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Quantum machine learning

Abstract

Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Quantum systems produce atypical patterns that classical systems are thought not to produce efficiently, so it is reasonable to postulate that quantum computers may outperform classical computers on machine learning tasks. The field of quantum machine learning explores how to devise and implement quantum software that could enable machine learning that is faster than that of classical computers. Recent work has produced quantum algorithms that could act as the building blocks of machine learning programs, but the hardware and software challenges are still considerable.

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Figure 1: Quantum tunnelling versus thermalization.

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References

  1. Rosenblatt, F. The perceptron: a probabilistic model for information storage and organization in the brain. Psychol. Rev. 65, 386 (1958)

    Article  CAS  Google Scholar 

  2. LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436–444 (2015)

    Article  ADS  CAS  Google Scholar 

  3. Le, Q. V. Building high-level features using large scale unsupervised learning. In IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP) 8595–8598 (IEEE, 2013)

    Google Scholar 

  4. Schuld, M., Sinayskiy, I. & Petruccione, F. An introduction to quantum machine learning. Contemp. Phys. 56, 172–185 (2015)

    Article  ADS  Google Scholar 

  5. Wittek, P. Quantum Machine Learning: What Quantum Computing Means to Data Mining (Academic Press, New York, NY, USA, 2014)

  6. Adcock, J. et al. Advances in quantum machine learning. Preprint at https://arxiv.org/abs/1512.02900 (2015)

  7. Arunachalam, S. & de Wolf, R. A survey of quantum learning theory. Preprint at https://arxiv.org/abs/1701.06806 (2017)

  8. Harrow, A. W., Hassidim, A. & Lloyd, S. Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103, 150502 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  9. Wiebe, N., Braun, D. & Lloyd, S. Quantum algorithm for data fitting. Phys. Rev. Lett. 109, 050505 (2012)

    Article  ADS  Google Scholar 

  10. Childs, A. M., Kothari, R. & Somma, R. D. Quantum linear systems algorithm with exponentially improved dependence on precision. Preprint at https://arxiv.org/abs/1511.02306 (2015)

  11. Lloyd, S., Mohseni, M. & Rebentrost, P. Quantum principal component analysis. Nat. Phys. 10, 631–633 (2014)

    Article  CAS  Google Scholar 

  12. Kimmel, S., Lin, C. Y.-Y., Low, G. H., Ozols, M. & Yoder, T. J. Hamiltonian simulation with optimal sample complexity. Preprint at https://arxiv.org/abs/1608.00281 (2016)

  13. Rebentrost, P., Mohseni, M. & Lloyd, S. Quantum support vector machine for big data classification. Phys. Rev. Lett. 113, 130503 (2014). This study applies quantum matrix inversion in a supervised discriminative learning algorithm.

    Article  ADS  Google Scholar 

  14. Lloyd, S., Garnerone, S. & Zanardi, P. Quantum algorithms for topological and geometric analysis of data. Nat. Commun. 7, 10138 (2016)

    Article  ADS  CAS  Google Scholar 

  15. Dridi, R. & Alghassi, H. Homology computation of large point clouds using quantum annealing. Preprint at https://arxiv.org/abs/1512.09328 (2015)

  16. Rebentrost, P., Steffens, A. & Lloyd, S. Quantum singular value decomposition of non-sparse low-rank matrices. Preprint at https://arxiv.org/abs/1607.05404 (2016)

  17. Schuld, M., Sinayskiy, I. & Petruccione, F. Prediction by linear regression on a quantum computer. Phys. Rev. A 94, 022342 (2016)

    Article  ADS  Google Scholar 

  18. Brandao, F. G. & Svore, K. Quantum speed-ups for semidefinite programming. Preprint at https://arxiv.org/abs/1609.05537 (2016)

  19. Rebentrost, P., Schuld, M., Petruccione, F. & Lloyd, S. Quantum gradient descent and Newton’s method for constrained polynomial optimization. Preprint at https://arxiv.org/abs/1612.01789 (2016)

  20. Wiebe, N., Kapoor, A. & Svore, K. M. Quantum deep learning. Preprint at https://arxiv.org/abs/1412.3489 (2014)

  21. Adachi, S. H. & Henderson, M. P. Application of quantum annealing to training of deep neural networks. Preprint at https://arxiv.org/abs/arXiv:1510.06356 (2015)

  22. Amin, M. H., Andriyash, E., Rolfe, J., Kulchytskyy, B. & Melko, R. Quantum Boltzmann machine. Preprint at https://arxiv.org/abs/arXiv:1601.02036 (2016)

  23. Sasaki, M., Carlini, A. & Jozsa, R. Quantum template matching. Phys. Rev. A 64, 022317 (2001)

    Article  ADS  Google Scholar 

  24. Bisio, A., Chiribella, G., D’Ariano, G. M., Facchini, S. & Perinotti, P. Optimal quantum learning of a unitary transformation. Phys. Rev. A 81, 032324 (2010)

    Article  ADS  Google Scholar 

  25. Bisio, A., D’Ariano, G. M., Perinotti, P. & Sedlák, M. Quantum learning algorithms for quantum measurements. Phys. Lett. A 375, 3425–3434 (2011)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  26. Sentís, G., Calsamiglia, J., Muñoz-Tapia, R. & Bagan, E. Quantum learning without quantum memory. Sci. Rep. 2, 708 (2012)

    Article  ADS  Google Scholar 

  27. Sentís, G., Gut¸a˘, M. & Adesso, G. Quantum learning of coherent states. EPJ Quant. Technol. 2, 17 (2015)

    Article  Google Scholar 

  28. Paparo, G. D., Dunjko, V., Makmal, A., Martin-Delgado, M. A. & Briegel, H. J. Quantum speedup for active learning agents. Phys. Rev. X 4, 031002 (2014)

    Google Scholar 

  29. Dunjko, V., Friis, N. & Briegel, H. J. Quantum-enhanced deliberation of learning agents using trapped ions. New J. Phys. 17, 023006 (2015)

    Article  ADS  Google Scholar 

  30. Dunjko, V., Taylor, J. M. & Briegel, H. J. Quantum-enhanced machine learning. Phys. Rev. Lett. 117, 130501 (2016). This paper investigates the theoretical maximum speedup achievable in reinforcement learning in a closed quantum system, which proves to be Grover-like if we wish to obtain classical verification of the learning process.

    Article  ADS  MathSciNet  Google Scholar 

  31. Sentís, G., Bagan, E., Calsamiglia, J., Chiribella, G. & Muñoz Tapia, R. Quantum change point. Phys. Rev. Lett. 117, 150502 (2016)

    Article  ADS  Google Scholar 

  32. Faccin, M., Migdał, P., Johnson, T. H., Bergholm, V. & Biamonte, J. D. Community detection in quantum complex networks. Phys. Rev. X 4, 041012 (2014). This paper defines closeness measures and then maximizes modularity with hierarchical clustering to partition quantum data.

    Google Scholar 

  33. Clader, B. D., Jacobs, B. C. & Sprouse, C. R. Preconditioned quantum linear system algorithm. Phys. Rev. Lett. 110, 250504 (2013)

    Article  ADS  CAS  Google Scholar 

  34. Lloyd, S., Mohseni, M. & Rebentrost, P. Quantum algorithms for supervised and unsupervised machine learning. Preprint at https://arxiv.org/abs/1307.0411 (2013)

  35. Wiebe, N., Kapoor, A. & Svore, K. M. Quantum algorithms for nearest-neighbor methods for supervised and unsupervised learning. Quantum Inf. Comput. 15, 316–356 (2015)

    MathSciNet  Google Scholar 

  36. Lau, H.-K., Pooser, R., Siopsis, G. & Weedbrook, C. Quantum machine learning over infinite dimensions. Phys. Rev. Lett. 118, 080501 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  37. Aïmeur, E ., Brassard, G . & Gambs, S. in Machine Learning in a Quantum World 431–442 (Springer, 2006)

    MATH  Google Scholar 

  38. Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)

    Article  MathSciNet  Google Scholar 

  39. Nielsen, M. A . & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000)

  40. Wossnig, L., Zhao, Z. & Prakash, A. A quantum linear system algorithm for dense matrices. Preprint at https://arxiv.org/abs/1704.06174 (2017)

  41. Giovannetti, V., Lloyd, S. & Maccone, L. Quantum random access memory. Phys. Rev. Lett. 100, 160501 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  42. Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  43. Vapnik, V. The Nature of Statistical Learning Theory (Springer, 1995)

  44. Anguita, D., Ridella, S., Rivieccio, F. & Zunino, R. Quantum optimization for training support vector machines. Neural Netw. 16, 763–770 (2003)

    Article  Google Scholar 

  45. Dürr, C. & Høyer, P. A quantum algorithm for finding the minimum. Preprint at https://arxiv.org/abs/quant-ph/9607014 (1996)

  46. Chatterjee, R. & Yu, T. Generalized coherent states, reproducing kernels, and quantum support vector machines. Preprint at https://arxiv.org/abs/1612.03713 (2016)

  47. Zhao, Z., Fitzsimons, J. K. & Fitzsimons, J. F. Quantum assisted Gaussian process regression. Preprint at https://arxiv.org/abs/1512.03929 (2015)

  48. Li, Z., Liu, X., Xu, N. & Du, J. Experimental realization of a quantum support vector machine. Phys. Rev. Lett. 114, 140504 (2015)

    Article  ADS  Google Scholar 

  49. Whitfield, J. D., Faccin, M. & Biamonte, J. D. Ground-state spin logic. Europhys. Lett. 99, 57004 (2012)

    Article  ADS  CAS  Google Scholar 

  50. Farhi, E., Goldstone, J. & Gutmann, S. A quantum approximate optimization algorithm. Preprint at https://arxiv.org/abs/1411.4028 (2014)

  51. Aaronson, S. Read the fine print. Nat. Phys. 11, 291–293 (2015)

    Article  CAS  Google Scholar 

  52. Arunachalam, S., Gheorghiu, V., Jochym-O’Connor, T., Mosca, M. & Srinivasan, P. V. On the robustness of bucket brigade quantum RAM. New J. Phys. 17, 123010 (2015)

    Article  ADS  Google Scholar 

  53. Scherer, A. et al. Concrete resource analysis of the quantum linear system algorithm used to compute the electromagnetic scattering cross section of a 2D target. Preprint at https://arxiv.org/abs/1505.06552 (2015)

  54. Denil, M . & De Freitas, N. Toward the implementation of a quantum RBM. In Neural Information Processing Systems (NIPS) Conf. on Deep Learning and Unsupervised Feature Learning Workshop Vol. 5 (2011)

    Google Scholar 

  55. Dumoulin, V., Goodfellow, I. J., Courville, A. & Bengio, Y. On the challenges of physical implementations of RBMs. Preprint at https://arxiv.org/abs/1312.5258 (2013)

  56. Benedetti, M., Realpe-Gómez, J., Biswas, R. & Perdomo-Ortiz, A. Estimation of effective temperatures in quantum annealers for sampling applications: a case study with possible applications in deep learning. Phys. Rev. A 94, 022308 (2016)

    Article  ADS  Google Scholar 

  57. Biamonte, J. D. & Love, P. J. Realizable Hamiltonians for universal adiabatic quantum computers. Phys. Rev. A 78, 012352 (2008). This study established the contemporary experimental target for non-stoquastic (that is, non-quantum stochastic) D-Wave quantum annealing hardware able to realize universal quantum Boltzmann machines.

