Contents

• Logical-level QEC optimization
  • Clifford Operation Implementation
    • General Clifford and Lattice-Surgery Primitives
    • Lattice Surgery Introduction
    • Surface Code Lattice Surgery Compilers
    • Beyond Surface-Code and qLDPC Code-Surgery Compilers
  • Non-Clifford Operation Implementation
    • Magic State Distillation
    • Code Switching
    • Early Fault-Tolerant Compiler
• Physical-level QEC Implementation
  • Code-Level Syndrome-Extraction Scheduling
  • Hardware-Aware QEC Realization on Superconducting Circuits
  • Hardware-Aware QEC Realization on Trapped-Ion
  • Hardware-Aware QEC Realization on Neutral Atom Arrays
• Decoding in the Classical Control Stack
  • Algorithms and Implementation Trade-offs
    • Algorithm Overview and Tools
    • Matching / MWPM
    • Search and Hypergraph Decoding
    • Union-Find
    • Belief Propagation
    • Neural-Network Decoding
  • Real-Time Decoder Integration
    • Runtime Integration Overview
    • Pauli and Clifford Frames
    • Window and Speculative Decoding
    • Noise- and Side-Information-Aware Decoding
• Conclusion and Future Direction
  • Future Directions

Logical-level QEC optimization

Clifford Operation Implementation

General Clifford and Lattice-Surgery Primitives

• Surface codes: Towards practical large-scale quantum computation Austin G Fowler, Matteo Mariantoni, John M Martinis, and Andrew N Cleland. Physical Review A—Atomic, Molecular, and Optical Physics, 2012.
• Low overhead quantum computation using lattice surgery Austin G Fowler, and Craig Gidney. arXiv preprint arXiv:1808.06709, 2018.

Lattice Surgery Introduction

• Surface code quantum computing by lattice surgery Dominic Horsman, Austin G Fowler, Simon Devitt, and Rodney Van Meter. New Journal of Physics, 2012.

Surface Code Lattice Surgery Compilers

• Mapping of lattice surgery-based quantum circuits on surface code architectures Lingling Lao, Bas van Wee, Imran Ashraf, J Van Someren, Nader Khammassi, Koen Bertels, and Carmen G Almudever. Quantum Science and Technology, 2018.
• Optimization of lattice surgery is NP-hard Daniel Herr, Franco Nori, and Simon J Devitt. Npj quantum information, 2017.
• A SAT Scalpel for Lattice Surgery: Representation and Synthesis of Subroutines for Surface-Code Fault-Tolerant Quantum Computing Daniel Bochen Tan, Murphy Yuezhen Niu, and Craig Gidney. Proceedings of the ACM/IEEE International Symposium on Computer Architecture (ISCA '24), 2024.
• Design automation and space-time reduction for surface-code logical operations using a SAT-based EDA kernel compatible with general encodings Wang Liao, Rei Tokami, and Yasunari Suzuki. arXiv preprint arXiv:2604.12560, 2026.
• Dependency-aware compilation for surface code quantum architectures Abtin Molavi, Amanda Xu, Swamit Tannu, and Aws Albarghouthi. Proceedings of the ACM on Programming Languages, 2025.
• A game of surface codes: Large-scale quantum computing with lattice surgery Daniel Litinski. Quantum, 2019.
• Assessing requirements to scale to practical quantum advantage Michael E Beverland, Prakash Murali, Matthias Troyer, Krysta M Svore, Torsten Hoefler, Vadym Kliuchnikov, Guang Hao Low, Mathias Soeken, et al. arXiv preprint arXiv:2211.07629, 2022.
• Locality-Aware Pauli-based Computation for Local Magic State Preparation Yutaka Hirano, and Keisuke Fujii. arXiv preprint arXiv:2504.12091, 2025.
• Multi-qubit lattice surgery scheduling Allyson Silva, Xiangyi Zhang, Zak Webb, Mia Kramer, Chan Woo Yang, Xiao Liu, Jessica Lemieux, Ka-Wai Chen, et al. arXiv preprint arXiv:2405.17688, 2024.
• A Substrate Scheduler for Compiling Arbitrary Fault-Tolerant Graph States Sitong Liu, Naphan Benchasattabuse, Darcy QC Morgan, Michal Hajdu sek, Simon J. Devitt, and Rodney Van Meter. Proceedings of the IEEE International Conference on Quantum Computing and Engineering (QCE '23), 2023.
• A High Performance Compiler for Very Large Scale Surface Code Computations George Watkins, Hoang Minh Nguyen, Keelan Watkins, Steven Pearce, Hoi-Kwan Lau, and Alexandru Paler. Quantum, 2024.
• Transpiler-Architecture Co-Design to Curb Clifford Costs in Fault-Tolerant Quantum Computing Meng Wang, Chenxu Liu, Samuel Stein, Yufei Ding, Poulami Das, Prashant J. Nair, and Ang Li. arXiv preprint arXiv:2412.15434, 2024.
• Tableau-Based Framework for Efficient Logical Quantum Compilation Meng Wang, Chenxu Liu, Sean Garner, Samuel Stein, Yufei Ding, Prashant J Nair, and Ang Li. arXiv preprint arXiv:2509.02721, 2025.
• Ecmas: Efficient circuit mapping and scheduling for surface code Mingzheng Zhu, Hao Fu, Jun Wu, Chi Zhang, Wei Xie, and Xiang-Yang Li. Proceedings of the IEEE/ACM International Symposium on Code Generation and Optimization (CGO '24), 2024.
• Surface Code Compilation via Edge-Disjoint Paths Michael Beverland, Vadym Kliuchnikov, and Eddie Schoute. PRX Quantum, 2022.
• Trace-Based Reconstruction of Quantum Circuit Dataflow in Surface Codes Theodoros Trochatos, Christopher Kang, Andrew Wang, Frederic T Chong, and Jakub Szefer. arXiv preprint arXiv:2508.14533, 2025.
• Efficient and High-Performance Routing of Lattice-Surgery Paths on Three-Dimensional Lattice Kou Hamada, Yasunari Suzuki, and Yuuki Tokunaga. arXiv preprint arXiv:2401.15829, 2024.
• TopoLS: Lattice Surgery Compilation via Topological Program Transformations Junyu Zhou, Yuhao Liu, Ethan Decker, Justin Kalloor, Mathias Weiden, Kean Chen, Costin Iancu, and Gushu Li. arXiv preprint arXiv:2601.23109, 2026.
• O3LS: Optimizing Lattice Surgery via Automatic Layout Searching and Loose Scheduling Chenghong Zhu, Xian Wu, Jiahan Chen, Keming He, Junjie Wu, Xin Wang, and Lingling Lao. arXiv preprint arXiv:2604.15099, 2026.
• High-Performance and Scalable Fault-Tolerant Quantum Computation with Lattice Surgery on a 2.5D Architecture Yosuke Ueno, Taku Saito, Teruo Tanimoto, Yasunari Suzuki, Yutaka Tabuchi, Shuhei Tamate, and Hiroshi Nakamura. arXiv preprint arXiv:2411.17519, 2024.
• SPARO: Surface-code Pauli-Based Architectural Resource Optimization for Fault-Tolerant Quantum Computing Shuwen Kan, Zefan Du, Chenxu Liu, Meng Wang, Yufei Ding, Ang Li, Ying Mao, and Samuel Stein. arXiv preprint arXiv:2504.21854, 2025.
• The Q-Spellbook: Crafting Surface Code Layouts and Magic State Protocols for Large-Scale Quantum Computing Avimita Chatterjee, Archisman Ghosh, and Swaroop Ghosh. arXiv preprint arXiv:2502.11253, 2025.
• Compilation of trotter-based time evolution for partially fault-tolerant quantum computing architecture Yutaro Akahoshi, Riki Toshio, Jun Fujisaki, Hirotaka Oshima, Shintaro Sato, and Keisuke Fujii. PRX Quantum, 2025.
• RESCQ: Realtime Scheduling for Continuous Angle Quantum Error Correction Architectures Sayam Sethi, and Jonathan Mark Baker. Proceedings of the ACM International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS '25), 2025.
• Variational quantum algorithms in the era of early fault tolerance Siddharth Dangwal, Suhas Vittal, Lennart Maximilian Seifert, Frederic T Chong, and Gokul Subramanian Ravi. Proceedings of the ACM/IEEE International Symposium on Computer Architecture (ISCA '25), 2025.
• The Solovay-Kitaev algorithm Christopher M. Dawson, and Michael A. Nielsen. Quantum Information and Computation, 2006.
• Optimal ancilla-free Clifford+T approximation of Z-rotations Neil J. Ross, and Peter Selinger. Quantum Information and Computation, 2016.
• Realistic Cost to Execute Practical Quantum Circuits using Direct Clifford+ T Lattice Surgery Compilation Tyler LeBlond, Christopher Dean, George Watkins, and Ryan Bennink. ACM Transactions on Quantum Computing, 2023.
• Lattice Surgery Compiler latticesurgery-com. 2025.
• Ecmas+: Efficient Circuit Mapping and Scheduling for Surface Code Encoded Circuit on Quantum Cloud Platform Mingzheng Zhu, Hao Fu, Haishan Song, Jun Wu, Chi Zhang, Wei Xie, and Xiangyang Li. ACM Transactions on Architecture and Code Optimization, 2025.
• PureMagic: A Dynamic Scheduler for Lattice Surgery Steven Hofmeyr, Mathias Weiden, Justin Kalloor, John Kubiatowicz, and Costin Iancu. arXiv preprint arXiv:2512.06484, 2026.
• Non-Clifford Fusion: T-Gate Optimization for Quantum Simulation Yingheng Li, Xulong Tang, Paul Hovland, and Ji Liu. 2025.

