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Quantum and quantum-like machine learning: a note on differences and similarities

  • Giuseppe SergioliEmail author
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Abstract

In the past few decades, researchers have extensively investigated the applications of quantum computation and quantum information to machine learning with remarkable results. This, in turn, has led to the emergence of quantum machine learning as a separate discipline, whose main goal is to transform standard machine learning algorithms into quantum algorithms which can be implemented on quantum computers. One further research programme has involved using quantum information to create new quantum-like algorithms for classical computers (Sergioli et al. in Int J Theor Phys 56(12):3880–3888, 2017; PLoS ONE 14:e0216224, 2019.  https://doi.org/10.1371/journal.pone.0216224; Int J Quantum Inf 16(8):1840011, 2018a; Soft Comput 22(3):691–705, 2018b). This brief survey summarises and compares both approaches and also outlines the main motivations behind them.

Keywords

Quantum machine learning Quantum information Binary classification 

Notes

Acknowledgements

I warmly thank Claudio Ternullo for the careful linguistic revision of the last version of the manuscript.

Funding

This work has been partially supported by the Project “Strategies and Technologies for Scientific Education and Dissemination” (CUP No. F71I17000330002) founded by Fondazione di Sardegna.

Compliance with ethical standards

Conflict of interest

The author does not have any conflicts of interest.

Ethical standard

This article does not contain any studies with human participants performed by any of the authors.