    Article  ADS  MathSciNet  Google Scholar 

  58. Temme, K., Osborne, T. J., Vollbrecht, K. G., Poulin, D. & Verstraete, F. Quantum metropolis sampling. Nature 471, 87–90 (2011)

    Article  ADS  CAS  Google Scholar 

  59. Yung, M.-H. & Aspuru-Guzik, A. A quantum–quantum metropolis algorithm. Proc. Natl Acad. Sci. USA 109, 754–759 (2012)

    Article  ADS  CAS  Google Scholar 

  60. Chowdhury, A. N. & Somma, R. D. Quantum algorithms for Gibbs sampling and hitting-time estimation. Quant. Inf. Comput. 17, 41–64 (2017)

    MathSciNet  Google Scholar 

  61. Kieferova, M. & Wiebe, N. Tomography and generative data modeling via quantum Boltzmann training. Preprint at https://arxiv.org/abs/1612.05204 (2016)

  62. Lloyd, S. & Terhal, B. Adiabatic and Hamiltonian computing on a 2D lattice with simple 2-qubit interactions. New J. Phys. 18, 023042 (2016)

    Article  ADS  Google Scholar 

  63. Ventura, D. & Martinez, T. Quantum associative memory. Inf. Sci. 124, 273–296 (2000)

    Article  MathSciNet  Google Scholar 

  64. Granade, C. E., Ferrie, C., Wiebe, N. & Cory, D. G. Robust online Hamiltonian learning. New J. Phys. 14, 103013 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  65. Wiebe, N., Granade, C., Ferrie, C. & Cory, D. G. Hamiltonian learning and certification using quantum resources. Phys. Rev. Lett. 112, 190501 (2014)

    Article  ADS  Google Scholar 

  66. Wiebe, N., Granade, C. & Cory, D. G. Quantum bootstrapping via compressed quantum Hamiltonian learning. New J. Phys. 17, 022005 (2015)

    Article  ADS  Google Scholar 

  67. Marvian, I. & Lloyd, S. Universal quantum emulator. Preprint at https://arxiv.org/abs/1606.02734 (2016)

  68. Dolde, F. et al. High-fidelity spin entanglement using optimal control. Nat. Commun. 5, 3371 (2014)

    Article  ADS  Google Scholar 

  69. Zahedinejad, E., Ghosh, J. & Sanders, B. C. Designing high-fidelity single-shot three-qubit gates: a machine-learning approach. Phys. Rev. Appl. 6, 054005 (2016)

    Article  ADS  Google Scholar 

  70. Zahedinejad, E., Ghosh, J. & Sanders, B. C. High-fidelity single-shot Toffoli gate via quantum control. Phys. Rev. Lett. 114, 200502 (2015)

    Article  ADS  Google Scholar 

  71. Zeidler, D., Frey, S., Kompa, K.-L. & Motzkus, M. Evolutionary algorithms and their application to optimal control studies. Phys. Rev. A 64, 023420 (2001)

    Article  ADS  Google Scholar 

  72. Las Heras, U., Alvarez-Rodriguez, U., Solano, E. & Sanz, M. Genetic algorithms for digital quantum simulations. Phys. Rev. Lett. 116, 230504 (2016)

    Article  ADS  CAS  Google Scholar 

  73. Banchi, L., Pancotti, N. & Bose, S. Quantum gate learning in qubit networks: Toffoli gate without time-dependent control. npj Quant. Inf. 2, 16019 (2016)

    Article  ADS  Google Scholar 

  74. August, M. & Ni, X. Using recurrent neural networks to optimize dynamical decoupling for quantum memory. Preprint at https://arxiv.org/abs/1604.00279 (2016)

  75. Amstrup, B., Toth, G. J., Szabo, G., Rabitz, H. & Loerincz, A. Genetic algorithm with migration on topology conserving maps for optimal control of quantum systems. J. Phys. Chem. 99, 5206–5213 (1995)

    Article  CAS  Google Scholar 

  76. Hentschel, A. & Sanders, B. C. Machine learning for precise quantum measurement. Phys. Rev. Lett. 104, 063603 (2010)

    Article  ADS  Google Scholar 

  77. Lovett, N. B., Crosnier, C., Perarnau-Llobet, M. & Sanders, B. C. Differential evolution for many-particle adaptive quantum metrology. Phys. Rev. Lett. 110, 220501 (2013)

