- Letter
- Open Access
Artificial neural network syndrome decoding on IBM quantum processors
Phys. Rev. Research 6, L032004 – Published 8 July, 2024
DOI: https://doi.org/10.1103/PhysRevResearch.6.L032004
Abstract
Syndrome decoding is an integral but computationally demanding step in the implementation of quantum error correction for fault-tolerant quantum computing. Here, we report the development and benchmarking of Artificial Neural Network (ANN) decoding on IBM quantum processors. We demonstrate that ANNs can efficiently decode syndrome measurement data from heavy-hexagonal code architecture and apply appropriate corrections to facilitate error protection. The current physical error rates of IBM devices are above the code's threshold and restrict the scope of our ANN decoder for logical error rate suppression. However, our work confirms the applicability of ANN decoding methods of syndrome data retrieved from experimental devices and establishes machine learning as a promising pathway for quantum error correction when quantum devices with below threshold error rates become available in the near future.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (53)
- H. Collins and C. Nay, IBM Unveils 400 Qubit-Plus Quantum Processor and Next-Generation IBM Quantum System Two, https://newsroom.ibm.com/2022-11-09-IBM-Unveils-400-Qubit-Plus-Quantum-Processor-and-Next-Generation-IBM-Quantum-System-Two (2022).
- L. S. Madsen et al., Quantum computational advantage with a programmable photonic processor, Nature (London) 606, 75 (2022).
- K. Barnes et al., Assembly and coherent control of a register of nuclear spin qubits, Nat. Commun. 13, 2779 (2022).
- 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.
- Y. Kim et al., Evidence for the utility of quantum computing before fault tolerance, Nature (London) 618, 500 (2023).
- S. Endo, S. C. Benjamin, and Y. Li, Practical quantum error mitigation for near-future applications, Phys. Rev. X 8, 031027 (2018).
- A. Strikis, D. Qin, Y. Chen, S. C. Benjamin, and Y. Li, Learning-based quantum error mitigation, PRX Quantum 2, 040330 (2021).
- S. Bravyi, S. Sheldon, A. Kandala, D. C. Mckay, and J. M. Gambetta, Mitigating measurement errors in multiqubit experiments, Phys. Rev. A 103, 042605 (2021).
- P. W. Shor, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A 52, R2493 (1995).
- A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. 303, 2 (2003).
- D. Aharonov and M. Ben-Or, Fault-tolerant quantum computation with constant error rate, SIAM J. Comput. 38, 1207 (2008).
- E. Knill, R. Laflamme, and W. H. Zurek, Resilient quantum computation: Error models and thresholds, Proc. R. Soc. A: Math. Phys. Eng. Sci. 454, 365 (1998).
- D. Gottesman, Stabilizer codes and quantum error correction, arXiv:quant-ph/9705052.
- A. M. Steane, Active stabilization, quantum computation, and quantum state synthesis. Phys. Rev. Lett. 78, 2252 (1997).
- A. Y. Kitaev, Quantum error correction with imperfect gates, in Quantum Communication, Computing, and Measurement, edited by O. Hirota, A. S. Holevo, and C. M. Caves (Springer, Boston, MA, USA, 1997), pp. 181–188.
- A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86, 032324 (2012).
- S. Varsamopoulos, B. Criger, and K. Bertels, Decoding small surface codes with feedforward neural networks, Quantum Sci. Technol. 3, 015004 (2017).
- K. Meinerz, C.-Y. Park, and S. Trebst, Scalable neural decoder for topological surface codes. Phys. Rev. Lett. 128, 080505 (2022).
- S. Varsamopoulos, K. Bertels, and C. G. Almudever, Comparing neural network based decoders for the surface code, IEEE Trans. Comput. 69, 300 (2020).
- S. Gicev, L. C. L. Hollenberg, and M. Usman, A scalable and fast artificial neural network syndrome decoder for surface codes, Quantum 7, 1058 (2023).
- R. W. J. Overwater, M. Babaie, and F. Sebastiano, Neural-network decoders for quantum error correction using surface codes: A space exploration of the hardware cost-performance tradeoffs, IEEE Trans. Quantum Eng. 3, 1 (2022).
- T. Wagner, H. Kampermann, and D. Bruß, Symmetries for a high-level neural decoder on the toric code, Phys. Rev. A 102, 042411 (2020).
- X. Ni, Neural network decoders for large-distance 2D toric codes, Quantum 4, 310 (2020).
- M. Zhang, X. Ren, G. Xi, Z. Zhang, Q. Yu, F. Liu, H. Zhang, S. Zhang, and Y.-C. Zheng, A scalable, fast and programmable neural decoder for fault-tolerant quantum computation using surface codes, arXiv:2305.15767.
- J. Bausch et al., Learning to decode the surface code with a recurrent, transformer-based neural network, arXiv:2310.05900.
- M. Lange, P. Havstrom, B. Srivastava, V. Bergentall, K. Hammar, O. Heuts, E. van Nieuwenburg, and M. Granath, Data-driven decoding of quantum error correcting codes using graph neural networks, arXiv:2307.01241.
