust framework for surface code decoding, advancing the path toward fault-tolerant quantum computing.

Seong-Joon Park, Hee-Youl Kwak, Yongjune Kim

Samsung Electronics Company, Ltd., Suwon 16677, South Korea · Institute of Artificial Intelligence, Pohang University of Science and Technology (POSTECH), Pohang 37673, South Korea · Department of Electrical, Electronic and Computer Engineering, University of Ulsan, Ulsan 44610, South Korea +1

Neural Decoding Quantum Error Correction Transformer Attention Quantum Error Correction Decoding

Oct 5, 2025

Toward Uncertainty-Aware and Generalizable Neural Decoding for Quantum LDPC Codes

Quantum error correction (QEC) is essential for scalable quantum computing, yet decoding errors via conventional algorithms result in limited accuracy (i.e., suppression of logical errors) and high overheads, both of which can be alleviated by inference-based decoders. To date, such machine-learning (ML) decoders lack two key properties crucial for practical fault tolerance: reliable uncertainty quantification and robust generalization to previously unseen QEC codes. To address this gap, we propose a Quantum Bayesian graph Attention decoder (QuBA) that enables expressive error-pattern recognition alongside calibrated uncertainty estimates. Building on QuBA, we further develop a multi-phase training framework with enhanced cross-domain robustness enabling decoding beyond the training set called Sequential Aggregate Generalization under Uncertainty (SAGU). Experiments on bivariate bicycle (BB) codes and their coprime variants demonstrate that (i) both QuBA and SAGU consistently outperform the classical baseline belief propagation (BP), achieving up to a two orders of magnitude reduction in logical error rate (LER) under confident-decision bounds on the coprime BB code

[[154,6,16]]

; (ii) SAGU achieves decoding performance comparable to or even outperforming QuBA's domain-specific training approach.

Xiangjun Mi, Frank Mueller

North Carolina State University, Raleigh, NC 27695, USA

Quantum LDPC Codes Quantum Error Correction Decoding OOD Generalization Uncertainty Quantification Graph Neural Networks