Beyond Surface-Code and qLDPC Code-Surgery Compilers

• Lattice Surgery Compilation beyond the Surface Code Laura S. Herzog, Lucas Berent, Aleksander Kubica, and Robert Wille. arXiv preprint arXiv:2504.10591, 2025.
• SSIP: automated surgery with quantum LDPC codes Alexander Cowtan. arXiv preprint arXiv:2407.09423, 2024.
• Engineering CSS surgery: compiling any CNOT in any code Clement Poirson, Joschka Roffe, and Robert I Booth. arXiv preprint arXiv:2505.01370, 2025.
• GeneCS: Synthesizing Resource-Efficient Code Surgery for Arbitrary Quantum Stabilizer Codes Junyu Zhou, Ali Javadi-Abhari, and Gushu Li. arXiv preprint arXiv:2605.21746, 2026.
• Extractors: QLDPC Architectures for Efficient Pauli-Based Computation Zhiyang He, Alexander Cowtan, Dominic J Williamson, and Theodore J Yoder. arXiv preprint arXiv:2503.10390, 2025.
• Tour de gross: A modular quantum computer based on bivariate bicycle codes Theodore J Yoder, Eddie Schoute, Patrick Rall, Emily Pritchett, Jay M Gambetta, Andrew W Cross, Malcolm Carroll, and Michael E Beverland. arXiv preprint arXiv:2506.03094, 2025.
• Assessing System Capabilities and Bottlenecks of an Early Fault-Tolerant Bicycle Architecture Kun Liu, Ben Foxman, Gian-Luca R Anselmetti, and Yongshan Ding. arXiv preprint arXiv:2604.20013, 2026.
• Low-overhead fault-tolerant quantum computing using long-range connectivity Lawrence Z Cohen, Isaac H Kim, Stephen D Bartlett, and Benjamin J Brown. Science Advances, 2022.
• Improved QLDPC surgery: Logical measurements and bridging codes Andrew W Cross, Zhiyang He, Patrick J Rall, and Theodore J Yoder. arXiv preprint arXiv:2407.18393, 2024.
• Time-efficient logical operations on quantum low-density parity check codes Guo Zhang, and Ying Li. Physical Review Letters, 2025.
• Low-overhead fault-tolerant quantum computation by gauging logical operators Dominic J Williamson, and Theodore J Yoder. Nature Physics, 2026.
• Fault-tolerant logical measurements via homological measurement Benjamin Ide, Manoj G Gowda, Priya J Nadkarni, and Guillaume Dauphinais. Physical Review X, 2025.
• Universal adapters between quantum low-density parity check codes Esha Swaroop, Tomas Jochym-O'Connor, and Theodore J Yoder. PRX Quantum, 2026.
• Parallel logical measurements via quantum code surgery Alexander Cowtan, Zhiyang He, Dominic J Williamson, and Theodore J Yoder. PRX Quantum, 2026.
• Fast surgery for quantum LDPC codes Nouedyn Baspin, Lucas Berent, and Lawrence Z Cohen. arXiv preprint arXiv:2510.04521, 2025.
• Parsimonious Quantum Low-Density Parity-Check Code Surgery Andrew C Yuan, Alexander Cowtan, Zhiyang He, Ting-Chun Lin, and Dominic J Williamson. arXiv preprint arXiv:2603.05082, 2026.
• Batched high-rate logical operations for quantum LDPC codes Qian Xu, Hengyun Zhou, Dolev Bluvstein, Madelyn Cain, Marcin Kalinowski, John Preskill, Mikhail D Lukin, and Nishad Maskara. arXiv preprint arXiv:2510.06159, 2025.

Non-Clifford Operation Implementation

Magic State Distillation

• Topological fault-tolerance in cluster state quantum computation Robert Raussendorf, Jim Harrington, and Kovid Goyal. New Journal of Physics, 2007.
• A fault-tolerant one-way quantum computer Robert Raussendorf, Jim Harrington, and Kovid Goyal. Annals of physics, 2006.
• Topological quantum distillation Hector Bombin, and Miguel Angel Martin-Delgado. Physical review letters, 2006.
• Magic-state distillation with low overhead Sergey Bravyi, and Jeongwan Haah. Physical Review A—Atomic, Molecular, and Optical Physics, 2012.
• Magic state distillation with low space overhead and optimal asymptotic input count Jeongwan Haah, Matthew B Hastings, David Poulin, and D Wecker. Quantum, 2017.
• Codes and Protocols for Distilling T, Controlled-S, and Toffoli Gates Jeongwan Haah, and Matthew B Hastings. Quantum, 2018.
• Constant-overhead magic state distillation Adam Wills, Min-Hsiu Hsieh, and Hayata Yamasaki. Nature Physics, 2025.
• Efficient Magic State Distillation by Zero-Level Distillation Tomohiro Itogawa, Yugo Takada, Yutaka Hirano, and Keisuke Fujii. PRX Quantum, 2025.
• Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits Christopher Chamberland, and Kyungjoo Noh. npj Quantum Information, 2020.
• Magic state cultivation: growing T states as cheap as CNOT gates Craig Gidney, Noah Shutty, and Cody Jones. arXiv preprint arXiv:2409.17595, 2024.
• Efficient magic state cultivation with lattice surgery Yutaka Hirano, Riki Toshio, Tomohiro Itogawa, and Keisuke Fujii. arXiv preprint arXiv:2510.24615, 2025.
• Magic State Cultivation on the Surface Code Yotam Vaknin, Shoham Jacoby, Arne Grimsmo, and Alex Retzker. arXiv preprint arXiv:2502.01743, 2025.
• Cultivating T states on the surface code with only two-qubit gates Jahan Claes. arXiv preprint arXiv:2509.05232, 2025.
• Fold-Transversal Surface Code Cultivation Kaavya Sahay, Pei-Kai Tsai, Kathleen Chang, Qile Su, Thomas B Smith, Shraddha Singh, and Shruti Puri. PRX Quantum, 2026.
• Magic-state functional units: Mapping and scheduling multi-level distillation circuits for fault-tolerant quantum architectures Yongshan Ding, Adam Holmes, Ali Javadi-Abhari, Diana Franklin, Margaret Martonosi, and Frederic Chong. Proceedings of the IEEE/ACM International Symposium on Microarchitecture (MICRO '18), 2018.
• Resource optimized quantum architectures for surface code implementations of magic-state distillation Adam Holmes, Yongshan Ding, Ali Javadi-Abhari, Diana Franklin, Margaret Martonosi, and Frederic T Chong. Microprocessors and Microsystems, 2019.
• Magic state distillation: Not as costly as you think Daniel Litinski. Quantum, 2019.
• Leveraging zero-level distillation to generate high-fidelity magic states Yutaka Hirano, Tomohiro Itogawa, and Keisuke Fujii. Proceedings of the IEEE International Conference on Quantum Computing and Engineering (QCE '24), 2024.
• MagicPool: Dealing with Magic State Distillation Failures on Large-Scale Fault-Tolerant Quantum Computer Yutaka Hirano, Yasunari Suzuki, and Keisuke Fujii. arXiv preprint arXiv:2407.07394, 2024.
• Universal quantum computation with ideal Clifford gates and noisy ancillas Sergey Bravyi, and Alexei Kitaev. Physical Review A, 2005.