- B. M. Varbanov, M. Serra-Peralta, D. Byfield, and B. M. Terhal, Neural network decoder for near-term surface-code experiments, arXiv:2307.03280.
- O. Higgott, PyMatching: A Python package for decoding quantum codes with minimum-weight perfect matching, ACM Trans. Quantum Comput. 3, 1 (2022).
- E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, Topological quantum memory, J. Math. Phys. 43, 4452 (2002).
- C. Chamberland, G. Zhu, T. J. Yoder, J. B. Hertzberg, and A. W. Cross, Topological and subsystem codes on low-degree graphs with flag qubits, Phys. Rev. X 10, 011022 (2020).
- P. Nation, H. Paik, A. Cross, and Z. Nazario, The IBM Quantum Heavy Hex Lattice, https://research.ibm.com/blog/heavy-hex-lattice (2021).
- N. Sundaresan, T. J. Yoder, Y. Kim, M. Li, E. H. Chen, G. Harper, T. Thorbeck, A. W. Cross, A. D. Corcoles, and M. Takita, Demonstrating multi-round subsystem quantum error correction using matching and maximum likelihood decoders, Nat. Commun. 14, 2852 (2023).
- E. H. Chen, T. J. Yoder, Y. Kim, N. Sundaresan, S. Srinivasan, M. Li, A. D. Corcoles, A. W. Cross, and M. Takita, Calibrated decoders for experimental quantum error correction, Phys. Rev. Lett. 128, 110504 (2022).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L032004 for additional details on methods.
- G. Torlai and R. G. Melko, Neural decoder for topological codes, Phys. Rev. Lett. 119, 030501 (2017).
- S. Krastanov and L. Jiang, Deep neural network probabilistic decoder for stabilizer codes, Sci. Rep. 7, 11003 (2017).
- P. Baireuther, T. E. O'Brien, B. Tarasinski, and C. W. J. Beenakker, Machine-learning-assisted correction of correlated qubit errors in a topological code, Quantum 2, 48 (2018).
- A. Davaasuren, Y. Suzuki, K. Fujii, and M. Koashi, General framework for constructing fast and near-optimal machine-learning-based decoder of the topological stabilizer codes, Phys. Rev. Res. 2, 033399 (2020).
- IBM, IBM Quantum, https://quantum-computing.ibm.com/ (2022).
- C. Chamberland, L. Goncalves, P. Sivarajah, E. Peterson, and S. Grimberg, Techniques for combining fast local decoders with global decoders under circuit-level noise, Quantum Sci. Technol. 8, 045011 (2023).
- Y. Ueno, M. Kondo, M. Tanaka, Y. Suzuki, and Y. Tabuchi, NEO-QEC: Neural network enhanced online superconducting decoder for surface codes, arXiv:2208.05758.
- L. Skoric, D. E. Browne, K. M. Barnes, N. I. Gillespie, and E. T. Campbell, Parallel window decoding enables scalable fault tolerant quantum computation, Nat. Commun. 14, 7040 (2023).
- F. Battistel, C. Chamberland, K. Johar, R. W. J. Overwater, F. Sebastiano, L. Skoric, Y. Ueno, and M. Usman, Real-time decoding for fault-tolerant quantum computing: Progress, challenges and outlook, Nano Futures 7, 032003 (2023).
- A. G. Fowler, Minimum weight perfect matching of fault-tolerant topological quantum error correction in average (1) parallel time, Quantum Inf. Comput. 15, 145 (2015).
- R. Acharya et al., Suppressing quantum errors by scaling a surface code logical qubit, Nature (London) 614, 676 (2023).
- A. G. Fowler, A. C. Whiteside, and L. C. L. Hollenberg, Towards practical classical processing for the surface code, Phys. Rev. Lett. 108, 180501 (2012).
- D. S. Wang, A. G. Fowler, A. M. Stephens, and L. C. L. Hollenberg, Threshold error rates for the toric and planar codes, Quantum Inf. Comput. 10, 456 (2010).
- N. Delfosse, A. Paz, A. Vaschillo, and K. M. Svore, How to choose a decoder for a fault-tolerant quantum computer? The speed vs accuracy trade-off, arXiv:2310.15313.
- C. Chamberland and P. Ronagh, Deep neural decoders for near term fault-tolerant experiments, Quantum Sci. Technol. 3, 044002 (2018).
- D. Bhoumik, R. Majumdar, D. Madan, D. Vinayagamurthy, S. Raghunathan, and S. Sur-Kolay, Efficient machine-learning-based decoder for heavy hexagonal QECC, arXiv:2210.08730.
- A. Li, F. Li, Q. Gan, and H. Ma, Convolutional-neural-network-based hexagonal quantum error correction decoder, Appl. Sci. 13, 9689 (2023).
- M. Abadi et al., TensorFlow: A system for large-scale machine learning, in Proceedings of the 12th USENIX conference on Operating Systems Design and Implementation, OSDI'16 (ACM, New York, 2016), pp. 265–283.
- Y. Tomita and K. M. Svore, Low-distance surface codes under realistic quantum noise, Phys. Rev. A 90, 062320 (2014).