Decoding surface code with a distributed neural network–based decoder

Springer Science and Business Media LLC - Tập 2 Số 1 - 2020
Savvas Varsamopoulos1, Koen Bertels1, Carmen G. Almudéver1
1Quantum Computer Architecture Lab, Delft University of Technology, Delft, The Netherlands

Tóm tắt

AbstractThere has been a rise in decoding quantum error correction codes with neural network–based decoders, due to the good decoding performance achieved and adaptability to any noise model. However, the main challenge is scalability to larger code distances due to an exponential increase of the error syndrome space. Note that successfully decoding the surface code under realistic noise assumptions will limit the size of the code to less than 100 qubits with current neural network–based decoders. Such a problem can be tackled by a distributed way of decoding, similar to the renormalization group (RG) decoders. In this paper, we introduce a decoding algorithm that combines the concept of RG decoding and neural network–based decoders. We tested the decoding performance under depolarizing noise with noiseless error syndrome measurements for the rotated surface code and compared against the blossom algorithm and a neural network–based decoder. We show that a similar level of decoding performance can be achieved between all tested decoders while providing a solution to the scalability issues of neural network–based decoders.

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Tài liệu tham khảo

Baireuther P, O’Brien TE, Tarasinski B, Beenakker CWJ (2018) Machine-learning-assisted correction of correlated qubit errors in a topological code. Quantum 2:48. https://doi.org/10.22331/q-2018-01-29-48

Bombin H (2010) Topological subsystem codes. Phys Rev A 81:032301. https://doi.org/10.1103/PhysRevA.81.032301

Bombin H (2011) Clifford gates by code deformation. New J Phys 13(4):043005. https://doi.org/10.1088/1367-2630/13/4/043005

Bombin H, Martin-Delgado MA (2009) Quantum measurements and gates by code deformation. J Phys A Math Theor 42(9):095302. https://doi.org/10.1088/1751-8113/42/9/095302

Bravyi S (2010) Stabilizer subsystem codes with spatially local generators. IEEE Information Theory Workshop, p 1–5. http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5592872&isnumber=5592637. Accessed 3 Mar 2020

Bravyi SB, Kitaev AY (1998) Quantum codes on a lattice with boundary. quant-ph/9811052

Bravyi S, Duclos-Cianci G, Poulin D, Suchara M (2013) Subsystem surface codes with three-qubit check operators. Quantum Inf Comput 13(11–12):963–985. http://dl.acm.org/citation.cfm?id=2535639.2535643. Accessed 3 Mar 2020

Bravyi S, Suchara M, Vargo A (2014) Efficient algorithms for maximum likelihood decoding in the surface code. Phys Rev A 90:032326. https://doi.org/10.1103/PhysRevA.90.032326

Chamberland C, Ronagh P (2018) Deep neural decoders for near term fault-tolerant experiments. Quantum Sci Technol 3(4):044002. http://stacks.iop.org/2058-9565/3/i=4/a=044002. Accessed 3 Mar 2020

Darmawan AS, Poulin D (2018) Linear-time general decoding algorithm for the surface code. Phys Rev E 97:051302. https://doi.org/10.1103/PhysRevE.97.051302

Davaasuren A, Suzuki Y, Fujii K, Koashi M (2018) General framework for constructing fast and near-optimal machine learning- based decoder of the topological stabilizer codes. arXiv:1801.04377

Dennis E, Kitaev A, Landahl A, Preskill J (2002) Topological quantum memory. J Math Phys 43(9):4452–4505. https://doi.org/10.1063/1.1499754

Devitt SJ, Munro WJ, Nemoto K (2013) Quantum error correction for beginners. Rep Prog Phys 76(7):076001. https://doi.org/10.1088/0034-4885/76/7/076001

Duclos-Cianci G, Poulin D (2010a) A renormalization group decoding algorithm for topological quantum codes. Information Theory Workshop (ITW), IEEE, p 1–5. https://doi.org/10.1109/CIG.2010.5592866

Duclos-Cianci G, Poulin D (2010b) Fast decoders for topological quantum codes. Phys Rev Lett 104:050504. https://doi.org/10.1103/PhysRevLett.104.050504

Edmonds J (1965) Paths, trees, and flowers. Can J Math 17:449–467. https://doi.org/10.4153/CJM-1965-045-4

Fowler A G (2013) Optimal complexity correction of correlated errors in the surface code. arXiv:1310.0863

Fowler AG (2015) Minimum weight perfect matching of fault tolerant topological quantum error correction in average o(1) parallel time. Quantum Inf Comput 15:145–158