Code Switching

• Minimizing the Number of Code Switching Operations in Fault-Tolerant Quantum Circuits Erik Weilandt, Tom Peham, and Robert Wille. arXiv preprint arXiv:2512.04170, 2025.
• Enabling Full-Stack Quantum Computing with Changeable Error-Corrected Qubits Anbang Wu, Keyi Yin, Andrew W. Cross, Ang Li, and Yufei Ding. arXiv preprint arXiv:2305.07072, 2023.
• Architectures for Heterogeneous Quantum Error Correction Codes Samuel Stein, Shifan Xu, Andrew W. Cross, Theodore J. Yoder, Ali Javadi-Abhari, Chenxu Liu, Kun Liu, Zeyuan Zhou, et al. arXiv preprint arXiv:2411.03202, 2024.

Early Fault-Tolerant Compiler

• Partially Fault-Tolerant Quantum Computing Architecture with Error-Corrected Clifford Gates and Space-Time Efficient Analog Rotations Yutaro Akahoshi, Kazunori Maruyama, Hirotaka Oshima, Shintaro Sato, and Keisuke Fujii. PRX Quantum, 2024.
• Fast and Parallel High-Rate STAR Architecture for Megaquop Quantum Simulation Refaat Ismail, Milan Kornjača, Hong-Ye Hu, Nishad Maskara, Sheng-Tao Wang, Hengyun Zhou, and Chen Zhao. 2026.

Physical-level QEC Implementation

Code-Level Syndrome-Extraction Scheduling

• Realization of Real-Time Fault-Tolerant Quantum Error Correction C. Ryan-Anderson, J. G. Bohnet, K. Lee, D. Gresh, A. Hankin, J. P. Gaebler, D. Francois, A. Chernoguzov, et al. Physical Review X, 2021.
• Realization of an error-correcting surface code with superconducting qubits Youwei Zhao, Yangsen Ye, He-Liang Huang, Yiming Zhang, Dachao Wu, Huijie Guan, Qingling Zhu, Zuolin Wei, et al. Physical Review Letters, 2022.
• QUITS: A modular Qldpc code circUIT Simulator Mingyu Kang, Yingjia Lin, Hanwen Yao, Mert Gokduman, Arianna Meinking, and Kenneth R Brown. Quantum, 2025.
• Magic Tricycles: Efficient Magic-State Generation with Finite Block-Length Quantum LDPC Codes Varun Menon, J Pablo Bonilla Ataides, Rohan Mehta, Andi Gu, Daniel Bochen Tan, and Mikhail D Lukin. Physical Review X, 2026.
• Surface code off-the-hook: diagonal syndrome-extraction scheduling Gilad Kishony, and Austin Fowler. arXiv preprint arXiv:2602.09099, 2026.
• High-threshold and low-overhead fault-tolerant quantum memory Sergey Bravyi, Andrew W Cross, Jay M Gambetta, Dmitri Maslov, Patrick Rall, and Theodore J Yoder. Nature, 2024.
• Tangling schedules eases hardware connectivity requirements for quantum error correction Gyorgy P Geher, Ophelia Crawford, and Earl T Campbell. PRX Quantum, 2024.
• Distance-preserving stabilizer measurements in hypergraph product codes Argyris Giannisis Manes, and Jahan Claes. Quantum, 2025.
• AlphaSyndrome: Tackling the syndrome measurement circuit scheduling problem for QEC codes Yuhao Liu, Shuohao Ping, Junyu Zhou, Ethan Decker, Justin Kalloor, Mathias Weiden, Kean Chen, Yunong Shi, et al. Proceedings of the ACM International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS '26), 2026.
• PropHunt: Automated optimization of quantum syndrome measurement circuits Joshua Viszlai, Satvik Maurya, Swamit Tannu, Margaret Martonosi, and Frederic T Chong. Proceedings of the ACM International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS '26), 2026.
• Optimal Compilation of Syndrome Extraction Circuits for General Quantum LDPC Codes Kai Zhang, Dingchao Gao, Zhaohui Yang, Runshi Zhou, Fangming Liu, Zhengfeng Ji, and Jianxin Chen. Proceedings of the Design, Automation & Test in Europe Conference (DATE '26), 2026.
• Syndrome Extraction Circuits with Near-Optimal Depths for Practical Quantum Error Correcting Code Families Daniel Bochen Tan, J. Pablo Bonilla Ataides, Varun Menon, Jin Ming Koh, Andrei C. Diaconu, and Mikhail D. Lukin. Proceedings of the ACM/IEEE Design Automation Conference (DAC '26), 2026.
• High-performance syndrome extraction circuits for quantum codes Armands Strikis, Dan E Browne, and Michael E Beverland. arXiv preprint arXiv:2603.05481, 2026.
• Scheduling of syndrome measurements with a few ancillary qubits Shintaro Sato, and Yasunari Suzuki. arXiv preprint arXiv:2508.07913, 2025.