    Article  ADS  Google Scholar 

  78. Palittapongarnpim, P., Wittek, P., Zahedinejad, E., Vedaie, S. & Sanders, B. C. Learning in quantum control: high-dimensional global optimization for noisy quantum dynamics. Neurocomputing https://doi.org/10.1016/j.neucom.2016.12.087 (in the press)

    Article  Google Scholar 

  79. Carrasquilla, J. & Melko, R. G. Machine learning phases of matter. Nat. Phys. 13, 431–434 (2017)

    Article  CAS  Google Scholar 

  80. Broecker, P., Carrasquilla, J., Melko, R. G. & Trebst, S. Machine learning quantum phases of matter beyond the fermion sign problem. Preprint at https://arxiv.org/abs/1608.07848 (2016)

  81. Carleo, G. & Troyer, M. Solving the quantum many-body problem with artificial neural networks. Science 355, 602–606 (2017)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  82. Brunner, D., Soriano, M. C., Mirasso, C. R. & Fischer, I. Parallel photonic information processing at gigabyte per second data rates using transient states. Nat. Commun. 4, 1364 (2013)

    Article  ADS  Google Scholar 

  83. Cai, X.-D. et al. Entanglement-based machine learning on a quantum computer. Phys. Rev. Lett. 114, 110504 (2015)

    Article  ADS  Google Scholar 

  84. Hermans, M., Soriano, M. C., Dambre, J., Bienstman, P. & Fischer, I. Photonic delay systems as machine learning implementations. J. Mach. Learn. Res. 16, 2081–2097 (2015)

    MathSciNet  MATH  Google Scholar 

  85. Tezak, N. & Mabuchi, H. A coherent perceptron for all-optical learning. EPJ Quant. Technol. 2, 10 (2015)

    Article  Google Scholar 

  86. Neigovzen, R., Neves, J. L., Sollacher, R. & Glaser, S. J. Quantum pattern recognition with liquid-state nuclear magnetic resonance. Phys. Rev. A 79, 042321 (2009)

    Article  ADS  Google Scholar 

  87. Pons, M. et al. Trapped ion chain as a neural network: error resistant quantum computation. Phys. Rev. Lett. 98, 023003 (2007)

    Article  ADS  Google Scholar 

  88. Neven, H . et al. Binary classification using hardware implementation of quantum annealing. In 24th Ann. Conf. on Neural Information Processing Systems (NIPS-09) 1–17 (2009). This paper was among the first experimental demonstrations of machine learning using quantum annealing.

    Google Scholar 

  89. Denchev, V. S ., Ding, N ., Vishwanathan, S . & Neven, H. Robust classification with adiabatic quantum optimization. In Proc. 29th Int. Conf. on Machine Learning (ICML-2012) (2012)

    Google Scholar 

  90. Karimi, K. et al. Investigating the performance of an adiabatic quantum optimization processor. Quantum Inform. Process. 11, 77–88 (2012)

    Google Scholar 

  91. O’Gorman, B. A. et al. Bayesian network structure learning using quantum annealing. EPJ Spec. Top. 224, 163–188 (2015)

    Article  Google Scholar 

  92. Denchev, V. S., Ding, N., Matsushima, S., Vishwanathan, S. V. N. & Neven, H. Totally corrective boosting with cardinality penalization. Preprint at https://arxiv.org/abs/1504.01446 (2015)

  93. Kerenidis, I. & Prakash, A. Quantum recommendation systems. Preprint at https://arxiv.org/abs/1603.08675 (2016)

  94. Alvarez-Rodriguez, U., Lamata, L., Escandell-Montero, P., Martín-Guerrero, J. D. & Solano, E. Quantum machine learning without measurements. Preprint at https://arxiv.org/abs/1612.05535 (2016)

