Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Calibration-conditioned featurewise linear modulation decoders for low-latency decoding of quantum error correction evaluated on IBM repetition-code experiments

Samuel Stein1,*, Shuwen Kan1,2, Chenxu Liu1, Adrian Harkness1,3, Sean Garner1,4, Zefan Du2, Yufei Ding5, Ying Mao2, and Ang Li1,4

  • *Contact author: samuel.stein@pnnl.gov

Phys. Rev. Research 8, 033194 – Published 17 August, 2026

DOI: https://doi.org/10.1103/ftdh-t3yg

Abstract

Real-time decoding of quantum error correction is essential for enabling fault-tolerant quantum computation. A practical decoder must operate with high accuracy at low latency, while remaining robust to spatial and temporal variations in hardware noise. We introduce a hardware-conditioned neural decoder framework designed to exploit the natural separation of timescales in superconducting processors, where calibration drifts occur over hours while error correction requires microsecond-scale responses. By processing calibration data through a graph-based encoder and conditioning a lightweight convolutional backbone via featurewise linear modulation (FiLM), we decouple the heavy processing of device statistics from the low-latency syndrome decoding. We evaluate this approach using the repetition code as a test bed on IBM Fez, Kingston, and Pittsburgh processors, collecting over 2.7 million experimental shots spanning distances up to d=11. Training one decoder per code distance, basis, and round count (d,r), we demonstrate that each trained model generalizes to unseen qubit chains and new calibration data acquired days later without retraining. The FiLM-conditioned decoder achieves up to a 11.1× reduction in logical error rate relative to modified minimum-weight perfect matching. Cross-conditioning ablations further show that the calibration input actively improves decoding, with performance degrading when the decoder is conditioned on incorrect backend data or the conditioning is disabled. We observe that by employing a network architecture that exploits the highly asynchronous nature of system calibration and decoding, hardware-conditioned neural decoding demonstrated promising, adaptive performance with negligible latency overhead relative to unconditioned baselines.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (37)