Hardware-Aware QEC Realization on Superconducting Circuits

• A Synthesis Framework for Stitching Surface Code with Superconducting Quantum Devices Anbang Wu, Gushu Li, Hezi Zhang, Gian Giacomo Guerreschi, Yufei Ding, and Yuan Xie. Proceedings of the ACM/IEEE International Symposium on Computer Architecture (ISCA '22), 2022.
• QECC-synth: A Layout Synthesizer for Quantum Error Correction Codes on Sparse Hardware Architectures Keyi Yin, Hezi Zhang, Xiang Fang, Yunong Shi, Travis Humble, Ang Li, and Yufei Ding. arXiv preprint arXiv:2308.06428, 2024.
• Flag-proxy networks: Overcoming the architectural, scheduling and decoding obstacles of quantum ldpc codes Suhas Vittal, Ali Javadi-Abhari, Andrew W Cross, Lev S Bishop, and Moinuddin Qureshi. Proceedings of the IEEE/ACM International Symposium on Microarchitecture (MICRO '24), 2024.
• Louvre: Relaxing Hardware Requirements of Quantum LDPC Codes by Routing with Expanded Quantum Instruction Set Runshi Zhou, Fang Zhang, Hui-Hai Zhao, Feng Wu, Linghang Kong, and Jianxin Chen. arXiv preprint arXiv:2508.20858, 2025.
• A simple universal routing strategy for reducing the connectivity requirements of quantum LDPC codes Guangqi Zhao, Fei Yan, and Xiaotong Ni. arXiv preprint arXiv:2509.00850, 2025.
• Placing and routing quantum LDPC codes in multilayer superconducting hardware Melvin Mathews, Lukas Pahl, David Pahl, Vaishnavi L Addala, Catherine Tang, William D Oliver, and Jeffrey A Grover. npj Quantum Information, 2026.
• CaliScalpel: In-Situ and Fine-Grained Qubit Calibration Integrated with Surface Code Quantum Error Correction Xiang Fang, Keyi Yin, Yuchen Zhu, Jixuan Ruan, Dean Tullsen, Zhiding Liang, Andrew Sornborger, Ang Li, et al. arXiv preprint arXiv:2412.02036, 2024.
• YOUTIAO: Hybrid Multiplexing with Dynamic Qubit Grouping for Low-cost and Scalable Quantum Wiring Wuwei Tian, Liqiang Lu, Siwei Tan, Shiyu Li, Hengyi Li, Tianyao Chu, Xuhong Zhang, Mingshuai Chen, et al. Proceedings of the IEEE/ACM International Symposium on Microarchitecture (MICRO '25), 2025.
• Tiscc: A surface code compiler and resource estimator for trapped-ion processors Tyler LeBlond, Ryan S Bennink, Justin G Lietz, and Christopher M Seck. Proceedings of the IEEE/ACM International Conference for High Performance Computing, Networking, Storage and Analysis Workshops (SC Workshops '23), 2023.
• Architecting scalable trapped ion quantum computers using surface codes Scott Jones, and Prakash Murali. Proceedings of the ACM International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS '26), 2026.
• iSwitch: QEC on Demand via In-Situ Encoding of Bare Qubits for Ion Trap Architectures Keyi Yin, Xiang Fang, Zhuo Chen, Ang Li, David Hayes, Eneet Kaur, Reza Nejabati, Hartmut Haeffner, et al. Proceedings of the ACM International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS '26), 2026.
• Ion-trap chip architecture optimized for the implementation of quantum error-correcting codes Jeonghoon Lee, Hyeongjun Jeon, and Taehyun Kim. Physical Review A, 2026.
• Moveless: Minimizing QEC Overhead on QCCDs via Versatile Execution and Low Excess Shuttling Sahil Khan, Suhas Vittal, Kenneth Brown, and Jonathan Baker. Proceedings of the IEEE International Conference on Quantum Computing and Engineering (QCE '25), 2025.
• Cyclone: Designing Efficient and Highly Parallel QCCD Architectural Codesigns for Fault Tolerant Quantum Memory Sahil Khan, Abhinav Anand, Kenneth R Brown, and Jonathan M Baker. arXiv preprint arXiv:2511.15910, 2025.
• Fault-Tolerant Quantum Computing with Trapped Ions: The Walking Cat Architecture Felix Tripier, Woo Chang Chung, Jacob Young, Safwan Alam, Bryce Bjork, Aharon Brodutch, Finn Lasse Buessen, Nolan J. Coble, et al. arXiv preprint arXiv:2604.19481, 2026.
• Logical quantum processor based on reconfigurable atom arrays Dolev Bluvstein, Simon J Evered, Alexandra A Geim, Sophie H Li, Hengyun Zhou, Tom Manovitz, Sepehr Ebadi, Madelyn Cain, et al. Nature, 2024.
• An Architecture for Improved Surface Code Connectivity in Neutral Atoms Joshua Viszlai, Sophia Fuhui Lin, Siddharth Dangwal, Jonathan M. Baker, and Frederic T. Chong. arXiv preprint arXiv:2309.13507, 2023.
• qSIEVE: Efficient qLDPC Memory via Systolic Movement in Atom Arrays Joshua Viszlai, Willers Yang, Sophia Fuhui Lin, Junyu Liu, Natalia Nottingham, Jonathan M Baker, and Frederic T Chong. ACM Transactions on Quantum Computing, 2026.
• High-rate quantum LDPC codes for long-range-connected neutral atom registers Laura Pecorari, Sven Jandura, Gavin K Brennen, and Guido Pupillo. Nature Communications, 2025.
• ConiQ: Enabling Concatenated Quantum Error Correction on Neutral Atom Arrays Pengyu Liu, Mingkuan Xu, Hengyun Zhou, Hanrui Wang, Umut A. Acar, and Yunong Shi. Proceedings of the IEEE International Conference on Quantum Computing and Engineering (QCE '25), 2025.
• An abstract model and efficient routing for logical entangling gates on zoned neutral atom architectures Yannick Stade, Ludwig Schmid, Lukas Burgholzer, and Robert Wille. Proceedings of the IEEE International Conference on Quantum Computing and Engineering (QCE '24), 2024.
• Quantum error correction resilient against atom loss Hugo Perrin, Sven Jandura, and Guido Pupillo. Quantum, 2025.
• Low-depth quantum error correction via three-qubit gates in Rydberg atom arrays Laura Pecorari, Sven Jandura, and Guido Pupillo. arXiv preprint arXiv:2507.06096, 2025.
• The IBM Quantum Heavy Hex Lattice IBM Quantum. 2021.
• Willow Spec Sheet Google Quantum AI. 2024.
• Amazon Braket Launches the Rigetti Ankaa-2 Superconducting Device Amazon Web Services. 2024.
• Fault-tolerant quantum error correction on near-term quantum processors using flag and bridge qubits Lingling Lao, and Carmen G Almudever. Physical Review A, 2020.
• Relaxing hardware requirements for surface code circuits using time-dynamics Matt McEwen, Dave Bacon, and Craig Gidney. Quantum, 2023.
• Lowering connectivity requirements for bivariate bicycle codes using morphing circuits Mackenzie H Shaw, and Barbara M Terhal. Physical Review Letters, 2025.
• Directional codes: a new family of quantum LDPC codes on hexagonal-and square-grid connectivity hardware Gyorgy P Geher, David Byfield, and Archibald Ruban. arXiv preprint arXiv:2507.19430, 2025.
• Constant-overhead quantum error correction with thin planar connectivity Maxime A Tremblay, Nicolas Delfosse, and Michael E Beverland. Physical Review Letters, 2022.

Hardware-Aware QEC Realization on Trapped-Ion

• Architecting noisy intermediate-scale trapped ion quantum computers Prakash Murali, Dripto M Debroy, Kenneth R Brown, and Margaret Martonosi. Proceedings of the ACM/IEEE International Symposium on Computer Architecture (ISCA '20), 2020.
• Muzzle the shuttle: Efficient compilation for multi-trap trapped-ion quantum computers Abdullah Ash Saki, Rasit Onur Topaloglu, and Swaroop Ghosh. Proceedings of the Design, Automation & Test in Europe Conference (DATE '22), 2022.

