Machine-Learning based Decoding of Surface Code Syndromes in Quantum Error Correction
by Debasmita Bhoumik 1,* 
, Pinaki Sen 2, Ritajit Majumdar 1, Susmita Sur-Kolay 1, Latesh Kumar KJ 3, Sundaraja Sitharama Iyengar 3
1 Advanced Computing & Microelectronics Unit, Indian Statistical Institute, Kolkata, 700108, India
2 Department of Electrical Engineering, National Institute of Technology, Agartala, India
3 KFSCIS, Florida International University, Miami, Florida, USA
* Author to whom correspondence should be addressed.
Journal of Engineering Research and Sciences, Volume 1, Issue 6, Page # 21-35, 2022; DOI: 10.55708/js0106004
Keywords: Quantum Error Correction, Surface code, Error decoding, Machine learning decoder
Received: 14 March 2022, Revised: 12 May 2022, Accepted: 20 May 2022, Published Online: 24 June 2022
APA Style
Bhoumik, D., Sen, P., Majumdar, R., Sur-Kolay, S., Kj, L. K., & Iyengar, S. S. (2022). Machine-Learning based Decoding of Surface Code Syndromes in Quantum Error Correction. Journal of Engineering Research and Sciences, 1(6), 21–35. https://doi.org/10.55708/js0106004
Chicago/Turabian Style
Bhoumik, Debasmita, Pinaki Sen, Ritajit Majumdar, Susmita Sur-Kolay, Latesh Kumar Kj, and Sundaraja Sitharama Iyengar. “Machine-Learning based Decoding of Surface Code Syndromes in Quantum Error Correction.” Journal of Engineering Research and Sciences 1, no. 6 (June 1, 2022): 21–35. https://doi.org/10.55708/js0106004.
IEEE Style
D. Bhoumik, P. Sen, R. Majumdar, S. Sur-Kolay, L. K. Kj, and S. S. Iyengar, “Machine-Learning based Decoding of Surface Code Syndromes in Quantum Error Correction,” Journal of Engineering Research and Sciences, vol. 1, no. 6, pp. 21–35, Jun. 2022, doi: 10.55708/js0106004.
Errors in surface code have typically been decoded by Minimum Weight Perfect Matching (MWPM) bas -based Machine Learning (ML) techniques have been employed for this purpose, although how an ML decoder will behave in a more realistic asymmetric noise model has not been studied. In this article we (i) establish a methodology to formulate the surface code decoding problem as an ML classification problem, and (ii) propose a two-level (low and high) ML-based decoding scheme, where the first (low) level corrects errors on physical qubits and the second (high) level corrects any existing logical errors, for various noise models. Our results show that our proposed decoding method achieves ~10x and ~2x higher values of pseudo-threshold and threshold respectively, than for those with MWPM. We also empirically establish that usage of more sophisticated ML models with higher training/testing time, do not provide significant improvement in the decoder performance.
- P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer”, SIAM J. Comput., vol. 26, no. 5, pp. 1484–1509, 1997, doi:10.1137/S0097539795293172.
- L. K. Grover, “A fast quantum mechanical algorithm for database search”, “Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing”, STOC ’96, pp. 212–219, ACM, New York, NY, USA, 1996, doi:10.1145/237814.237866.
- A. M. Childs, N. Wiebe, “Hamiltonian simulation using linear com- unitary operations”, Quantum Info. Comput., vol. 12, no.
12, p. 901–924, 2012. - J. R. McClean, J. Romero, R. Babbush, A. Aspuru-Guzik, “The theory of variational hybrid quantum-classical algorithms”, New Journal of Physics, vol. 18, no. 2, p. 023023, 2016.
- M. A. Nielsen, I. Chuang, Quantum computation and quantum informa- tion, AAPT, 2002.
- P. W. Shor, “Scheme for reducing decoherence in quantum com- puter memory”, Phys. Rev. A, vol. 52, pp. R2493–R2496, 1995, doi: 10.1103/PhysRevA.52.R2493.
- A. M. Steane, “Error correcting codes in quantum theory”, Phys. Rev. Lett., vol. 77, pp. 793–797, 1996, doi:10.1103/PhysRevLett.77.793.
- R. Laflamme, C. Miquel, J. P. Paz, W. H. Zurek, “Perfect quantum error correcting code”, Phys. Rev. Lett., vol. 77, pp. 198–201, 1996, doi:10.1103/PhysRevLett.77.198.
