Quantum Bootstrap Aggregation

  • David WindridgeEmail author
  • Rajagopal Nagarajan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10106)


We set out a strategy for quantizing attribute bootstrap aggregation to enable variance-resilient quantum machine learning. To do so, we utilise the linear decomposability of decision boundary parameters in the Rebentrost et al. Support Vector Machine to guarantee that stochastic measurement of the output quantum state will give rise to an ensemble decision without destroying the superposition over projective feature subsets induced within the chosen SVM implementation. We achieve a linear performance advantage, O(d), in addition to the existing O(log(n)) advantages of quantization as applied to Support Vector Machines. The approach extends to any form of quantum learning giving rise to linear decision boundaries.


Support Vector Machine Training Vector Quantum Superposition Query Oracle Random Subspace Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The first author would like to acknowledge financial support from the Horizon 2020 European Research project DREAMS4CARS (#731593). The second author is partially supported by EU ICT COST Action IC1405 “Reversible Computation—Extending Horizons of Computing”.


  1. 1.
    Rebentrost, P., Mohseni, M., Lloyd, S.: Quantum support vector machine for big data classification. Phys. Rev. Lett. 113 (2014). 130501Google Scholar
  2. 2.
    Aïmeur, E., Brassard, G., Gambs, S.: Quantum speed-up for unsupervised learning. Mach. Learn. 90(2), 261–287 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Altaisky, M., Zolnikova, N., Kaputkina, N., Krylov, V., Lozovik, Y.E., Dattani, N.S.: Towards a feasible implementation of quantum neural networks using quantum dots, arXiv preprint arXiv:1503.05125
  4. 4.
    Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum principal component analysis. Nat. Phys. 10(9), 631–633 (2014)CrossRefGoogle Scholar
  5. 5.
    Barry, J., Barry, D.T., Aaronson, S.: Quantum partially observable markov decision processes. Phys. Rev. A 90(3), 032311 (2014)CrossRefGoogle Scholar
  6. 6.
    Lu, S., Braunstein, S.L.: Quantum decision tree classifier. Quantum Inf. Process. 13(3), 757–770 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Tucci, R.R.: Quantum circuit for discovering from data the structure of classical bayesian networks, arXiv preprint arXiv:1404.0055
  8. 8.
    Wiebe, N., Kapoor, A., Svore, K.: Quantum algorithms for nearest-neighbor methods for supervised and unsupervised learning, arXiv preprint arXiv:1401.2142
  9. 9.
    Cortes, C., Vapnik, V.: Support-vector networks. Mach. Learn. 20(3), 273–297 (1995). doi: 10.1007/BF00994018 zbMATHGoogle Scholar
  10. 10.
    Harrow, A.W., Hassidim, A., Lloyd, S.: Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103(15), 150502 (2009). arXiv:0811.3171 MathSciNetCrossRefGoogle Scholar
  11. 11.
    Breiman, L.: Bagging predictors. Mach. Learn. 24(2), 123–140 (1996)zbMATHGoogle Scholar
  12. 12.
    Valentini, G., Dietterich, T.G.: Low bias bagged support vector machines. In: International Conference on Machine Learning, ICML-2003, pp. 752–759. Morgan Kaufmann (2003)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer Science, School of Science and TechnologyMiddlesex UniversityLondonUK

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