Hardware-Aware QEC Realization on Neutral Atom Arrays

• Qubit Mapping for Reconfigurable Atom Arrays Bochen Tan, Dolev Bluvstein, Mikhail D Lukin, and Jason Cong. Proceedings of the IEEE/ACM International Conference on Computer-Aided Design (ICCAD '22), 2022.
• Compiling Quantum Circuits for Dynamically Field-Programmable Neutral Atoms Array Processors Daniel Bochen Tan, Dolev Bluvstein, Mikhail D Lukin, and Jason Cong. Quantum, 2024.
• Compilation for Dynamically Field-Programmable Qubit Arrays with Efficient and Provably Near-Optimal Scheduling Daniel Bochen Tan, Wan-Hsuan Lin, and Jason Cong. arXiv preprint arXiv:2405.15095, 2024.
• Q-Pilot: field programmable quantum array compilation with flying ancillas Hanrui Wang, Bochen Tan, Pengyu Liu, Yilian Liu, Jiaqi Gu, Jason Cong, and Song Han. arXiv preprint arXiv:2311.16190, 2023.
• Atomique: A quantum compiler for reconfigurable neutral atom arrays Hanrui Wang, Pengyu Liu, Daniel Bochen Tan, Yilian Liu, Jiaqi Gu, David Z Pan, Jason Cong, Umut A Acar, et al. Proceedings of the ACM/IEEE International Symposium on Computer Architecture (ISCA '24), 2024.
• Circuit decompositions and scheduling for neutral atom devices with limited local addressability Natalia Nottingham, Michael A Perlin, Dhirpal Shah, Ryan White, Hannes Bernien, Frederic T Chong, and Jonathan M Baker. Proceedings of the IEEE International Conference on Quantum Computing and Engineering (QCE '24), 2024.
• Reuse-aware compilation for zoned quantum architectures based on neutral atoms Wan-Hsuan Lin, Daniel Bochen Tan, and Jason Cong. arXiv preprint arXiv:2411.11784, 2024.
• PowerMove: Optimizing Compilation for Neutral Atom Quantum Computers with Zoned Architecture Jixuan Ruan, Xiang Fang, Hezi Zhang, Ang Li, Travis Humble, and Yufei Ding. Proceedings of the ACM International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS '25), 2025.
• ZAP: Zoned Architecture and Performant Compiler for Field Programmable Atom Array Chen Huang, Xi Zhao, Hongze Xu, Weifeng Zhuang, Meng-Jun Hu, Dong E Liu, and Jingbo Wang. IEEE Transactions on Quantum Engineering, 2026.
• A quantum processor based on coherent transport of entangled atom arrays Dolev Bluvstein, Harry Levine, Giulia Semeghini, Tout T. Wang, Sepehr Ebadi, Marcin Kalinowski, Alexander Keesling, Nishad Maskara, et al. Nature, 2022.
• Fault-tolerant quantum computation with a neutral atom processor Ben W Reichardt, Adam Paetznick, David Aasen, Ivan Basov, Juan M Bello-Rivas, Parsa Bonderson, Rui Chao, Wim van Dam, et al. arXiv preprint arXiv:2411.11822, 2024.
• A fault-tolerant neutral-atom architecture for universal quantum computation Dolev Bluvstein, Alexandra A. Geim, Sophie H. Li, Simon J. Evered, J. Pablo Bonilla Ataides, Gefen Baranes, Andi Gu, Tom Manovitz, et al. Nature, 2026.
• Circuit-based leakage-to-erasure conversion in a neutral-atom quantum processor Matthew NH Chow, Vikas Buchemmavari, Sivaprasad Omanakuttan, Bethany J Little, Saurabh Pandey, Ivan H Deutsch, and Yuan-Yu Jau. PRX Quantum, 2024.
• Long-range-enhanced surface codes Yifan Hong, Matteo Marinelli, Adam M Kaufman, and Andrew Lucas. Physical Review A, 2024.
• Transversal Logical Clifford gates on rotated surface codes with reconfigurable neutral atom arrays Zi-Han Chen, Ming-Cheng Chen, Chao-Yang Lu, and Jian-Wei Pan. arXiv preprint arXiv:2412.01391, 2024.
• Constant-Overhead Fault-Tolerant Quantum Computation with Reconfigurable Atom Arrays Qian Xu, J. Pablo Bonilla Ataides, Christopher A. Pattison, Nithin Raveendran, Dolev Bluvstein, Jonathan Wurtz, Bane Vasic, Mikhail D. Lukin, et al. Nature Physics, 2024.
• Towards Ultra-High-Rate Quantum Error Correction with Reconfigurable Atom Arrays Chen Zhao, Casey Duckering, Andi Gu, Nishad Maskara, and Hengyun Zhou. arXiv preprint arXiv:2604.16209, 2026.
• High-threshold codes for neutral-atom qubits with biased erasure errors Kaavya Sahay, Junlan Jin, Jahan Claes, Jeff D. Thompson, and Shruti Puri. Physical Review X, 2023.
• Quantum low-density parity-check codes for erasure-biased atomic quantum processors Laura Pecorari, and Guido Pupillo. Physical Review A, 2025.
• Optimal state preparation for logical arrays on zoned neutral atom quantum computers Yannick Stade, Ludwig Schmid, Lukas Burgholzer, and Robert Wille. Proceedings of the Design, Automation & Test in Europe Conference (DATE '25), 2025.
• Efficient fault-tolerant implementations of non-Clifford gates with reconfigurable atom arrays Yifei Wang, Yixu Wang, Yu-An Chen, Wenjun Zhang, Tao Zhang, Jiazhong Hu, Wenlan Chen, Yingfei Gu, et al. npj Quantum Information, 2024.
• Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays Yue Wu, Shimon Kolkowitz, Shruti Puri, and Jeff D. Thompson. Nature Communications, 2022.
• Erasure-tolerance scheme for the surface codes on neutral atom quantum computers Fumiyoshi Kobayashi, and Shota Nagayama. IEEE Transactions on Quantum Engineering, 2025.
• Correlated Atom Loss as a Resource for Quantum Error Correction Hugo Perrin, Gatien Roger, and Guido Pupillo. arXiv preprint arXiv:2603.24237, 2026.
• Resource Analysis of Low-Overhead Transversal Architectures for Reconfigurable Atom Arrays Hengyun Zhou, Casey Duckering, Chen Zhao, Dolev Bluvstein, Madelyn Cain, Aleksander Kubica, Sheng-Tao Wang, and Mikhail D. Lukin. Proceedings of the ACM/IEEE International Symposium on Computer Architecture (ISCA '25), 2025.

Decoding in the Classical Control Stack

Algorithms and Implementation Trade-offs

Algorithm Overview and Tools

• Hardness of Decoding Quantum Stabilizer Codes Pavithran Iyer, and David Poulin. IEEE Transactions on Information Theory, 2015.
• Decoding Algorithms for Surface Codes Antonio deMarti iOlius, Patricio Fuentes, Roman Orus, Pedro M. Crespo, and Josu Etxezarreta Martinez. Quantum, 2024.
• Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code Sergey Bravyi, Martin Suchara, and Alexander Vargo. Physical Review A, 2014.
• Statistical Mechanical Models for Quantum Codes with Correlated Noise Christopher T. Chubb, and Steven T. Flammia. Annales de l'Institut Henri Poincare D, 2021.
• Stim: a fast stabilizer circuit simulator Craig Gidney. Quantum, 2021.
• LightStim: A Framework for QEC Protocol Evaluation and Prototyping with Automated DEM Construction Xiang Fang, Ming Wang, Yue Wu, Sharanya Prabhu, Dean Tullsen, Narasinga Rao Miniskar, Frank Mueller, Travis Humble, et al. 2026.