Fowler AJ, Stephens AM, Groszkowski P (2009) High threshold universal quantum computation on the surface code. Phys Rev A 80:052312. https://link.aps.org/doi/10.1103/PhysRevA.80.052312. Accessed 3 Mar 2020

Fowler AG, Mariantoni M, Martinis JM, Cleland AN (2012a) Surface codes: towards practical large-scale quantum computation. Phys Rev A 86:032324. https://doi.org/10.1103/PhysRevA.86.032324

Fowler AG, Whiteside AC, Hollenberg LCL (2012b) Towards practical classical processing for the surface code. Phys Rev Lett 108:180501. https://doi.org/10.1103/PhysRevLett.108.180501

Freedman MH, Meyer DA (2001) Projective plane and planar quantum codes. Found Comput Math 1(3):325–332

Gottesman D (1997) Stabilizer codes and quantum error correction. Dissertation, Caltech

Herold M, Campbell E T, Eisert J, Kastoryano M J (2015) Cellular-automaton decoders for topological quantum memories. Npj Quantum Information 1. https://www.nature.com/articles/npjqi201510. Accessed 3 Mar 2020

Horsman C, Fowler AG, Devitt S, Meter RV (2012) Surface code quantum computing by lattice surgery. New J Phys 14(12):123011. https://doi.org/10.1088/1367-2630/14/12/123011

Hutter A, Wootton JR, Loss D (2014) Efficient Markov chain Monte Carlo algorithm for the surface code. Phys Rev A 89:022326. https://doi.org/10.1103/PhysRevA.89.022326

Kitaev A (2003) Fault-tolerant quantum computation by anyons. Ann Phys 303(1):2–30. http://www.sciencedirect.com/science/article/pii/S0003491602000180. Accessed 3 Mar 2020

Kolmogorov V (2009) Blossom V: a new implementation of a minimum cost perfect matching algorithm. Math Program Comput 1:43–67. https://doi.org/10.1007/s12532-009-0002-8

Krastanov S, Jiang L (2017) Deep neural network probabilistic decoder for stabilizer codes. Sci Rep 7:11003

Landahl A J, Anderson J T, Rice P R (2011) Fault-tolerant quantum computing with color codes. arXiv:1108.5738

Maskara M, Kubica A, Jochym-O’Connor T (2018) Advantages of versatile neural-network decoding for topological codes. arXiv:1802.08680

Ni X (2018) Neural network decoders for large-distance 2d toric codes. arXiv:1809.06640

Nielsen MA, Chuang IL (2002) Quantum computation and quantum information. Cambridge University Press, Cambridge

Raussendorf R, Harrington J (2007) Fault-tolerant quantum computation with high threshold in two dimensions. Phys Rev Lett 98:190504. https://doi.org/10.1103/PhysRevLett.98.190504

Raussendorf R, Harrington J, Goyal K (2007) Topological fault-tolerance in cluster state quantum computation. New J Phys 9(6):199–199. https://doi.org/10.1088/1367-2630/9/6./199

Suchara M, Bravyi S, Terhal B (2011) Constructions and noise threshold of topological subsystem codes. J Phys A Math Theor 44(15):155301. http://stacks.iop.org/1751-8121/44/i=15/a=155301. Accessed 3 Mar 2020

Sweke R, Kesselring M S, van Nieuwenburg E P L, Eisert J (2018) Reinforcement learning decoders for fault-tolerant quantum computation. arXiv:1810.07207

Terhal BM (2015) Quantum error correction for quantum memories. Rev Mod Phys 87:307–346. https://doi.org/10.1103/RevModPhys.87.307

Torlai G, Melko RG (2017) Neural decoder for topological codes. Phys Rev Lett 119:030501 7. https://doi.org/10.1103/PhysRevLett.119.030501

Varsamopoulos S, Criger B, Bertels K (2017) Decoding small surface codes with feedforward neural networks. Quantum Sci Technol 3(1):015004. http://stacks.iop.org/2058-9565/3/i=1/a=015004. Accessed 3 Mar 2020

Varsamopoulos S, Bertels K, Almudever CG (2019) Designing neural network based decoders for surface codes. IEEE Trans Comput. https://doi.org/10.1109/TC.2019.2948612

Wang DS, Fowler AG, Hollenberg LCL (2011) Surface code quantum computing with error rates over 1%. Phys Rev A 83:020302. https://doi.org/10.1103/PhysRevA.83.020302

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