전자통신동향분석 (Electronics and Telecommunications Trends)

한국전자통신연구원 (Electronics and Telecommunications Research Institute)
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결함허용 양자 컴퓨팅을 위한 양자 오류 복호기 연구 동향

Research Trends in Quantum Error Decoders for Fault-Tolerant Quantum Computing

  • 조은영 (클라우드기반SW연구실) ;
  • 온진호 (클라우드기반SW연구실) ;
  • 김재열 (클라우드기반SW연구실) ;
  • 차규일 (클라우드기반SW연구실)
  • E.Y. Cho ;
  • J.H. On ;
  • C.Y. Kim ;
  • G. Cha
  • 발행 : 2023.10.01
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초록

Quantum error correction is a key technology for achieving fault-tolerant quantum computation. Finding the best decoding solution to a single error syndrome pattern counteracting multiple errors is an NP-hard problem. Consequently, error decoding is one of the most expensive processes to protect the information in a logical qubit. Recent research on quantum error decoding has been focused on developing conventional and neural-network-based decoding algorithms to satisfy accuracy, speed, and scalability requirements. Although conventional decoding methods have notably improved accuracy in short codes, they face many challenges regarding speed and scalability in long codes. To overcome such problems, machine learning has been extensively applied to neural-network-based error decoding with meaningful results. Nevertheless, when using neural-network-based decoders alone, the learning cost grows exponentially with the code size. To prevent this problem, hierarchical error decoding has been devised by combining conventional and neural-network-based decoders. In addition, research on quantum error decoding is aimed at reducing the spacetime decoding cost and solving the backlog problem caused by decoding delays when using hardware-implemented decoders in cryogenic environments. We review the latest research trends in decoders for quantum error correction with high accuracy, neural-network-based quantum error decoders with high speed and scalability, and hardware-based quantum error decoders implemented in real qubit operating environments.

키워드

과제정보

본 연구 논문은 정부(과학기술정보통신부)의 재원으로 정보통신기획평가원의 지원을 받아 수행된 연구임[No. 2020-0-00014, 결함 허용 논리양자큐빗 컴퓨팅 환경을 제공하는 양자운영체제 원천기술 개발].

