Encyclopedia of Machine Learning and Data Mining

Living Edition
| Editors: Claude Sammut, Geoffrey I. Webb

Quantum Machine Learning

Living reference work entry
DOI: https://doi.org/10.1007/978-1-4899-7502-7_913-1


Quantum machine learning is a young research area investigating which consequences the emerging technology of quantum computing has for machine learning. This article introduces into basic concepts of quantum information and summarises some major strategies of implementing machine learning algorithms on a quantum computer.


Quantum System Quantum Algorithm Boltzmann Machine Qubit System Probabilistic Description 
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.
This is a preview of subscription content, log in to check access

Recommended Reading

  1. Aaronson S (2015) Read the fine print. Nat Phys 11(4):291–293CrossRefGoogle Scholar
  2. Adachi SH, Henderson MP (2015) Application of quantum annealing to training of deep neural networks. arXiv preprint arXiv:1510.06356Google Scholar
  3. Adcock J, Allen E, Day M, Frick S, Hinchliff J, Johnson M, Morley-Short S, Pallister S, Price A, Stanisic S (2015) Advances in quantum machine learning. arXiv preprint arXiv:1512.02900Google Scholar
  4. Amin MH, Andriyash E, Rolfe J, Kulchytskyy B, Melko R (2016) Quantum boltzmann machine. arXiv preprint arXiv:1601.02036Google Scholar
  5. Barry J, Barry DT, Aaronson S (2014) Quantum partially observable markov decision processes. Phys Rev A 90:032311CrossRefGoogle Scholar
  6. Cai X-D, Wu D, Su Z-E, Chen M-C, Wang X-L, Li L, Liu N-L, Lu C-Y, Pan J-W (2015) Entanglement-based machine learning on a quantum computer. Phys Rev Lett 114(11):110504CrossRefGoogle Scholar
  7. Das A, Chakrabarti BK (2008) Colloquium: quantum annealing and analog quantum computation. Rev Mod Phys 80(3):1061MathSciNetCrossRefMATHGoogle Scholar
  8. Denchev V, Ding N, Neven H, Vishwanathan S (2012) Robust classification with adiabatic quantum optimization. In: Proceedings of the 29th international conference on machine learning (ICML-12), Edinburgh, pp 863–870Google Scholar
  9. Deutsch D (1985) Quantum theory, the church-turing principle and the universal quantum computer. Proc R Soc Lond A: Math Phys Eng Sci 400:97–117. The Royal SocietyGoogle Scholar
  10. DiVincenzo DP (2000) The physical implementation of quantum computation. Fortschritte der Physik 48(9–11):771–783 ISSN 1521–3978Google Scholar
  11. Grover LK (1996) A fast quantum mechanical algorithm for database search. In: Proceedings of the twenty-eighth annual ACM symposium on theory of computing. ACM, New York, pp 212–219Google Scholar
  12. Harrow AW, Hassidim A, Lloyd S (2009) Quantum algorithm for linear systems of equations. Phys Rev Lett 103(15):150502MathSciNetCrossRefGoogle Scholar
  13. Kak SC (1995) Quantum neural computing. Adv Imaging Electron Phys 94:259–313CrossRefGoogle Scholar
  14. Li Z, Liu X, Xu N, Du J (2015) Experimental realization of a quantum support vector machine. Phys Rev Lett 114(14):140504CrossRefGoogle Scholar
  15. Lloyd S, Garnerone S, Zanardi P (2016) Quantum algorithms for topological and geometric analysis of data. Nat Commun 7:10138CrossRefGoogle Scholar
  16. Low GH, Yoder TJ, Chuang IL (2014) Quantum inference on Bayesian networks. Phys Rev A 89:062315CrossRefGoogle Scholar
  17. Neigovzen R, Neves JL, Sollacher R, Glaser SJ (2009) Quantum pattern recognition with liquid-state nuclear magnetic resonance. Phys Rev A 79(4):042321CrossRefGoogle Scholar
  18. Neven H, Rose G, Macready WG (2008) Image recognition with an adiabatic quantum computer i. Mapping to quadratic unconstrained binary optimization. arXiv preprint arXiv:0804.4457Google Scholar
  19. Nielsen MA, Chuang IL (2010) Quantum computation and quantum information. Cambridge University Press, CambridgeCrossRefMATHGoogle Scholar
  20. O’Gorman B, Babbush R, Perdomo-Ortiz A, Aspuru-Guzik A, Smelyanskiy V (2015) Bayesian network structure learning using quantum annealing. Eur Phys J Spec Top 224(1):163–188CrossRefGoogle Scholar
  21. Paparo GD, Dunjko V, Makmal A, Martin-Delgado MA, Briegel HJ (2014) Quantum speedup for active learning agents. Phys Rev X 4(3):031002Google Scholar
  22. Rebentrost P, Mohseni M, Lloyd S (2014) Quantum support vector machine for big data classification. Phys Rev Lett 113:130503CrossRefGoogle Scholar
  23. Schuld M, Sinayskiy I, Petruccione F (2014a) The quest for a quantum neural network. Q Inf Process 13 (11):2567–2586MathSciNetCrossRefMATHGoogle Scholar
  24. Schuld M, Sinayskiy I, Petruccione F (2014b) Quantum computing for pattern classification. Pham, Duc-Nghia, Park, Seong-Bae (Eds.) Springer International Publishing In: Lecture notes in computer science, vol 8862. Springer, pp 208–220Google Scholar
  25. Schuld M, Sinayskiy I, Petruccione F (2015) Introduction to quantum machine learning. Contemp Phys 56(2):172–185CrossRefMATHGoogle Scholar
  26. Schuld M, Sinayskiy I, Petruccione F (2016) Prediction by linear regression on a quantum computer. Phys Rev A 94(2):022342CrossRefGoogle Scholar
  27. Shor PW (1997) Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J Comput 26(5):1484–1509MathSciNetCrossRefMATHGoogle Scholar
  28. Ventura D, Martinez T (2000) Quantum associative memory. Inf Sci 124(1):273–296MathSciNetCrossRefGoogle Scholar
  29. Wiebe N, Granade C (2015) Can small quantum systems learn? arXiv preprint arXiv:1512.03145Google Scholar
  30. Wiebe N, Braun D, Lloyd S (2012) Quantum algorithm for data fitting. Phys Rev Lett 109(5):050505CrossRefGoogle Scholar
  31. Wiebe N, Kapoor A, Svore K (2014) Quantum deep learning. arXiv: 1412.3489v1Google Scholar
  32. Wiebe N, Kapoor A, Svore K (2015) Quantum nearest-neighbor algorithms for machine learning. Q Inf Comput 15:0318–0358MathSciNetGoogle Scholar
  33. Zhao Z, Fitzsimons JK, Fitzsimons JF (2015) Quantum assisted Gaussian process regression. arXiv preprint arXiv:1512.03929Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Quantum Research GroupSchool of Chemistry & Physics, University of KwaZulu-NatalDurbanSouth Africa
  2. 2.National Institute of Theoretical Physics (NITheP)KwaZulu-NatalSouth Africa