References

  1. Aaronson S (2007) The learnability of quantum states. Proc R Soc Lond A Math Phys Eng Sci 463:3089–3114MathSciNetCrossRefGoogle Scholar
  2. Aïmeur E, Brassard G, Gambs S (2006) Machine learning in a quantum world. In: Conference of the Canadian Society for Computational Studies of Intelligence. Springer, BerlinCrossRefGoogle Scholar
  3. Audenaert KMR, Calsamiglia J, Munoz-Tapia R, Bagan E, Masanes LI, Acin A, Verstraete F (2017) Discriminating states: the quantum Chernof bound. Phys Rev Lett 98:160501CrossRefGoogle Scholar
  4. Bergou J, Herzog U, Hillery M (2004) Discrimination of quantum states. In: Lectures notes in Physics, vol 649. Springer, Berlin, pp 417–465Google Scholar
  5. Bisio A, Chiribella G, Mauro G, Ariano D, Facchini S, Perinotti P (2010) Optimal quantum learning of unitary transformation. Phys Rev A 82(3):032324MathSciNetCrossRefGoogle Scholar
  6. Carrasquilla J, Melko RG (2017) Machine learning phases of matter. Nat Phys 13:431–434CrossRefGoogle Scholar
  7. Castelvecchi D (2017) IBM’s quantum cloud computer goes commercial. Nature 543(7664):159CrossRefGoogle Scholar
  8. Chefles A (2000) Quantum state discriminator. Contemp Phys 41(6):401–424CrossRefGoogle Scholar
  9. Dalla Chiara ML, Giuntini R, Leporini R, Negri E, Sergioli G (2015) Quantum information, cognition and music. Front Psychol 6:1583CrossRefGoogle Scholar
  10. Deutsch D (1985) Quantum theory, the Church–Turing principle and the universal quantum computer. Proc R Soc Lond A 400:97–117MathSciNetCrossRefGoogle Scholar
  11. Duda RO, Hart PE, Stork DG (2000) Pattern classification, 2nd edn. Wiley Interscience, New YorkzbMATHGoogle Scholar
  12. Feynamn R (1982) Simulating physics with computers. Int J Theor Phys 21(6/7):467–488MathSciNetCrossRefGoogle Scholar
  13. Freytes H, Sergioli G (2014) Fuzzy approach for Toffoli gate in quantum computation with mixed states. Rep Math Phys 74(2):159–180MathSciNetCrossRefGoogle Scholar
  14. Gambs S (2008) Quantum classification. arXiv:0809.0444v2
  15. Guta M, Kotlowski W (2010) Quantum learning: asymptotically optimal classification of qubit states. New J Phys 12:123032MathSciNetCrossRefGoogle Scholar
  16. Hayashi A, Horibe M, Hashimoto T (2005) Quantum pure-state identification. Phys Rev A 72(5):052306CrossRefGoogle Scholar
  17. Helstrom CW (1976) Quantum detection and estimation theory. Academic Press, New York zbMATHGoogle Scholar
  18. Hilbert M, Lopez P (2011) The World’s technological capacity to store, communicate, and compute information. Science 332:60CrossRefGoogle Scholar
  19. Holik F, Sergioli G, Freytes H, Plastino A (2017) Pattern recognition in non-Kolmogorovian structures. Found Sci 23(1):119–132CrossRefGoogle Scholar
  20. Lloyd S, Mohseni M, Rebentrost P (2013) Quantum algorithms for supervised and unsupervised machine learning. arXiv:1307.0411
  21. Lloyd S, Mohseni M, Rebentrost P (2014) Quantum principal component analysis. Nat Phys 10(9):631–633CrossRefGoogle Scholar
  22. Lu S, Braunstein SL (2014) Quantum decision tree classifier. Quantum Inf Process 13(3):757–770MathSciNetCrossRefGoogle Scholar
  23. Manju A, Nigam MJ (2014) Applications of quantum inspired computational intelligence: a survey. Artif Intell Rev 42(1):79–156CrossRefGoogle Scholar
  24. Melkikh AV, Khrennikov A, Yampolskiy RV (2019) Quantum metalanguage and new cognitive synthesis. NeuroQuantology 17:72–96CrossRefGoogle Scholar
  25. Nielsen MA, Chuang IL (2010) Quantum computation and quantum information, 10th Anniversary edn. Cambridge University Press, CambridgeGoogle Scholar
  26. Qiu D (2007) Minimum-error discrimination between mixed states. arXiv:0707.3970 [quant-phis]
  27. Santucci E (2017) Quantum minimum distance classifier. Entropy 19(12):659MathSciNetCrossRefGoogle Scholar
  28. Santucci E, Sergioli G (2018) Classification problem in a quantum framework. In: Khrennikov A, Bourama T (eds) Quantum foundations, probability and information, proceedings of the quantum and beyond conference, Vaxjo, Sweden, 13–16 June 2016. Springer, Berlin, Germany, in pressGoogle Scholar
  29. Sasaki M, Carlini A (2002) Quantum learning and universal quantum matching machine. Phys Rev A 66(2):022303MathSciNetCrossRefGoogle Scholar
  30. Schuld M, Petruccione F (2018) Supervised learning with quantum computers. In: Quantum science and technology. Springer, Berlin zbMATHGoogle Scholar
  31. Schuld M, Sinayskiy I, Petruccione F (2014a) An introduction to quantum machine learning. Contemp Phys 56(2):172–185CrossRefGoogle Scholar
  32. Schuld M, Sinayskiy I, Petruccione F (2014b) The quest for a quantum neural network. Quantum Inf Process 13(11):2567–2586MathSciNetCrossRefGoogle Scholar
  33. Schuld M, Fingerhuth M, Petruccione F (2017) Implementing distance-based classifier with a quantum interference circuit. Europhys Lett 119(6):60002CrossRefGoogle Scholar
  34. Sergioli G, Santucci E, Didaci L, Miszczak J, Giuntini R (2016) A quantum-inspired version of the nearest mean classifier. Soft Comput 22(3):691–705CrossRefGoogle Scholar
  35. Sergioli G, Bosyk GM, Santucci E, Giuntini R (2017) A quantum-inspired version of the classification problem. Int J Theor Phys 56(12):3880–3888MathSciNetCrossRefGoogle Scholar
  36. Sergioli G, Santucci E, Didaci L, Miszczak JA, Giuntini R (2018a) A quantum inspired version of the NMC classifier. Soft Comput 22(3):691–705CrossRefGoogle Scholar
  37. Sergioli G, Russo G, Santucci E, Stefano A, Torrisi SE, Palmucci S, Vancheri C, Giuntini R (2018b) Quantum-inspired minimum distance classification in biomedical context. Int J Quantum Inf 16(8):1840011CrossRefGoogle Scholar
  38. Sergioli G, Giuntini R, Freytes H (2019) A new quantum approach to binary classification. PLoS ONE 14:e0216224.  https://doi.org/10.1371/journal.pone.0216224 CrossRefGoogle Scholar
  39. Trugenberg CA (2002) Quantum pattern recognition. Quantum Inf Process 1(6):471–493MathSciNetCrossRefGoogle Scholar
  40. Wiebe N, Kapoor A, Svore KM (2015) Quantum nearest-neighbor algorithms for machine learning. Quantum Inf Comput 15(34):318–358Google Scholar
  41. Wittek P (2014) Quantum machine learning: what quantum computing means to data mining. Academic Press, New YorkzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of CagliariCagliariItaly

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