- S. B. Bravyi, A. Y. Kitaev, “Quantum codes on a lattice with boundary”,
arXiv preprint quant-ph/9811052, 1998. - E. Dennis, A. Kitaev, A. Landahl, J. Preskill, “Topological quantum memory”, Journal of Mathematical Physics, vol. 43, no. 9, pp. 4452–4505, 2002.
- A. G. Fowler, A. M. Stephens, P. Groszkowski, “High-threshold uni- versal quantum computation on the surface code”, Physical Review A, vol. 80, no. 5, p. 052312, 2009.
- D. S. Wang, A. G. Fowler, L. C. Hollenberg, “Surface code quantum computing with error rates over 1%”, Physical Review A, vol. 83, no. 2, p. 020302, 2011.
- L. Riesebos, X. Fu, S. Varsamopoulos, C. G. Almudever, K. Bertels, “Pauli frames for quantum computer architectures”, “Proceedings of the 54th Annual Design Automation Conference 2017”, pp. 1–6, 2017.
- A. G. Fowler, A. C. Whiteside, L. C. Hollenberg, “Towards practical classical processing for the surface code”, Physical review letters, vol. 108, no. 18, p. 180501, 2012.
- R. Majumdar, S. Basu, P. Mukhopadhyay, S. Sur-Kolay, “Error trac- ing in linear and concatenated quantum circuits”, arXiv preprint arXiv:1612.08044, 2016.
- J. Edmonds, “Paths, trees, and flowers”, Canadian Journal of Mathemat- ics, vol. 17, p. 449–467, 1965, doi:10.4153/CJM-1965-045-4.
- S. Varsamopoulos, K. Bertels, C. G. Almudever, “Comparing neural network based decoders for the surface code”, IEEE Transactions on Computers, vol. 69, no. 2, pp. 300–311, 2019.
- C. Chamberland, P. Ronagh, “Deep neural decoders for near term fault-tolerant experiments”, Quantum Science and Technology, vol. 3, no. 4, p. 044002, 2018.
- S. Varsamopoulos, B. Criger, K. Bertels, “Decoding small surface codes with feedforward neural networks”, Quantum Science and Technology, vol. 3, no. 1, p. 015004, 2017.
- R. Sweke, M. S. Kesselring, E. P. van Nieuwenburg, J. Eisert, “Rein- forcement learning decoders for fault-tolerant quantum computation”, Machine Learning: Science and Technology, vol. 2, no. 2, p. 025005, 2020.
- L. Ioffe, M. Mézard, “Asymmetric quantum error-correcting codes”,
Phys. Rev. A, vol. 75, p. 032345, 2007, doi:10.1103/PhysRevA.75.032345. - D. Gottesman, “Stabilizer codes and quantum error correction”, arXiv preprint quant-ph/9705052, 1997.
- R. Hill, A first course in coding theory, Oxford University Press, 1986.
- V. Kumar, J. S. Malhotra, S. Sharma, P. Bhardwaj, “Soil Properties Pre- diction for Agriculture using Machine Learning Techniques”, Journal of Engineering Research and Sciences, vol. 1, no. 3, pp. 9–18, 2022.
- H.-Y. Tran, T.-M. Bui, T.-L. Pham, V.-H. Le, “An Evaluation of 2D Human Pose Estimation based on ResNet Back-”, Journal of Engineering Research and Sciences, vol. 1, no. 3, pp. 59–67, 2022.
- M. A. Danlami, A. O. Oluwaseun, M. S. Adam, S. M. Abubakar, E. Ay- obami, “Cascaded Keypoint Detection and Description for Object on”, Journal of Engineering Research and Sciences, vol. 1, no. 3,
. 164–169, 2022. - S. K. Pal, D. Bhoumik, D. Bhunia Chakraborty, “Granulated deep learning and z-numbers in motion detection and object recognition”, Neural Computing and Applications, vol. 32, no. 21, pp. 16533–16548, 2020.
- A. V. Singhania, S. L. Mukherjee, R. Majumdar, A. Mehta, P. Banerjee,
D. Bhoumik, “A machine learning based heuristic to predict the ef- ficacy of online sale”, “Emerging Technologies in Data Mining and Information Security”, pp. 439–447, Springer, 2021. - S. Varsamopoulos, K. Bertels, C. G. Almudever, “Designing neu- ral network based decoders for surface codes”, arXiv preprint arXiv:1811.12456, 2018.
- S. Krastanov, L. Jiang, “Deep neural network probabilistic decoder for stabilizer codes”, Scientific reports, vol. 7, no. 1, pp. 1–7, 2017.
- vid, Understanding machine learning: From algorithms, Cambridge university press, 2014.