Matching / MWPM

• Paths, Trees, and Flowers Jack Edmonds. Canadian Journal of Mathematics, 1965.
• Sparse blossom: correcting a million errors per core second with minimum-weight matching Oscar Higgott, and Craig Gidney. Quantum, 2025.
• Fusion Blossom: Fast MWPM Decoders for QEC Yue Wu, and Lin Zhong. Proceedings of the IEEE International Conference on Quantum Computing and Engineering (QCE '23), 2023.
• Improved decoding of circuit noise and fragile boundaries of tailored surface codes Oscar Higgott, Thomas C Bohdanowicz, Aleksander Kubica, Steven T Flammia, and Earl T Campbell. Physical Review X, 2023.
• Belief propagation as a partial decoder Laura Caune, Brendan Reid, Joan Camps, and Earl Campbell. arXiv preprint arXiv:2306.17142, 2023.
• Multi-path summation for decoding 2D topological codes Ben Criger, and Imran Ashraf. Quantum, 2018.
• Optimal complexity correction of correlated errors in the surface code Austin G Fowler. arXiv preprint arXiv:1310.0863, 2013.
• Pipelined correlated minimum weight perfect matching of the surface code Alexandru Paler, and Austin G Fowler. Quantum, 2023.
• Enhancing Fault-Tolerant Surface Code Decoding with Iterative Lattice Reweighting Yi Tian, Y Zheng, Xiaoting Wang, and Ching-Yi Lai. arXiv preprint arXiv:2509.06756, 2025.
• Micro Blossom: Accelerated Minimum-Weight Perfect Matching Decoding for Quantum Error Correction Yue Wu, Namitha Liyanage, and Lin Zhong. Proceedings of the ACM International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS '25), 2025.
• Astrea: Accurate Quantum Error-Decoding via Practical Minimum-Weight Perfect-Matching Suhas Vittal, Poulami Das, and Moinuddin Qureshi. Proceedings of the ACM/IEEE International Symposium on Computer Architecture (ISCA '23), 2023.
• LILLIPUT: A Lightweight Low-Latency Lookup-Table Decoder for Near-Term Quantum Error Correction Poulami Das, Aditya Locharla, and Cody Jones. Proceedings of the ACM International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS '22), 2022.
• NISQ+: Boosting Quantum Computing Power by Approximating Quantum Error Correction Adam Holmes, Mohammad Reza Jokar, Ghasem Pasandi, Yongshan Ding, Massoud Pedram, and Frederic T. Chong. Proceedings of the ACM/IEEE International Symposium on Computer Architecture (ISCA '20), 2020.
• QECOOL: On-Line Quantum Error Correction with a Superconducting Decoder for Surface Code Yosuke Ueno, Masaaki Kondo, Masamitsu Tanaka, Yasunari Suzuki, and Yutaka Tabuchi. Proceedings of the ACM/IEEE Design Automation Conference (DAC '21), 2021.
• QULATIS: A Quantum Error Correction Methodology toward Lattice Surgery Yosuke Ueno, Masaaki Kondo, Masamitsu Tanaka, Yasunari Suzuki, and Yutaka Tabuchi. Proceedings of the IEEE International Symposium on High-Performance Computer Architecture (HPCA '22), 2022.
• Better Than Worst-Case Decoding for Quantum Error Correction Gokul Subramanian Ravi, Jonathan M. Baker, Arash Fayyazi, Sophia Fuhui Lin, Ali Javadi-Abhari, Massoud Pedram, and Frederic T. Chong. Proceedings of the ACM International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS '23), 2023.
• Promatch: Extending the Reach of Real-Time Quantum Error Correction with Adaptive Predecoding Narges Alavisamani, Suhas Vittal, Ramin Ayanzadeh, Poulami Das, and Moinuddin Qureshi. Proceedings of the ACM International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS '24), 2024.
• Pinball: A Cryogenic Predecoder for Quantum Error Correction Decoding Under Circuit-Level Noise Alexander Knapen, Guanchen Tao, Jacob Mack, Tomas Bruno, Mehdi Saligane, Dennis Sylvester, Qirui Zhang, and Gokul Subramanian Ravi. Proceedings of the IEEE International Symposium on High-Performance Computer Architecture (HPCA '26), 2026.
• PyMatching: A Python package for decoding quantum codes with minimum-weight perfect matching Oscar Higgott. ACM Transactions on Quantum Computing, 2022.
• Minimising surface-code failures using a color-code decoder Asmae Benhemou, Kaavya Sahay, Lingling Lao, and Benjamin J. Brown. Quantum, 2025.
• The correlated matching decoder for the 4.8.8 color code Yantong Liu, Junjie Wu, and Lingling Lao. Science China Information Sciences, 2026.

Search and Hypergraph Decoding

• Tesseract: A Search-Based Decoder for Quantum Error Correction Laleh Aghababaie Beni, Oscar Higgott, and Noah Shutty. arXiv preprint arXiv:2503.10988, 2025.
• Minimum-Weight Parity Factor Decoder for Quantum Error Correction Yue Wu, Binghong Li, Kathleen Chang, Shruti Puri, and Lin Zhong. arXiv preprint arXiv:2508.04969, 2025.

Union-Find

• Almost-linear time decoding algorithm for topological codes Nicolas Delfosse, and Naomi H Nickerson. Quantum, 2021.
• Fault-tolerant weighted union-find decoding on the toric code Shilin Huang, Michael Newman, and Kenneth R Brown. Physical Review A, 2020.
• Toward a union-find decoder for quantum LDPC codes Nicolas Delfosse, Vivien Londe, and Michael E Beverland. IEEE Transactions on Information Theory, 2022.
• Actis: a strictly local union-find decoder Tim Chan, and Simon C Benjamin. Quantum, 2023.
• AFS: Accurate, Fast, and Scalable Error-Decoding for Fault-Tolerant Quantum Computers Poulami Das, Christopher A. Pattison, Srilatha Manne, Douglas M. Carmean, Krysta M. Svore, Moinuddin Qureshi, and Nicolas Delfosse. Proceedings of the IEEE International Symposium on High-Performance Computer Architecture (HPCA '22), 2022.
• Scalable quantum error correction for surface codes using FPGA Namitha Liyanage, Yue Wu, Alexander Deters, and Lin Zhong. Proceedings of the IEEE International Conference on Quantum Computing and Engineering (QCE '23), 2023.
• A real-time, scalable, fast and resource-efficient decoder for a quantum computer Ben Barber, Kenton M. Barnes, Tomasz Bialas, Okan Bugdayc, Earl T. Campbell, Neil I. Gillespie, Kauser Johar, Ram Rajan, et al. Nature Electronics, 2025.
• Network-Integrated Decoding System for Real-Time Quantum Error Correction with Lattice Surgery Namitha Liyanage, Yue Wu, Emmet Houghton, and Lin Zhong. Proceedings of the IEEE International Conference on Quantum Computing and Engineering (QCE '25), 2025.
• Coset Ensemble Decoder for Quantum Error Correction with Algorithm-Hardware Co-Design Shuang Liang, Jubo Xu, Giulio Bassanino, Qianzhou Wang, Yidong Zhou, Yuncheng Lu, Zhiwen Mo, Paul H. J. Kelly, et al. Proceedings of the ACM/IEEE International Symposium on Computer Architecture (ISCA '26), 2026.
• Local clustering decoder as a fast and adaptive hardware decoder for the surface code Abbas B. Ziad, Ankit Zalawadiya, Canberk Topal, Joan Camps, Gyorgy P. Geher, Matthew P. Stafford, and Mark L. Turner. Nature Communications, 2025.

