量子纠错（QEC）是容错量子计算（FTQC）的关键组成部分；QEC解码器是量子经典计算（Classical Computing for Quantum，简称C4Q）的重要环节。近年来，实时QEC解码器发展迅速，但现有实时解码器的构建工作尚未达成一项关键里程碑：实现带纠错读出和前馈的动态逻辑电路解码。要实现这一目标，需要大量工程工作来根据逻辑电路的分支在运行时调整和重新配置解码器。\n我们提出了一种名为LEGO的QEC解码器架构，其宏大目标是支持动态逻辑操作。LEGO采用了一种名为解码块的新型抽象来描述动态逻辑电路的解码问题。此外，解码块可与另外三种思路结合，以提升解码器的效率、准确性和延迟表现：第一，当与基于融合的解码结合时，解码块可提供数据并行和任务并行；第二，解码块可利用多级解码器内部的流水线并行；第三，解码块可作为计算资源管理的基本工作单元。\n借助解码块，LEGO可轻松重新配置以支持所有QEC设置，并且能很好地适配三个相互依赖领域的创新：编码、逻辑操作以及量子比特硬件。相比之下，现有解码器高度专用于特定QEC设置，这会导致研究和工程工作冗余，减缓创新速度，还会进一步割裂尚处发展初期的量子计算产业。
英文摘要：
Quantum error correction (QEC) is a critical component of FTQC; the QEC decoder is an important part of Classical Computing for Quantum or C4Q. Recent years have seen fast development in real-time QEC decoders. Existing efforts to build real-time decoders have yet to achieve a critical milestone: decoding dynamic logical circuits with error-corrected readout and feed forward. Achieving this requires significant engineering effort to adapt and reconfigure the decoders during runtime, depending on the branching of the logical circuit.
We present a QEC decoder architecture called LEGO, with the ambitious goal of supporting dynamic logical operations. LEGO employs a novel abstraction called the decoding block to describe the decoding problem of a dynamic logical circuit. Moreover, decoding blocks can be combined with three other ideas to improve the efficiency, accuracy and latency of the decoder. First, they provide data and task parallelisms when combined with fusion-based decoding. Second, they can exploit the pipeline parallelism inside multi-stage decoders. Finally, they serve as basic units of work for computational resource management.
Using decoding blocks, LEGO can be easily reconfigured to support all QEC settings and to easily accommodate innovations in three interdependent fields: code, logical operations and qubit hardware. In contrast, existing decoders are highly specialized to a specific QEC setting, which leads to redundant research and engineering efforts, slows down innovation, and further fragments the nascent quantum computing industry.
LEGO_HQEC: Automating the Analysis, Construction, and Decoding of Holographic Quantum Codes
QuTech, Delft University of Technology（代尔夫特理工大学量子技术研究所）；Quantum and Computer Engineering Department, Delft University of Technology（代尔夫特理工大学量子与计算机工程系）；Freie Universität Berlin（柏林自由大学）；Virginia Tech（弗吉尼亚理工大学）
A Scalable Open-Source QEC System with Sub-Microsecond Decoding-Feedback Latency
Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学量子信息与计算科学联合中心）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Transformer-QEC: Quantum Error Correction Code Decoding with Transferable Transformers
Massachusetts Institute of Technology（麻省理工学院）；Carnegie Mellon University（卡内基梅隆大学）；Yale University（耶鲁大学）；Arizona State University（亚利桑那州立大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
qecGPT: decoding Quantum Error-correcting Codes with Generative Pre-trained Transformers
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）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院基础物理与数学科学学院）；International Centre for Theoretical Physics Asia-Pacific（国际理论物理中心亚太地区）
Rethink the Role of Neural Decoders in Quantum Error Correction
College of Computing；Data Science, Nanyang Technological University, Singapore 639798, Singapore；Department of Electrical Engineering；Computer Science, Tokyo University of Agriculture \& Technology, Koganei, Tokyo, 184-8588, Japan；School of Physical；Mathematical Sciences, Nanyang Technological University, Singapore 639798, Singapore
Quantum error correction and fault tolerance: A comprehensive tutorial
Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算机联合中心，美国国家标准与技术研究院/马里兰大学）；Department of Physics, University of Maryland（马里兰大学物理系）；Joint Quantum Institute, NIST/University of Maryland（量子联合研究所，美国国家标准与技术研究院/马里兰大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学理学院南洋量子枢纽）；Quantum Research Center, Technology Innovation Institute（技术创新研究所量子研究中心）；Department of Computer Science and Institute for Advanced Co（计算机科学系与高级合作研究所）
Performance Limits of Fault-Tolerant Quantum Error Correction Schemes
University of Bologna（博洛尼亚大学）；CNIT/WiLab（国家信息技术研究与开发中心/无线实验室）；Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi”（“古列尔莫·马可尼”电气、电子和信息工程系）；Quantinuum
Quantum Compiler Design for Fault-Tolerant Quantum Computing
QudeLeap Research；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）；Shanghai Jiao Tong University（上海交通大学）；Hangzhou MatriQ Computing Co., Ltd（杭州矩阵量子计算有限公司）；Atomqubic Quantum Technology Co., Ltd（上海原子立方量子科技有限公司）；State Key Laboratory of Quantum Optics Technologies and Devices, and Institute of Opto-Electronics, Shanxi University（山西大学光电研究所及量子光学技术与器件国家重点实验室）；CAS Cold Atom Technology (Wuhan) Co., Ltd.（中科院冷原子技术（武汉）有限公司）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）
Demonstrating Noise-adapted Quantum Error Correction With Break-Even Performance
Indian Institute of Technology Madras（印度理工学院马德拉斯分校）；Center for Quantum Information, Communication and Computing, IIT Madras（印度理工学院马德拉斯量子信息、通信与计算中心）；University College London（伦敦大学学院）