  95. Wittek, P. & Gogolin, C. Quantum enhanced inference in Markov logic networks. Sci. Rep. 7, 45672 (2017)

    Article  ADS  CAS  Google Scholar 

  96. Lamata, L. Basic protocols in quantum reinforcement learning with superconducting circuits. Sci. Rep. 7, 1609 (2017)

    Article  ADS  Google Scholar 

  97. Schuld, M., Fingerhuth, M. & Petruccione, F. Quantum machine learning with small-scale devices: implementing a distance-based classifier with a quantum interference circuit. Preprint at https://arxiv.org/abs/1703.10793 (2017)

  98. Monràs, A., Sentís, G. & Wittek, P. Inductive supervised quantum learning. Phys. Rev. Lett. 118, 190503 (2017). This paper proves that supervised learning protocols split into a training and application phase in both the classical and the quantum cases.

    Article  ADS  MathSciNet  Google Scholar 

  99. Tiersch, M., Ganahl, E. J. & Briegel, H. J. Adaptive quantum computation in changing environments using projective simulation. Sci. Rep. 5, 12874 (2015)

    Article  ADS  CAS  Google Scholar 

  100. Zahedinejad, E., Ghosh, J. & Sanders, B. C. Designing high-fidelity single-shot three-qubit gates: a machine learning approach. Preprint at https://arxiv.org/abs/1511.08862 (2015)

  101. Palittapongarnpim, P ., Wittek, P . & Sanders, B. C. Controlling adaptive quantum phase estimation with scalable reinforcement learning. In Proc. 24th Eur. Symp. Artificial Neural Networks (ESANN-16) on Computational Intelligence and Machine Learning 327–332 (2016)

    Google Scholar 

  102. Wan, K. H., Dahlsten, O., Kristjánsson, H., Gardner, R. & Kim, M. S. Quantum generalisation of feedforward neural networks. Preprint at https://arxiv.org/abs/1612.01045 (2016)

  103. Lu, D. et al. Towards quantum supremacy: enhancing quantum control by bootstrapping a quantum processor. Preprint at https://arxiv.org/abs/1701.01198 (2017)

  104. Mavadia, S., Frey, V., Sastrawan, J., Dona, S. & Biercuk, M. J. Prediction and real-time compensation of qubit decoherence via machine learning. Nat. Commun. 8, 14106 (2017)

    Article  ADS  CAS  Google Scholar 

  105. Rønnow, T. F. et al. Defining and detecting quantum speedup. Science 345, 420–424 (2014)

    Article  ADS  Google Scholar 

  106. Low, G. H., Yoder, T. J. & Chuang, I. L. Quantum inference on Bayesian networks. Phys. Rev. A 89, 062315 (2014)

    Article  ADS  Google Scholar 

  107. Wiebe, N. & Granade, C. Can small quantum systems learn? Preprint at https://arxiv.org/abs/1512.03145 (2015)

  108. Wiebe, N., Kapoor, A. & Svore, K. M. Quantum perceptron models. Adv. Neural Inform. Process. Syst. 29, 3999–4007 (2016)

    Google Scholar 

  109. Scherer, A. et al. Concrete resource analysis of the quantum linear-system algorithm used to compute the electromagnetic scattering cross section of a 2D target. Quantum Inform. Process. 16, 60 (2017)

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

J.B. acknowledges financial support from AFOSR grant FA9550-16-1-0300, Models and Protocols for Quantum Distributed Computation. P.W. acknowledges financial support from the ERC (Consolidator Grant QITBOX), Spanish Ministry of Economy and Competitiveness (Severo Ochoa Programme for Centres of Excellence in R&D SEV-2015-0522 and QIBEQI FIS2016-80773-P), Generalitat de Catalunya (CERCA Programme and SGR 875), and Fundacio Privada Cellex. P.R. and S.L. acknowledge funding from ARO and AFOSR under MURI programmes. We thank L. Zheglova for producing Fig. 1.

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Correspondence to Jacob Biamonte.

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Biamonte, J., Wittek, P., Pancotti, N. et al. Quantum machine learning. Nature 549, 195–202 (2017). https://doi.org/10.1038/nature23474

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