Belief Propagation

• Exploiting degeneracy in belief propagation decoding of quantum codes Kao-Yueh Kuo, and Ching-Yi Lai. npj Quantum Information, 2022.
• On the iterative decoding of sparse quantum codes David Poulin, and Yeojin Chung. arXiv preprint arXiv:0801.1241, 2008.
• Decoding Across the Quantum Low-Density Parity-Check Code Landscape Joschka Roffe, David R. White, Simon Burton, and Earl T. Campbell. Physical Review Research, 2020.
• Degenerate quantum LDPC codes with good finite length performance Pavel Panteleev, and Gleb Kalachev. Quantum, 2021.
• Localized statistics decoding for quantum low-density parity-check codes Timo Hillmann, Lucas Berent, Armanda O. Quintavalle, Jens Eisert, Robert Wille, and Joschka Roffe. Nature Communications, 2025.
• An almost-linear time decoding algorithm for quantum LDPC codes under circuit-level noise Antonio deMarti iOlius, Imanol Etxezarreta Martinez, Joschka Roffe, and Josu Etxezarreta Martinez. arXiv preprint arXiv:2409.01440, 2024.
• Introducing Ambiguity Clustering: An Accurate and Efficient Decoder for qLDPC Codes Stasiu Wolanski, and Ben Barber. Proceedings of the IEEE International Conference on Quantum Computing and Engineering (QCE '24), 2024.
• Belief propagation decoding of quantum LDPC codes with guided decimation Hanwen Yao, Waleed Abu Laban, Christian Hager, Alexandre Graell i Amat, and Henry D Pfister. Proceedings of the IEEE International Symposium on Information Theory (ISIT '24), 2024.
• Beam search decoder for quantum LDPC codes Min Ye, Dave Wecker, and Nicolas Delfosse. arXiv preprint arXiv:2512.07057, 2025.
• Improved belief propagation is sufficient for real-time decoding of quantum memory Tristan Muller, Thomas Alexander, Michael E Beverland, Markus Buhler, Blake R Johnson, Thilo Maurer, and Drew Vandeth. arXiv preprint arXiv:2506.01779, 2025.
• Improved belief propagation decoding algorithms for surface codes Jiahan Chen, Zhengzhong Yi, Zhipeng Liang, and Xuan Wang. IEEE Transactions on Quantum Engineering, 2025.
• Restart Belief: A General Quantum LDPC Decoder Lorenzo Valentini, Diego Forlivesi, Andrea Talarico, and Marco Chiani. IEEE Communications Letters, 2026.
• Fully Parallelized BP Decoding for Quantum LDPC Codes Can Outperform BP-OSD Ming Wang, Ang Li, and Frank Mueller. Proceedings of the IEEE International Symposium on High-Performance Computer Architecture (HPCA '26), 2026.
• Automorphism Ensemble Decoding of Quantum LDPC Codes Stergios Koutsioumpas, Hasan Sayginel, Mark Webster, and Dan E. Browne. arXiv preprint arXiv:2503.01738, 2025.
• Decoding correlated errors in quantum LDPC codes Arshpreet Singh Maan, Francisco Miguel Garcia Herrero, Alexandru Paler, and Valentin Savin. Nature Communications, 2026.
• Colour Codes Reach Surface Code Performance using Vibe Decoding Stergios Koutsioumpas, Tamas Noszko, Hasan Sayginel, Mark Webster, and Joschka Roffe. arXiv preprint arXiv:2508.15743, 2025.
• Real-time decoding of the gross code memory with FPGAs Thilo Maurer, Markus Buhler, Michael Kroner, Frank Haverkamp, Tristan Muller, Drew Vandeth, and Blake R Johnson. arXiv preprint arXiv:2510.21600, 2025.
• Vegapunk: Accurate and Fast Decoding for Quantum LDPC Codes with Online Hierarchical Algorithm and Sparse Accelerator Kaiwen Zhou, Liqiang Lu, Debin Xiang, Chenning Tao, Anbang Wu, Jingwen Leng, Fangxin Liu, Mingshuai Chen, et al. Proceedings of the IEEE/ACM International Symposium on Microarchitecture (MICRO '25), 2025.
• Syndrome-based min-sum vs OSD-0 decoders: FPGA implementation and analysis for quantum LDPC codes Javier Valls, Francisco Garcia-Herrero, Nithin Raveendran, and Bane Vasic. IEEE Access, 2021.
• A Scalable FPGA Architecture for Real-Time Decoding of Quantum LDPC Codes Using GARI Daniel Bascones, Arshpreet Singh Maan, Valentin Savin, and Francisco Garcia-Herrero. arXiv preprint arXiv:2605.01035, 2026.

Neural-Network Decoding

• Learning high-accuracy error decoding for quantum processors Johannes Bausch, Andrew W Senior, Francisco JH Heras, Thomas Edlich, Alex Davies, Michael Newman, Cody Jones, Kevin Satzinger, et al. Nature, 2024.
• Efficient and universal neural-network decoder for stabilizer-based quantum error correction Gengyuan Hu, Wanli Ouyang, Chao-Yang Lu, Chen Lin, and Han-Sen Zhong. arXiv preprint arXiv:2502.19971, 2025.
• Scalable Neural Decoders for Practical Real-Time Quantum Error Correction Changwon Lee, Tak Hur, and Daniel K. Park. arXiv preprint arXiv:2510.22724, 2025.
• Sparse Mamba Decoder for Quantum Error Correction: Efficient Defect-Centric Processing of Surface Code Syndromes Samira Sayedsalehi, Nader Bagherzadeh, Maxim Shcherbakov, and Jean-Luc Gaudiot. arXiv preprint arXiv:2605.17156, 2026.
• SAQ: Stabilizer-Aware Quantum Error Correction Decoder David Zenati, and Eliya Nachmani. arXiv preprint arXiv:2512.08914, 2025.
• DiffQEC: A versatile diffusion model for quantum error correction Tianyi Xu, Qinglong Liu, Maolin Wang, Fei Zhang, Zhe Zhao, Yang Wang, and Ye Wei. arXiv preprint arXiv:2604.24640, 2026.
• Fast and accurate AI-based pre-decoders for surface codes Christopher Chamberland, Jan Olle, Muyuan Li, Scott Thornton, and Igor Baratta. arXiv preprint arXiv:2604.12841, 2026.
• Real-time Surface-Code Error Correction Using an FPGA-based Neural-Network Decoder Xiaohan Yang, Xuandong Sun, Zhiyi Wu, Jiawei Zhang, Ji Jiang, Xiayu Linpeng, Yuxuan Zhou, Ji Chu, et al. arXiv preprint arXiv:2605.04892, 2026.
• Rethink the Role of Neural Decoders in Quantum Error Correction Ge Yan, Shanchuan Li, and Yuxuan Du. arXiv preprint arXiv:2605.12046, 2026.
• A scalable and real-time neural decoder for topological quantum codes Andrew W. Senior, Thomas Edlich, Francisco J. H. Heras, Lei M. Zhang, Oscar Higgott, James S. Spencer, et al. arXiv preprint arXiv:2512.07737, 2025.
• Learning to Decode in Parallel: Self-Coordinating Neural Network for Real-Time Quantum Error Correction Kai Zhang, Zhengzhong Yi, Shaojun Guo, Linghang Kong, Situ Wang, Xiaoyu Zhan, Tan He, Weiping Lin, et al. arXiv preprint arXiv:2601.09921, 2026.
• Neural Decoders for Universal Quantum Algorithms J. Pablo Bonilla Ataides, Andi Gu, Susanne F. Yelin, and Mikhail D. Lukin. PRX Intelligence, 2026.
• Fast and Accurate AI-Based Pre-Decoders for Color Codes Jan Olle, Christopher Chamberland, Muyuan Li, and Igor Baratta. 2026.
• Ising-Decoding: A Set of Training Recipes for AI Quantum Error Correction Decoders NVIDIA Corporation. 2026.