참고문헌

  1. 이종현 외, "양자 오류 정정 부호와 서피스 부호," 전자공학회지, 제46권 제9호, 2019, pp. 738-745.
  2. 황용수 외, "결함허용 양자컴퓨팅 시스템 기술 연구개발 동향," 전자통신동향분석, 제37권 제2호, 2022, pp. 1-10.
  3. P. Das et al., "A scalable decoder micro-architecture for fault-tolerant quantum computing," arXiv preprint, CoRR, 2020, arXiv: 2001.06598.
  4. D. Poulin, "Optimal and efficient decoding of concatenated quantum block codes," Phys. Rev. A, vol. 74, no. 5, 2006, article no. 052333.
  5. K. Meinerz et al., "Scalable neural decoder for topological surface codes," Phys. Rev. Lett., vol. 128, 2021, article no. 080505.
  6. R.E. Tarjan, "Efficiency of a good but not linear set union algorithm," J. ACM, vol. 22, no. 2, 1975, pp. 215-225. https://doi.org/10.1145/321879.321884
  7. J.W. Harrington, "Analysis of quantum error-correcting codes: Symplectic lattice codes and toric codes," Ph.D. Thesis, California Institute of Technology, 2004.
  8. N. Delfosse and N.H. Nickerson, "Almost-linear time decoding algorithm for topological codes," Quantum, vol. 5, 2021.
  9. G. Duclos-Cianci and D. Poulin, "Fast decoders for topological quantum codes," Phys. Rev. Lett. vol. 104, 2010, article no. 050504.
  10. A.G. Fowler, "Minimum weight perfect matching of fault-tolerant topological quantum error correction in average O(1) parallel time," Quantum Info. Comput., vol. 15, 2015, pp. 145-158. https://doi.org/10.26421/QIC15.1-2-9
  11. O. Higgott, "PyMatching: A python package for decoding quantum codes with minimum-weight perfect matching," ACM Trans. Quantum Comput., vol. 3, no. 3, 2022, pp. 1-16. https://doi.org/10.1145/3505637
  12. O. Higgott et al., "Sparse blossom: Correcting a million errors per core second with minimum-weight matching," arXiv preprint, CoRR, 2023, arXiv: 2303.15933.
  13. Y. Yuan et al., "A modified MWPM decoding algorithm for quantum surface codes over depolarizing channels," arXiv preprint, CoRR, 2022, arXiv: 2202.11239. 2202
  14. N. Delfosse, "Hierarchical decoding to reduce hardware requirements for quantum computing," arXiv preprint, CoRR, 2020, arXiv: 2001.11427.
  15. H. Anwar et al., "Fast decoders for qudit topological codes," New J. Phys., vol. 16, no. 6, 2014.
  16. S. Bravyi et al., "Quantum self-correction in the 3d cubic code mode," Phys. Rev. Lett., vol. 111, no. 20, 2013.
  17. G. Duclos-cianci et al., "Fault-tolerant renormalization group decoder for abelian topological codes," arXiv preprint, CoRR, 2013, arXiv: 1304.6100.
  18. S. Varsamopoulos, "Neural network based decoders for the surface code," Ph.D. Thesis, Delft University of Technology, 2019.
  19. A.J. Ferris et al., "Tensor networks and quantum error correction," Phys. Rev. Lett., vol. 113, 2014, article no. 030501.
  20. A.J. Ferris and D. Poulin, "Branching MERA codes: A natural extension of classical and quantum polar codes," in Proc. IEEE Int. Symp. Inf. Theory, (Honolulu, HI, USA), June 2014, pp. 1081-1085.
  21. C.T. Chubb, "General tensor network decoding of 2D Pauli codes," arXiv preprint, CoRR, 2021, arXiv: 2101.04125.
  22. S. Varsamopoulos et al., "Decoding small surface codes with feedforward neural networks," Quantum Sci. Technol., vol. 3, 2017, article no. 015004.
  23. G. Torlai et al., "Neural decoder for topological codes," Phys. Rev. Lett., vol. 119, 2017, article no. 030501.
  24. S. Krastanov et al., "Deep neural network probabilistic decoder for stabilizer codes," Sci. Rep., vol. 7, 2017, article no. 11003.
  25. C. Chamberland et al., "Deep neural decoders for near term fault-tolerant experiments," Quantum Sci. Technol., vol. 3, no. 4, 2018, article no. 044002.
  26. P. Baireuther et al., "Neural network decoder for topological color codes with circuit level noise," New J. Phys., vol. 21, 2019, article no. 013003.
  27. Y.H. Liu et al., "Neural belief-propagation decoders for quantum error-correcting codes," Phys. Rev. Lett., vol. 122, 2019, article no. 200501.
  28. T. Wagner et al., "Symmetries for a high-level neural decoder on the toric code," Phys. Rev. A, vol. 102, 2020, article no. 042411.
  29. X. Ni, "Neural network decoders for large-distance 2D toric codes," Quantum, vol. 4, 2020.
