Neural network decoder confidence as a learned proxy for the logical gap
David Dentelski
备注：
Major revisions. Added post-selected exchange confidence in new Fig. 2. Total of 4 figures in the Main text. Added three appendices (total of four), with additional information
To utilize quantum error-correcting codes, a decoder must infer the logical sector from the measured syndrome. Beyond a hard logical decision, some decoders provide soft information estimating its reliability. For minimum-weight perfect matching (MWPM), a common confidence measure is the complementary, or logical, gap. Neural-network decoders trained with binary cross entropy naturally output a different score, the logit, whose relation to the matching gap remains unclear. Here, we test whether the logit of a graph neural network (GNN) decoder behaves as a learned proxy for the logical gap. Using a pretrained GNN for the rotated surface code under uniform circuit-level noise [PRR, 7(2):023181, 2025], we compare its logit with the MWPM gap shot by shot on identical syndromes. The native GNN decoder-logit pair yields a lower post-selected logical error rate than the native MWPM decoder-gap pair over the operationally relevant range of acceptance rates. Exchanging the scores between decoders isolates score discrimination from hard-decision accuracy and shows that both contribute to the advantage. At larger distances each score best ranks failures of its own decoder, whereas at small distance, where the bounded matching gap saturates, the learned confidence better discriminates MWPM failures than the gap itself. Finally, GNN confidence is substantially better described by the posterior logistic form implied by an ideal log-likelihood ratio, while the MWPM gap shows systematic departures. Thus, a neural-network decoder trained only on syndromes and logical labels learns a gap-like confidence proxy whose native scale more closely follows the expected posterior calibration form, supporting learned soft output when MWPM gap estimates are unavailable, costly, or insufficiently expressive.
We consider tensor-network stabilizer codes and show that their tensor-network decoder has the property that independent logical qubits can be decoded in parallel. As long as the error rate is below threshold, we show that this parallel decoder is essentially optimal. As an application, we verify this for the max-rate holographic Steane (heptagon) code. For holographic codes this tensor-network decoder was shown to be efficient with complexity polynomial in n, the number of physical qubits. Here we show that, by using the parallel decoding scheme, the complexity is also linear in k, the number…
Decoder Model Compatibility Provides Information beyond the Logical Gap under Drifting and Correlated Quantum Noise
University of Washington（华盛顿大学）；Pacific Northwest National Laboratory（太平洋西北国家实验室）；Fordham University（福特汉姆大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；NASA Ames Research Center（美国宇航局艾姆斯研究中心）
Surface codes are a promising method of quantum error correction and the basis of many proposed quantum computation implementations. However, their efficient decoding is still not fully explored. Recently, approaches based on machine learning techniques have been proposed by Torlai and Melko as well as Varsamopoulos et al. In these approaches, a so called high level decoder is used to post-correct an underlying decoder by correcting logical errors. A significant problem is that these methods require large amounts of training data even for relatively small code distances. The above-mentioned me…
Impacts of Decoder Latency on a Utility-Scale Quantum Computer Architecture
QB Information Technologies (1QBit)（1QB信息技术公司）；Department of Physics & Astronomy, University of Waterloo（滑铁卢大学物理与天文系）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；Quantum Machines（量子机器公司）；HPE Quantum, Hewlett Packard Labs（惠普实验室HPE量子部门）；Emergent Machine Intelligence, Hewlett Packard Labs（惠普实验室涌现人工智能部门）
Logical error estimation from syndrome data of surface-code experiments
Duke Quantum Center, Duke University（杜克量子中心，杜克大学）；Department of Electrical and Computer Engineering, Duke University（电气与计算机工程系，杜克大学）；Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid（马德里自治大学-西班牙国家科研委员会理论物理研究所，马德里自治大学）；Department of Electrical & Computer Engineering, University of Southern California（电气与计算机工程系，南加州大学）；Center for Quantum Information Science & Technology, University of Southern California（量子信息与科技中心，南加州大学）；Quantum Elements, Inc.（量子元素公司）；Department of Physics & Astronomy, University of Southern California（物理与天文学系，南加州大学）；Department of Chemistry, University of Southern California（化学系，南加州大学）；Department of Physics, Duke University（物理系，杜克大学）；Department of Chemistry, Duke University（化学系，杜克大学）