Real-Time Decoder Integration

Runtime Integration Overview

• Real-Time Decoding for Fault-Tolerant Quantum Computing: Progress, Challenges and Outlook Francesco Battistel, Christopher Chamberland, Kauser Johar, Ramon W. J. Overwater, Fabio Sebastiano, Luka Skoric, Yosuke Ueno, and Muhammad Usman. Nano Futures, 2023.
• Demonstrating Real-Time and Low-Latency Quantum Error Correction with Superconducting Qubits Laura Caune, Luka Skoric, Nick S. Blunt, Archibald Ruban, Jimmy McDaniel, Joseph A. Valery, Andrew D. Patterson, Alexander V. Gramolin, et al. Nature Communications, 2026.
• deq: Dynamic and Generic QEC Decoding System Microsoft. 2026.
• CUDA-QX NVIDIA Corporation, CUDA-QX Development Team. 2026.
• CUDA-Q The CUDA-Q Development Team. 2026.
• Platform Architecture for Tight Coupling of High-Performance Computing with Quantum Processors Shane A. Caldwell, Moein Khazraee, Elena Agostini, Tom Lassiter, Corey Simpson, Omri Kahalon, Mrudula Kanuri, Jin-Sung Kim, et al. 2025.
• Introducing cudaq-realtime for Programming the Logical QPU Shane Caldwell, Chuck Ketcham, Thien Nguyen, Bruno Schmitt, Elena Agostini, Corey Simpson, Jeffrey Bonde, Tom Lassiter, et al. 2026.
• Real-time decoding of quantum error correction codes using high-performance computing Lingling Lao, Qiang Wang, Yuanqi Liu, Yantong Liu, Haowen Wang, Yitao Chen, Yankang Zhao, Zhenwei Wu, et al. arXiv preprint arXiv:2608.03948, 2026.

Pauli and Clifford Frames

• Quantum computing with realistically noisy devices Emanuel Knill. Nature, 2005.
• Effective fault-tolerant quantum computation with slow measurements David P DiVincenzo, and Panos Aliferis. Physical review letters, 2007.
• Pauli frames for quantum computer architectures Leon Riesebos, Xiang Fu, Savvas Varsamopoulos, Carmen G Almudever, and Koen Bertels. Proceedings of the ACM/IEEE Design Automation Conference (DAC '17), 2017.
• Quantum Teleportation Is a Universal Computational Primitive Daniel Gottesman, and Isaac L Chuang. arXiv preprint quant-ph/9908010, 1999.
• Flexible layout of surface code computations using AutoCCZ states Craig Gidney, and Austin G. Fowler. arXiv preprint arXiv:1905.08916, 2019.
• Quantum error correction below the surface code threshold Rajeev Acharya, Dmitry A Abanin, Laleh Aghababaie-Beni, Igor Aleiner, Trond I Andersen, Markus Ansmann, Frank Arute, Kunal Arya, et al. Nature, 2025.
• Fault-tolerant quantum computing in the Pauli or Clifford frame with slow error diagnostics Christopher Chamberland, Pavithran Iyer, and David Poulin. Quantum, 2018.
• Hard decoding algorithm for optimizing thresholds under general markovian noise Christopher Chamberland, Joel Wallman, Stefanie Beale, and Raymond Laflamme. Physical Review A, 2017.

Window and Speculative Decoding

• Modular decoding: parallelizable real-time decoding for quantum computers Hector Bombin, Chris Dawson, Ye-Hua Liu, Naomi Nickerson, Fernando Pastawski, and Sam Roberts. arXiv preprint arXiv:2303.04846, 2023.
• Spatially parallel decoding for multi-qubit lattice surgery Sophia Fuhui Lin, Eric C. Peterson, Krishanu Sankar, and Prasahnt Sivarajah. Quantum Science and Technology, 2025.
• ADaPT: Adaptive-window Decoding for Practical fault-Tolerance Tina Oberoi, Joshua Viszlai, and Frederic T. Chong. arXiv preprint arXiv:2605.01149, 2026.
• Adaptive Window Decoding based on Spatiotemporal Complementary Gap Moeto Mishima, Riki Toshio, Kaito Kishi, Jun Fujisaki, Hirotaka Oshima, Shintaro Sato, and Keisuke Fujii. arXiv preprint arXiv:2605.14637, 2026.
• Topological quantum memory Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill. Journal of Mathematical Physics, 2002.
• Parallel window decoding enables scalable fault tolerant quantum computation Luka Skoric, Dan E Browne, Kenton M Barnes, Neil I Gillespie, and Earl T Campbell. Nature Communications, 2023.
• Scalable surface-code decoders with parallelization in time Xinyu Tan, Fang Zhang, Rui Chao, Yaoyun Shi, and Jianxin Chen. PRX Quantum, 2023.
• SWIPER: Minimizing Fault-Tolerant Quantum Program Latency via Speculative Window Decoding Joshua Viszlai, Jason D Chadwick, Sarang Joshi, Gokul Subramanian Ravi, Yanjing Li, and Frederic T Chong. Proceedings of the ACM/IEEE International Symposium on Computer Architecture (ISCA '25), 2025.
• Triage: An Adaptive Parallel Window Decoding Scheduler for Real-time Fault-Tolerant Quantum Computation Jiahan Chen, Chenghong Zhu, Ge Bai, and Xin Wang. arXiv preprint arXiv:2605.04459, 2026.
• A Case for Elastic Quantum Error Correction Decoders Satvik Maurya, Abtin Molavi, Aws Albarghouthi, and Swamit Tannu. Proceedings of the 21st European Conference on Computer Systems (EuroSys '26), 2026.

Noise- and Side-Information-Aware Decoding

• Thresholds for topological codes in the presence of loss Thomas M. Stace, Sean D. Barrett, and Andrew C. Doherty. Physical Review Letters, 2009.
• Erasure qubits: Overcoming the T_1 limit in superconducting circuits Aleksander Kubica, Arbel Haim, Yotam Vaknin, Harry Levine, Fernando Brandao, and Alex Retzker. Physical Review X, 2023.
• Coping with qubit leakage in topological codes Austin G. Fowler. Physical Review A, 2013.
• Alibaba Cloud Quantum Development Platform: Surface code simulations with crosstalk Cupjin Huang, Xiaotong Ni, Fang Zhang, Michael Newman, Dawei Ding, Xun Gao, Tenghui Wang, Hui-Hai Zhao, et al. arXiv preprint arXiv:2002.08918, 2020.
• Improved quantum error correction using soft information Christopher A. Pattison, Michael E. Beverland, Marcus P. da Silva, and Nicolas Delfosse. arXiv preprint arXiv:2107.13589, 2021.
• Low overhead fault-tolerant quantum error correction with the surface-GKP code Kyungjoo Noh, Christopher Chamberland, and Fernando G. S. L. Brandao. PRX Quantum, 2022.
• Correlated decoding of logical algorithms with transversal gates Madelyn Cain, Chen Zhao, Hengyun Zhou, Nadine Meister, J. Pablo Bonilla Ataides, Arthur Jaffe, Dolev Bluvstein, and Mikhail D. Lukin. Physical Review Letters, 2024.
• Fast correlated decoding of transversal logical algorithms Madelyn Cain, Dolev Bluvstein, Chen Zhao, Shouzhen Gu, Nishad Maskara, Marcin Kalinowski, Alexandra A. Geim, Aleksander Kubica, et al. arXiv preprint arXiv:2505.13587, 2025.
• Logical Qubits with Erasure Conversion Using Metastable Neutral Atoms Bichen Zhang, Genyue Liu, Guillaume Bornet, Sebastian P. Horvath, Pai Peng, Shuo Ma, Shilin Huang, Shruti Puri, et al. Nature Physics, 2026.
• Low-overhead transversal fault tolerance for universal quantum computation Hengyun Zhou, Chen Zhao, Madelyn Cain, Dolev Bluvstein, Nishad Maskara, Casey Duckering, Hong-Ye Hu, Sheng-Tao Wang, et al. Nature, 2025.

Conclusion and Future Direction

Future Directions

• Transversal architecture for megaquop-scale quantum simulation with neutral atoms Refaat Ismail, I-Chi Chen, Chen Zhao, Ronen Weiss, Fangli Liu, Hengyun Zhou, Sheng-Tao Wang, Andrew Sornborger, et al. PRX Quantum, 2026.
• decoder-bench: Benchmarking Decoders for Quantum Error Correction Satvik Maurya, Joshua Viszlai, Nithin Raveendran, Poulami Das, and Swamit Tannu. Proceedings of the IEEE International Symposium on Workload Characterization (IISWC '25), 2025.