  30. S. Varona et al., "Determination of the semion code threshold using neural decoders," Phys. Rev. A, vol. 102, 2020, article no. 032411.
  31. S. Gicev et al., "A scalable and fast articial neural network syndrome decoder for surface codes," arXiv preprint, CoRR, 2021, arXiv: 2110.05854.
  32. H.P. Nautrup et al., "Optimizing quantum error correction codes with reinforcement learning," Quantum, vol. 3, 2019.
  33. T. Fosel et al., "Reinforcement learning with neural networks for quantum feedback," Phys. Rev. X, vol. 8, 2018, article no. 031084.
  34. P. Andreasson et al., "Quantum error correction for the toric code using deep reinforcement learning," Quantum, vol. 3, 2019.
  35. D. Fitzek, "Error correction for depolarising noise on a quantum system using deep RL," Master's Thesis at Chalmers University of Technology, 2019.
  36. D. Fitzek et al., "Deep Q-learning decoder for depolarizing noise on the toric code," Phys. Rev. Research, vol. 2, 2020, article no. 023230.
  37. L. Domingo Colomer et al., "Reinforcement learning for optimal error correction of toric codes," Phys. Lett. A, vol. 384, 2020, article no. 126353.
  38. R. Sweke et al., "Reinforcement learning decoders for fault-tolerant quantum computation," arXiv preprint, CoRR, 2018, arXiv: 1810.07207.
  39. T. Hugo et al., "A NEAT quantum error decoder," SciPost Phys., vol. 11, 2021.
  40. D. Horgan et al., "Distributed prioritized experience replay," arXiv preprint, CoRR, 2018, arXiv: 1803.00933.
  41. K. He et al., "Deep residual learning for image recognition," in Proc. IEEE CVPR 2016, (Las Vegas, NV, USA), June 2016, pp. 770-778.
  42. R.S. Sutton et al., "Policy gradient methods for reinforcement learning with function approximation," in Advances in Neural Information Processing Systems, MIT Press, Cambridge, Massachusetts, USA, 2000, pp. 1057-1063.
  43. J.R. Wootton et al., "High threshold error correction for the surface code," Phys. Rev. Lett., vol. 109, 2012, article no. 160503.
  44. A. Hutter et al., "Efficient markov chain monte carlo algorithm for the surface code," Phys. Rev. A, vol. 89, 2014, article no. 022326.
  45. F. Battistel et al., "Real-time decoding for fault-tolerant quantum computing: Progress, challenges and outlook," arXiv preprint, CoRR, 2023, arXiv: 2303.00054.
  46. A. Holmes et al., "NISQ+: Boosting quantum computing power by approximating quantum error correction," in Proc. ACM/IEEE ISCA 2020, (Valencia, Spain), May 2020, pp. 556-569.
  47. Y. Ueno et al., "QECOOL: On-line quantum error correction with a superconducting decoder for surface code," in Proc. ACM/IEEE DAC 2021, (San Francisco, CA, USA), Dec. 2021, pp. 451-456.
  48. P. Das et al., "LILLIPUT: A lightweight low-latency lookup-table based decoder for near-term quantum error correction," in Proc. ASPLOS 2022, (Lausanne, Switzerland), Feb. 2021, pp. 541-553.
  49. R.W.J. Overwater et al., "Neural-network decoders for quantum error correction using surface codes: A space exploration of the hardware cost-performance tradeoffs," IEEE Trans. Quantum Engineering, vol. 3, 2022, pp. 1-19. https://doi.org/10.1109/TQE.2022.3174017
  50. P. Das et al., "AFS: Accurate, fast, and scalable error-decoding for fault-tolerant quantum computers," in Proc. IEEE HPCA 2022, (Seoul, Republic of Korea), Apr. 2022, pp. 259-273.
  51. Y. Ueno et al., "QULATIS: A quantum error correction methodology toward lattice surgery," in Proc. IEEE HPCA 2022, (Seoul, Republic of Korea), Apr. 2022, pp. 274-287.
  52. Y. Ueno et al., "NEO-QEC: Neural network enhanced online superconducting decoder for surface codes," arXiv preprint, CoRR, 2022, arXiv: 2208.05758.
  53. G.S. Ravi et al., "Better than worst-case decoding for quantum error correction," in Proc. ASPLOS 2023, vol. 2, (Vancouver, Canada), Mar. 2023, pp. 88-102.
  54. N. Liyanage et al., "Scalable quantum error correction for surface codes using FPGA," arXiv preprint, CoRR, 2023, arXiv: 2301.08419.
  55. L. Skoric et al., "Parallel window decoding enables scalable fault tolerant quantum computation," arXiv preprint, CoRR, 2023, arXiv: 2209.08552.
  56. T. Xinyu et al., "Scalable surface code decoders with parallelization in time," arXiv preprint, CoRR, 2022, arXiv: 2209.09219.