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been proposed that achieve approximately optimal error thresholds. Due to practical constraints, it is not known if there exists an obvious choice for a decoder. In this paper, we introduce a framework which can combine arbitrary decoders for any given code to significantly reduce the logical error rates. We rely on the crucial observation that two different decodin…
A Unified Hardware-to-Decoder Architecture for Hybrid Continuous-Variable and Discrete-Variable Quantum Error Correction in LiDMaS+
College of Computing, Georgia Institute of Technology（佐治亚理工学院计算学院）；Independent Quantum Architecture Researcher & Software Developer, SchroSIM Quantum Software Project（独立量子架构研究员及软件开发者，SchroSIM量子软件项目）；Volkswagen AG（大众汽车集团）；Department of Physics, RWTH Aachen（亚琛工业大学物理系）；Department of Computational and Applied Mechanics, Federal University of Juiz de Fora（朱伊斯德福拉联邦大学计算与应用力学系）；Institut für Informatik, Fakultät für Mathematik und Informatik, TU Bergakademie Freiberg（弗莱贝格矿业技术大学数学与信息技术学院计算机科学研究所）
Quantum error correction (QEC) is essential for quantum computing to mitigate the effect of errors on qubits, and surface code (SC) is one of the most promising QEC methods. Decoding SCs is the most computational expensive task in the control device of quantum computers (QCs), and many works focus on accurate decoding algorithms for SCs, including ones with neural networks (NNs). Practical QCs also require low-latency decoding because slow decoding leads to the accumulation of errors on qubits, resulting in logical failures. For QCs with superconducting qubits, a practical decoder must be very…
Matching algorithms can be used for identifying errors in quantum systems, being the most famous the Blossom algorithm. Recent works have shown that small distance quantum error correction codes can be efficiently decoded by employing machine learning techniques based on neural networks (NN). Various NN-based decoders have been proposed to enhance the decoding performance and the decoding time. Their implementation differs in how the decoding is performed, at logical or physical level, as well as in several neural network related parameters. In this work, we implement and compare two NN-based …
Forschungszentrum Jülich（于利希研究中心）；RWTH Aachen University（亚琛工业大学）；University of Tübingen（蒂宾根大学）；Tübingen AI Center（蒂宾根人工智能中心）；Institute for Theoretical Nanoelectronics (PGI-2)（理论纳米电子学研究所 (PGI-2)）；Institute for Quantum Information（量子信息研究所）；Institute for Quantum Control (PGI-8)（量子控制研究所 (PGI-8)）；Institute of Theoretical Physics, University of Regensburg（雷根斯堡大学理论物理研究所）
AlphaSyndrome: Tackling the Syndrome Measurement Circuit Scheduling Problem for QEC Codes
University of Pennsylvania（宾夕法尼亚大学）；University of California, Berkeley（加州大学伯克利分校）；Amazon Quantum Technologies（亚马逊量子技术）；University of Michigan, Ann Arbor（密歇根大学安娜堡分校）
Logical Neural Belief Propagation for Linear-Complexity Decoding of Surface Codes
University of Ulsan（蔚山科学技术院）；Pohang University of Science and Technology (POSTECH)（浦项科技大学）；Ben-Gurion University of the Negev（内盖夫本古里安大学）；Gyeongsang National University（庆尚国立大学）
A quantum computer needs the assistance of a classical algorithm to detect and identify errors that affect encoded quantum information. At this interface of classical and quantum computing the technique of machine learning has appeared as a way to tailor such an algorithm to the specific error processes of an experiment --- without the need for a priori knowledge of the error model. Here, we apply this technique to topological color codes. We demonstrate that a recurrent neural network with long short-term memory cells can be trained to reduce the error rate $ε_{\rm L}$ of the encoded logical …
QAdapt: A Noise-Adaptive Neural Pre-Decoding Framework for Quantum Error Correction
Beijing Zhongke Qhub Technology Co., Ltd.（北京中科瓴湖科技有限公司）；Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院量子信息中心）；Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）
Machine-learned syndrome post-selection for reliable quantum error correction
Quantum Research Center, Technology Innovation Institute, Abu Dhabi, UAE（量子研究中心、技术创新研究所、阿布扎比、阿联酋）；Campus Arapiraca, Federal University of Alagoas, Arapiraca-AL, Brazil（阿拉戈斯联邦大学阿帕里卡校区、巴西）
Differentiable Maximum Likelihood Noise Estimation for Quantum Error Correction
Singapore University of Technology and Design（新加坡科技设计大学）；CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