  1. D. A. Lidar and T. A. Brun, Quantum Error Correction (Cambridge University Press, Cambridge, England, 2013).
  2. M. E. Beverland, P. Murali, M. Troyer, K. M. Svore, T. Hoefler, V. Kliuchnikov, G. H. Low, M. Soeken, A. Sundaram, and A. Vaschillo, Assessing requirements to scale to practical quantum advantage, arXiv:2211.07629.
  3. B. M. Terhal, Quantum error correction for quantum memories, Rev. Mod. Phys. 87, 307 (2015).
  4. D. Gottesman, Stabilizer Codes and Quantum Error Correction (California Institute of Technology, Pasadena, California, 1997).
  5. A. G. Fowler, A. C. Whiteside, and L. C. Hollenberg, Towards practical classical processing for the surface code: Timing analysis, Phys. Rev. A 86, 042313 (2012).
  6. J. Chiaverini, D. Leibfried, T. Schaetz, M. D. Barrett, R. B. Blakestad, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, R. Ozeri, and D. J. Wineland, Realization of quantum error correction, Nature (London) 432, 602 (2004).
  7. L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, Preparation and measurement of three-qubit entanglement in a superconducting circuit, Nature (London) 467, 574 (2010).
  8. P. Schindler, J. T. Barreiro, T. Monz, V. Nebendahl, D. Nigg, M. Chwalla, M. Hennrich, and R. Blatt, Experimental repetitive quantum error correction, Science 332, 1059 (2011).
  9. J. R. Wootton and D. Loss, Repetition code of 15 qubits, Phys. Rev. A 97, 052313 (2018).
  10. I. Besedin, M. Kerschbaum, J. Knoll, I. Hesner, L. Bödeker, L. Colmenarez, L. Hofele, N. Lacroix, C. Hellings, F. Swiadek, et al., Realizing lattice surgery on two distance-three repetition codes with superconducting qubits, Nat. Phys. 22, 189 (2026).
  11. A. R. Calderbank and P. W. Shor, Good quantum error-correcting codes exist, Phys. Rev. A 54, 1098 (1996).
  12. A. G. Fowler, Proof of finite surface code threshold for matching, Phys. Rev. Lett. 109, 180502 (2012).
  13. J. Bausch, A. W. Senior, F. J. Heras, T. Edlich, A. Davies, M. Newman, C. Jones, K. Satzinger, M. Y. Niu, S. Blackwell, et al., Learning high-accuracy error decoding for quantum processors, Nature (London) 635, 834 (2024).
  14. R. Acharya, et al. (Google Quantum AI and Collaborators), Quantum error correction below the surface code threshold, Nature (London) 638, 920 (2025).
  15. H. Wang, P. Liu, K. Shao, D. Li, J. Gu, D. Z. Pan, Y. Ding, and S. Han, Transformer-QEC: Quantum error correction code decoding with transferable transformers, arXiv:2311.16082.
  16. M. Lange, P. Havstrom, B. Srivastava, I. Bengtsson, V. Bergentall, K. Hammar, O. Heuts, E. van Nieuwenburg, and M. Granath, Data-driven decoding of quantum error correcting codes using graph neural networks, Phys. Rev. Res. 7, 023181 (2025).
  17. M. Carroll, S. Rosenblatt, P. Jurcevic, I. Lauer, and A. Kandala, Dynamics of superconducting qubit relaxation times, npj Quantum Inf. 8, 132 (2022).
  18. E. Perez, F. Strub, H. De Vries, V. Dumoulin, and A. Courville, Film: Visual reasoning with a general conditioning layer, in Proceedings of the AAAI Conference on Artificial Intelligence (AAAI, New Orleans, Louisiana, USA, 2018), Vol. 32.
  19. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2010).
  20. G. S. Ravi, J. M. Baker, A. Fayyazi, S. F. Lin, A. Javadi-Abhari, M. Pedram, and F. T. Chong, Better than worst-case decoding for quantum error correction, in Proceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems (ACM Press, New York, NY, 2023), Vol. 2, pp. 88–102.
  21. S. J. Devitt, W. J. Munro, and K. Nemoto, Quantum error correction for beginners, Rep. Prog. Phys. 76, 076001 (2013).
  22. M.-H. Hsieh and F. Le Gall, NP-hardness of decoding quantum error-correction codes, Phys. Rev. A 83, 052331 (2011).
  23. S. Krastanov and L. Jiang, Deep neural network probabilistic decoder for stabilizer codes, Sci. Rep. 7, 11003 (2017).
  24. N. Maskara, A. Kubica, and T. Jochym-O’Connor, Advantages of versatile neural-network decoding for topological codes, Phys. Rev. A 99, 052351 (2019).
  25. S. Varsamopoulos, K. Bertels, and C. G. Almudever, Comparing neural network based decoders for the surface code, IEEE Trans. Comput. 69, 300 (2019).
  26. P. Baireuther, T. E. O’Brien, B. Tarasinski, and C. W. Beenakker, Machine-learning-assisted correction of correlated qubit errors in a topological code, Quantum 2, 48 (2018).
  27. A. Strikis, D. Qin, Y. Chen, S. C. Benjamin, and Y. Li, Learning-based quantum error mitigation, PRX Quantum 2, 040330 (2021).
  28. H. Liao, D. S. Wang, I. Sitdikov, C. Salcedo, A. Seif, and Z. K. Minev, Machine learning for practical quantum error mitigation, Nat. Mach. Intell. 6, 1478 (2024).
  29. M. Liao, Y. Zhu, G. Chiribella, and Y. Yang, Noise-agnostic quantum error mitigation with data augmented neural models, npj Quantum Inf. 11, 8 (2025).
  30. O. Higgott, PyMatching: A Python package for decoding quantum codes with minimum-weight perfect matching, ACM Trans. Quantum Comput. 3, 1 (2022).
  31. Y. Hu, Y. Liu, and Z. Liu, A survey on convolutional neural network accelerators: GPU, FPGA and ASIC, in Proceedings of the 2022 14th International Conference on Computer Research and Development (ICCRD) (IEEE, Piscataway, NJ, 2022), pp. 100–107.
  32. S. S. Lee, T. D. Nguyen, P. K. Meher, and S. Y. Park, Energy-efficient high-speed ASIC implementation of convolutional neural network using novel reduced critical-path design, IEEE Access 10, 34032 (2022).
  33. C. N. Self, M. Benedetti, and D. Amaro, Protecting expressive circuits with a quantum error detection code, Nat. Phys. 20, 219 (2024).
  34. K. Y. Yu, A. Sarkar, E. Hua, M. Rimbach-Russ, R. Ishihara, and S. Feld, From characterization to construction: Generative quantum circuit synthesis from gate set tomography data, arXiv:2605.01367.
  35. J. P. Bonilla Ataides, A. Gu, S. F. Yelin, and M. D. Lukin, Neural decoders for universal quantum algorithms, arXiv:2509.11370.
  36. Y. Zhou, C. Wan, Y. Xu, J. P. Zhou, K. Q. Weinberger, and E.-A. Kim, Learning to decode logical circuits, Nat. Comput. Sci. 5, 1158 (2025).
  37. S. Stein, Calibration-conditioned FiLM decoders for low-latency decoding of quantum error correction evaluated on IBM repetition-code experiments - Datasets (Version 0.1) [Dataset], Zenodo, 2026, https://doi.org/10.5281/zenodo.20768087.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation